Method And Apparatus For Creating Entanglements And Quantum Repeater Utilising The Same

The present invention relates method and apparatus for creating entanglements and to quantum repeater utilising the same.

BACKGROUND OF THE INVENTION

In quantum information systems, information is held in the “state” of a quantum system; typically this will be a two-level quantum system providing for a unit of quantum information called a quantum bit or “qubit”. Unlike classical digital states which are discrete, a qubit is not restricted to discrete states but can be in a superposition of two states at any given time.

Any two-level quantum system can be used for a qubit and several physical implementations have been realized including ones based on the polarization states of single photons, electron spin, nuclear spin, and the coherent state of light.

Quantum network connections provide for the communication of quantum information between remote end points. Potential uses of such connections include the networking of quantum computers, and “quantum key distribution” (QKD) in which a quantum channel and an authenticated (but not necessarily secret) classical channel with integrity are used to create shared, secret, random classical bits. Generally, the processes used to convey the quantum information over a quantum network connection provide degraded performance as the transmission distance increases thereby placing an upper limit between end points. Since in general it is not possible to copy a quantum state, the separation of endpoints cannot be increased by employing repeaters in the classical sense.

One way of transferring quantum information between two spaced locations uses the technique known as ‘quantum teleportation’. This makes uses of two entangled qubits, known as a Bell pair, situated at respective ones of the spaced locations; the term “entanglement” is also used in the present specification to refer to two entangled qubits. The creation of such a distributed Bell pair is generally mediated by photons sent over an optical channel (for example an optical waveguide such as optical fibre). Although this process is distance limited, where a respective qubit from two separate Bell Pairs are co-located, it is possible to combine (or ‘merge’) the Bell pairs by a local quantum operation effected between the co-located qubits. This process, known as ‘entanglement swapping’, results in an entanglement between the two non co-located qubits of the Bell pairs while the co-located qubits cease to be entangled at all.

The device hosting the co-located qubits and which performs the local quantum operation to merge the Bell pairs is called a “quantum repeater”. The basic role of a quantum repeater is to create a respective Bell pair with each of two neighbouring spaced nodes and then to merge the Bell pairs. By chaining multiple quantum repeaters, an end-to-end entanglement can be created between end points separated by any distance thereby permitting the transfer of quantum information between arbitrarily-spaced end points.

It may be noted that while QKD does not directly require entangled states, the creation of long-distance Bell pairs through the use of quantum repeaters facilitates long-distance QKD. Furthermore, most other applications of distributed quantum computation will use distributed Bell pairs.

The present invention is concerned with the creation of entanglement between spaced qubits.

SUMMARY OF THE INVENTION

According to the present invention, there is provided an apparatus and method for entangling spaced qubits as set out in accompanying claims 1 and 7 respectively and corresponding quantum repeaters as set out in claims 11 and 12.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the invention will now be described, by way of non-limiting example, with reference to the accompanying diagrammatic drawings, in which:

FIG. 1A is a diagram depicting a known operation for entangling two qubits;

FIG. 1B is a diagram depicting an elongate operation for extending an existing entanglement to create a new entanglement involving one of the originally-entangled qubits and a new qubit;

FIG. 1C is a diagram depicting a merge operation for extending an existing entanglement by merging it with another entanglement to create a new entanglement involving one qubit from each of the original entanglements;

FIG. 2 is a diagram depicting an entanglement creation subsystem for carrying out an entanglement operation between two qubits located in respective, spaced, nodes;

FIG. 3A is a diagram depicting how a quantum repeater can be used to create an entanglement between two qubits over a distance greater than that possible using the FIG. 1A entanglement operation alone;

FIG. 3B is a diagram illustrating how a chain of quantum repeaters, can be used to create an extended entanglement between any arbitrarily spaced pair of nodes;

FIG. 4 is a diagram illustrating three varieties of a basic quantum physical hardware block, herein a “Q-block”, for carrying out various quantum interactions;

FIG. 5 is a diagram illustrating an implementation of the FIG. 2 entanglement creation subsystem using Q-blocks;

FIG. 6 is a generic diagram of quantum physical hardware of a quantum repeater;

FIG. 7 is a diagram of a local link entanglement creation subsystem (LLE) embodying the present invention;

FIG. 8 is a diagram of a modified form of the FIG. 7 LLE creation subsystem;

FIG. 9 is a diagram depicting a first form of quantum repeater built around the FIG. 7 form of LLE creation subsystem;

FIG. 10 is a diagram showing how the first form of quantum repeater cooperates with neighbouring nodes to form two LLE creation subsystems;

FIG. 11 is a diagram showing how quantum repeaters of the first form can be serially optically coupled to provide LLE creation subsystems between neighbouring repeaters;

FIG. 12A is a diagram showing a first implementation of quantum physical hardware of the FIG. 9 quantum repeater;

FIG. 12B is a diagram showing a second implementation of quantum physical hardware of the FIG. 9 quantum repeater;

FIGS. 13A & 13B show how respective varieties of a quantum repeater embodying the invention cooperate with neighbouring nodes to form LLE creation subsystems; and

FIG. 13C is a diagram showing how the FIG. 13A and FIG. 13B varieties of quantum repeater can be serially optically coupled in alternation to provide LLE creation subsystems between neighbouring repeaters.

BEST MODE OF CARRYING OUT THE INVENTION
Basic Entanglement Creation and Extension Operations
Entanglement Operation (FIG. 1A)

FIG. 1A depicts, in general terms, a known process (herein referred to as an “entanglement operation”) for entangling two qubits qb1, qb2 (referenced 1) to create a Bell pair, the Figure showing a time series of snapshots (a) to (g) taken over the course of the entanglement operation. Where, as in the present case, the qubits qb1, qb2 are separated by a distance greater than a few millimeters, the creation of a Bell pair is mediated by photons, which may be sent through free space or over a waveguide such as optical fibre 4. Very generally, processes for Bell-pair creation may be divided into those that use very weak amounts of light (single photons, pairs of photons, or laser pulses of very few photons) and those that use pulses of many photons from a coherent source, such as a laser. As will be understood by persons skilled in the art, the details of the methods of creating photons, performing entanglement operations, and making measurements differ depending on whether very weak amounts of light or laser pulses of many photons are used; however, as the present invention can be implemented using any such approach, the following description will be couched simply in terms of a “light field” being used to create (and subsequently extend) Bell Pairs.

Considering FIG. 1A in more detail, a light field 5 emitted by an emitter 2 (snapshot (a)) is passed through the physical qubit qb1 (snapshot (b)) which is in a prepared non-classical state (for example: 0, +1); typically, the physical qubit implementation is as electron spin, the electron being set into a predetermined state immediately prior to passage of the light field. The light field 5 and qubit qb1 interact, with the light field 5 effectively ‘capturing’ the quantum state of the qubit qb1. The light field 5 then travels down the optical fibre 4 (snapshots (c) and (d)) and interacts with qubit qb2 (snapshot (e)) before being measured at detector 3 (snapshot (f)); if successful, this results in the ‘transfer’ of the quantum state of qubit qb1 to qubit qb2, entangling these qubits (in FIG. 1A, this entanglement is represented by double-headed arrowed arc 8, this form of representation being used generally throughout the drawings to depict entanglements). The properties of the light field 5 measured by detector 13 enable a determination to be made as whether or not the entanglement operation was successful. The success or failure of the entanglement operation is then passed back to the qb1 end of the fibre 4 in a classical (non-quantum) message 9 (snapshot (g)). This message can be very simple in form (the presence or absence of a single pulse) and as used herein the term “message” is to be understood to encompass both such simple forms as well as structured messages of any degree of complexity (subject to processing time constraints); in embodiments where the message 9 needs to identify a particular qubit amongst several as well as the success or failure of an entanglement operation, the message may still take the form of the presence or absence of a single pulse with the timing of the latter being used to identify the qubit concerned. Where there is a need to transmit information about the success/failure of the entanglement operation (or to identify an involve qubit) back to the qb1 end of the fibre 4, the overall elapsed time for the entanglement operation is at least the round trip propagation time along the fibre 4, even where the entanglement operation is successful.

An entanglement operation can be performed to entangle qubits qb1 and qb2 whether or not qb2 is already entangled with another qubit (in the case of qb2 already being entangled with another qubit qbj when an entanglement operation is performed between qb1 and qb2, this results in the states of all three qubits qb1, qb2 and qbj becoming entangled).

The properties of the light field 5 measured by detector 3 also enable a determination to be made, in the case of a successful entanglement operation, as to whether the entangled states of the qb1 and qb2 are correlated or anti-correlated, this generally being referred to as the ‘parity’ of the entanglement (even and odd parity respectively corresponding to correlated and anti-correlated qubit states). It is normally important to know the parity of an entanglement when subsequently using it; as a result, either parity information must be stored or steps taken to ensure that the parity always ends up the same (for example, if an odd parity is determined, the state of qb2 can be flipped to produce an even parity whereby the parity of the entanglement between qb1 and qb2 always ends up even).

In fact, the relative parity of two entangled qubits is a two dimensional quantity often called the “generalized parity” and comprising both a qubit parity value and a conjugate qubit parity value. For a simple entanglement operation as depicted in FIG. 1A, the conjugate qubit parity value information is effectively even parity and need not be measured. “Generalized parity” requires two classical bits to represent it. In certain applications (such as QKD), knowledge of the conjugate qubit parity value information may not be required. Hereinafter, except where specific reference is being made to one of the components of “generalized parity” (that is, to the qubit parity value or the conjugate qubit parity value), reference to “parity” is to be understood to mean “generalized parity” but with the understanding that in appropriate cases, the conjugate qubit parity value information can be omitted.

As already indicated, the qubits qb1 and qb2 are typically physically implemented as electron spin. However, the practical lifetime of quantum information stored in this way is very short (of the order of 10⁻⁶seconds cumulative) and therefore generally, immediately following the interaction of the light field 5 with qb1 and qb2, the quantum state of the qubit concerned is transferred to nuclear spin which has a much longer useful lifetime (typically of the order of a second, cumulatively). The quantum state can be later transferred back to electron spin for a subsequent light field interaction (such as to perform a merge of two entanglements, described below).

Another practical feature worthy of note is that the physical qubits qb1 and qb2 are generally kept shuttered from light except for the passage of light field 5. To facilitate this at the qb2 end of the fibre 4 (and to trigger setting the qubit into a prepared state immediately prior to its interaction with light field 5), the light field 5 can be preceded by a ‘herald’ light pulse 6; this light pulse is detected at the qb2 end of the fibre 14 and used to trigger priming of the qubit qb2 and then its un-shuttering for interaction with the light field 5. Other ways of triggering these tasks are alternatively possible.

The relationship between the probability of successfully creating a Bell pair, the distance between qubits involved, and the fidelity of the created pair is complex. By way of example, for one particular implementation using a light field in the form of a laser pulse of many photons, Bell pairs are created with fidelities of 0.77 or 0.638 for lain and 20 km distances respectively between qubits, and the creation succeeds on thirty eight to forty percent of the attempts. The main point is that the entanglement operation depicted in FIG. 1A is distance limited; for simplicity, in the following a probability of success of 0.25 is assumed at a distance of 10 km.

LLE Creation Subsystem (FIG. 2)

An assembly of components for carrying out an entanglement operation is herein referred to as an “entanglement creation subsystem” and may be implemented locally within a piece of apparatus or between remotely located pieces of apparatus (generally referred to as nodes). FIG. 2 depicts an example of the latter case where two nodes 21 and 22 are optically coupled by an optical fibre 23; optical fibres, such as the fibre 23, providing a node-to-node link are herein called “local link” fibres. The nodes 21, 22 of FIG. 2 include components for implementing respective qubits qb1 and qb2 (for ease of understanding, the same qubit designations are used in FIG. 2 as in FIG. 1A). The qubits qb1 and qb2, together with an emitter 2 associated with qb1, a detector 3 associated with qb3, the local link fibre 23 and entanglement-operation control logic in each node (not shown), form an entanglement creation subsystem 25 for creating an entanglement 8 between qubits qb1 and qb2. An entanglement of this sort created by a light field passed across a local link fibre between nodes is herein called a “local link entanglement” or “LLE”; the node-spanning entanglement creation subsystem 25 is correspondingly called an “LLE creation subsystem”.

Elongate Operation (FIG. 1B)

An entanglement such as created by a FIG. 1A entanglement operation can be ‘extended’ to create a new entanglement involving one of the originally-entangled qubits and a new qubit, the latter typically being located at a greater distance from the involved originally-entangled qubit than the other originally-entangled qubit. FIGS. 1B and 1C illustrate two ways of extending an initial entanglement 8 between qubits qb1 and qb2 (referenced 1) to form an entanglement between qubit qb1 and another qubit; both ways involve the passing of light fields through various qubits followed by measurement of the light fields but, for simplicity, the light fields themselves and the optical fibres typically used to channel them have been omitted from FIGS. 1B and 1C.

FIG. 1B illustrates, by way of a time series of snapshots (a) to (d), an entanglement extension process that is herein referred to as an “elongate operation”. In general terms, an elongate operation involves further entangling a qubit of an existing first entanglement with a qubit that is not involved in the first entanglement (though it may already be involved in a different entanglement) to form a linked series of entanglements from which the intermediate qubit (that is, the qubit at the end of the first entanglement being extended) is then removed by measurement to leave an ‘extended’ entanglement between the remaining qubit of the first entanglement and the newly entangled qubit. FIG. 1B illustrates an elongate operation for the simplest case where the qubit that is not involved in the first entanglement is not itself already entangled. More particularly, as shown in snapshot (a) of FIG. 1B, qubit qb2 of an existing entanglement 8 involving qubits qb1 and qb2 (both referenced 1), is further entangled with a qubit qb3 (referenced 10) by means of an entanglement operation. This entanglement operation involves a light field, emitted by an emitter 2, being passed through qubits qb2 and qb3 before being measured by a detector 3. Snapshot (b) depicts the resulting entanglement 11 between qb2 and qb3. The entanglements 8 and 11 form a linked series of entanglements—which is another way of saying that the states of qb1, qb2 and qb3 are now entangled with each other. A particular type of measurement, herein an “X measurement” (referenced 12 in FIG. 1B), is then effected on the intermediate qubit qb2 by sending a light field from an emitter 2 through qb2 and detecting it with a detector 3, thereby to eliminate qb2 from entanglement with qb1 and qb3 (see snapshot (c)) leaving qb1 and qb3 entangled. A characteristic of the X measurement 12 is that it is done in a manner so as to give no information about the rest of the quantum state of entangled qubits qb1 and qb3; for example, for a joint state between qubits qb1, qb2 and qb3 like “a|000>+b|111>” where a and b are probability amplitudes, an X measurement on qubit qb2 would give a state for the entanglement between qb1 and qb3 of either “a|00>+b|11>” (for an X measurement result of +1) or “a|00>−b|11>” (for an X measurement result of −1). This measurement does not give any information about a or b.

After the X measurement 12 has been made to eliminate qb2 from entanglement, an extended entanglement is left between qb1 and qb3—this extended entanglement is depicted as medium thick arc 13 in snapshot (d) of FIG. 1B.

The parity of the extended entanglement 13 is a combination of the parities of the entanglements 8 and 11 and a conjugate qubit parity value determined from the X measurement (in the above example, the X measurement gives either a +1 or −1 result—this sign is the conjugate qubit parity value). Where qubit parity value information and conjugate qubit parity value information are each represented by binary values ‘0’ and ‘1’ for even and odd parity respectively, the qubit parity value information and conjugate qubit parity value information of the extended entanglement are respective XOR (Exclusive OR) combinations of the corresponding component parities.

It may be noted that a functionally equivalent result to the FIG. 1B elongate operation can be obtained by first entangling qb3 with qb2 by means of an entanglement operation in which the mediating light field passes first through qb3, and then removing qb2 from entanglement by effecting an X measurement on it. In the present specification, for linguistic clarity, reference to an ‘elongate operation’ (with its integral X measurement) only encompasses the case where the initial entanglement performed as part of the elongate operation is effected by a light field first passing through a qubit of the entanglement being extended; the above described functional equivalent to the elongate operation is treated as being separate entanglement and X measurement operations.

Where the objective is to set up an entanglement between two qubits spaced by a substantial distance, the elongate operation described above with reference to FIG. 1B is not that useful by itself. This is because should the component entanglement operation (see (a) of FIG. 1B) fail, then the pre-existing entanglement that is being extended (entanglement 8 in FIG. 1B) will be destroyed. In effect, the probability of successfully creating the extended entanglement 13 is the product of the success probabilities of the entanglement operations used to create entanglements 8 and 11. As already noted, the probability of a successful entanglement operation is distance related so the chances of successfully creating an entanglement over long distances using only elongate operations to successively extend an initial entanglement, are poor. The same problem exists with the described functional equivalent of the elongate operation.

Merge Operation (FIG. 1C)

A better approach is to use the merge operation illustrated in FIG. 1C to knit together independently created entanglements that individually span substantial distances; this approach effectively decouples the success probabilities associated with the individual entanglements as a failure of one attempt to create such an entanglement does not destroy the other entanglements. Of course, to be useful, the merge operation used to join the individual entanglements must itself be highly reliable and this is achieved by carrying it out over extremely short distances.

FIG. 1C illustrates, by way of a time series of snapshots (a) to (e), an example embodiment of a merge operation for ‘extending’ an entanglement 8 existing between qubits qb1 and qb2 by merging it with another entanglement 16 that exists between qubits qb4 (referenced 14) and qb5 (referenced 15), in order to end up with an ‘extended entanglement’ between qb1 and qb5 (medium thick arc 19 in FIG. 1C). The qubits qb2 and qb4 are located in close proximity to each other (typically within tens of millimeters). The order in which the entanglements 8 and 16 are created is not relevant (indeed they could be created simultaneously); all that is required is that both entanglements exist in a usable condition at a common point in time. At such a time, the entanglements 8 and 16 are “merged” by a quantum operation carried out locally on qubits qb2 and qb4. (Where the quantum states of qubits qb2, qb4 have been transferred from electron spin to nuclear spin immediately following the creation of the LLEs 8, 16 respectively, these states need to be transferred back to electron spin before the merge operation is effected).The local merge operation involves a first process akin to that of FIG. 1A entanglement operation effected by passing a light field, emitted by an emitter 2, successively through the two qubits qb2 and qb4, or vice versa, and then measuring the light field (see snapshot (b) of FIG. 1C). This first process, if successful, results in the qubits qb2 and qb4 becoming entangled (as indicated by entanglement 17 in snapshot (c) of FIG. 1C) creating a linked series of entanglements by which qubits qb1 and qb5 are entangled with each other. A second measurement process comprising one or more X measurements 18 (see snapshot (d) of FIG. 1C) is then used to remove the intermediate qubits qb2 and qb4 from the entangled whole leaving an ‘extended’ entanglement 19 between the qubits qb1 and qb5 The qubits qb2 and qb4 finish up neither entangled with each other nor with the qubits qb1, qb5. Because the merge operation is a local operation between two co-located qubits, the probability of success is very high.

The measurements made as part of the merge operation provide both an indication of the success or otherwise of the merge, and an indication of the “generalized parity” of the merge operation. For example, the first merge-operation process may measure a qubit parity value and the second merge-operation process, the conjugate qubit parity value. In this case, the second process can be effected either as a single X measurement using a light field passed through both qubits qb2 and qb4 (in which case the light field has a different value to that used in the first process e.g. 0,+1 as opposed to 0,−1), or as individual X measurements, subsequently combined, made individually on qb2, and qb4, the latter approach being depicted in FIG. 1C. The parity of the extended entanglement 19 will be a combination of the parities of the entanglements 8 and 15 and the parity of the merge operation. As before, where qubit parity value information and conjugate qubit parity value information are each represented by binary values ‘0’ and ‘1’ for even and odd parity respectively, the qubit parity value information and conjugate qubit parity value information of the extended entanglement are respective XOR (Exclusive OR) combinations of the corresponding component parities.

Information about the success or otherwise of the merge operation is passed in classical messages to the end qubit locations as otherwise these locations do not know whether the qubits qb1, qb5 are entangled; alternatively since the failure probability of a merge operation is normally very low, success can be assumed and no success/failure message sent—in this case, it will be up to applications consuming the extended entanglement 19 to detect and compensate for merge failure leading to absence of entanglement. As the parity of the extended entanglement will normally need to be known to make use of the entangled qubits, parity information needed to determine the parity of the extended entanglement 19 is also passed on to one or other of the end qubit locations.

It will be appreciated that the form of merge operation described above with respect to FIG. 1C is effectively an elongate operation carried out over a very short distance between qb2 and qb4 to extend entanglement 8, together with an X measurement on qb4 to remove it from entanglement (qb2 having been removed from entanglement by the X measurement performed as part of the elongate operation). Of course, unlike the FIG. 1B example elongate operation where the qubit qb3 to which the entanglement 8 is being extended is not itself already entangled, the equivalent qubit qb4 in FIG. 1C is already involved in a″ second entanglement 16; however, as already noted, an elongate operation encompasses this possibility.

As already noted, the merge operation is a local operation (between qubits qb2 and qb3 in FIG. 1C) that is effected over a very short distance and thus has a high probability of success. A merge operation takes of the order of 10⁻⁹secs.

Quantum Repeater (FIGS. 3A & 3B)

In practice, when seeking to create an extended entanglement between two qubits which are located in respective end nodes separated by a distance greater than that over which a basic entanglement operation can be employed with any reasonable probability of success, one or more intermediate nodes, called quantum repeaters, are used to merge basic entanglements that together span the distance between the end nodes. Each quantum repeater node effectively implements a merge operation on a local pair of qubits that correspond to the qubits qb2 and qb4 of FIG. 1C and are involved in respective entanglements with qubits in other nodes. FIG. 3A depicts such a quantum repeater node 30 forming one node in a chain (sequential series) of nodes terminated by left and right end nodes 31 and 32 that respectively accommodate the qubits qb1, qb5 it is desired to entangle (but which are too far apart to entangle directly using an entanglement operation). In the present example, the chain of nodes comprises three nodes with the left and right end nodes 31, 32 also forming the left and right neighbour nodes of the quantum repeater 30. The quantum repeater 30 is connected to its left and right neighbour nodes 31, 32 by left and right local link optical fibres 33L and 33R respectively. It is to be noted that the terms “left” and “right” as used throughout the present specification are simply to be understood as convenient labels for distinguishing opposite senses (directions along; ends of and the like) of the chain of nodes that includes a quantum repeater.

The quantum repeater 30 effectively comprises left and right portions or sides (labeled “L” and “R” in FIG. 3A) each comprising a respective qubit qb2, qb4 (for ease of understanding, the same qubit designation are used in FIG. 3A as in FIG. 1C). The qubit qb1 of the left neighbour node 31 and qb2 of the quantum repeater node 30 are part of a LLE creation subsystem formed between these nodes and operative to create a left LLE 8 (shown as a dashed arrowed arc 8 in FIG. 3A) between qb1 and qb2. Similarly, the qubit qb5 of the right neighbour node 32 and qb4 of the quantum repeater node 30 are part of a LLE creation subsystem formed between these nodes and operative to create a right LLE 16 between qb5 and q4.

It may be noted that the direction of travel (left-to-right or right-to-left) of the light field used to set up each LLE is not critical whereby the disposition of the associated emitters and detectors can be set as desired. For example, the light fields involved in creating LLEs 8 and 16 could both be sent out from the quantum repeater 30 meaning that the emitters are disposed in the quantum repeater 30 and the detectors in the left and right neighbour nodes 31, 32. However, to facilitate chaining of quantum repeaters of the same form, it is convenient if the light fields all travel in the same direction along the chain of nodes; for example, the light fields can be arranged all to travel from left to right in which case the left side L of the quantum repeater 30 will include the detector for creating the left LLE 8 and the right side R will include the emitter for creating the right LLE 16. For simplicity, and unless otherwise stated, a left-to-right direction of travel of the light field between the nodes will be assumed hereinafter unless otherwise stated; the accompanying Claims are not, however, to be interpreted as restricted to any particular direction of travel of the light field, . or to the direction of travel being the same across different links, unless so stated or implicitly required.

In operation of the quantum repeater 30, after creation, in any order, of the left and right LLEs 8 and 16, a local merge operation 34 involving the qubits qb2 and qb4 is effected thereby to merge the left LLE 8 and the right LLE 16 and form extended entanglement 19 between the qubits qb1 and qb5 in the end nodes 31 and 32 respectively.

If required, information about the success or otherwise of the merge operation and about parity is passed in classical messages 35 from the quantum repeater 30 to the nodes 31, 32.

Regarding the parity information, where the parity of the local link entanglements has been standardized (by qubit state flipping as required), only the merge parity information needs to be passed on by the quantum repeater and either node 31 or 32 can make use of this information. However, where LLE parity information has simply been stored, then the quantum repeater needs to pass on whatever parity information it possesses; for example, where the parities of the left and right LLEs 8, 16 are respectively known by the quantum repeater 30 and the node 32, the quantum repeater 30 needs to pass on to node 32 both the parity information on LLE 8 and the merge parity information, typically after combining the two. Node 32 can now determine the parity of the extended entanglement by combining the parity information it receives from the quantum repeater 30 with the parity information it already knows about LLE 16.

From the foregoing, it can be seen that although the merge operation itself is very rapid (of the order of 10⁻⁹seconds), there is generally a delay corresponding to the message propagation time to the furthest one of the nodes 31, 32 before the extended entanglement 19 is usefully available to these nodes.

By chaining together multiple quantum repeaters, it is possible to create an extended entanglement between any arbitrarily spaced pair of nodes. FIG. 3B illustrates this for a chain of N nodes comprising left and right end nodes 31 and 32 respectively, and a series of (N−2) quantum repeaters 30 (each labeled “QR” and diagrammatically depicted for simplicity as a rectangle with two circles that represent L and R qubits). The nodes 30-32 are interconnected into a chain by optical fibres (not shown) and are numbered from left to right—the number n of each node is given beneath each node and node number “j” represents an arbitrary QR node 30 along the chain. The node number of a QR node can be used as a suffix to identify the node; thus “QR_j” is a reference to the quantum repeater node numbered j. This node representation, numbering and identification is used generally throughout the present specification.

In FIG. 3B, three existing entanglements 36, 37, and 38 are shown between qubits in respective node pairings; for convenience, when referring at a high level to entanglements along a chain of nodes, a particular entanglement will herein be identified by reference to the pair of nodes holding the qubits between which the entanglement exists, this reference taking the form of a two-element node-number tuple. Thus, entanglement 38, which is a local link entanglement LLE between qubits in the neighbouring nodes numbered (N−1) and N, is identifiable by the node number tuple {(N−1), N}. Entanglements 36 and 37 (shown by medium thick arcs in FIG. 3B) are extended entanglements existing between qubits in the node pairings {1, j} and {j, (N−1)} respectively, these entanglements having been created by the merging of LLEs. To create an end-to-end (abbreviated herein to “E2E”) entanglement between qubits in the left and right end nodes 31, 32 (see thick arc 39 in FIG. 3), entanglements 36 and 37 can first be merged by QR_jwith the resultant extended entanglement then being merged with LLE 38 by QR_(N-1); alternatively, entanglements 37 and 38 can first be merged by QR_(N-1)with the resultant extended entanglement then being merged with entanglement 36 by QR_j.

Entanglement Build Path

The “entanglement build path” (EBP) of an entanglement is the aggregate qubit-to-qubit path taken by the mediating light field or fields used in the creation of an un-extended or extended entanglement; where there are multiple path segments (that is, the path involves more than two qubits), the light fields do not necessarily traverse their respective segments in sequence as will be apparent from a consideration of how the FIG. 3B E2E entanglement is built (in this example, the entanglement build path is the path from one end node to the other via the left and right side qubits of the chain of quantum repeaters).

Representation of Low Level Quantum Physical Hardware

The particular form of physical implementation of a qubit and the details of the methods of performing entanglement, elongate, and merge operations (for example, whether very weak amounts of light or laser pulses of many photons are used) are not of direct relevance to the present invention and accordingly will not be further described herein, it being understood that appropriate implementations will be known to persons skilled in the art. Instead, the physical hardware for implementing the quantum operations (the “quantum physical hardware”) will be represented in terms of a basic block, herein called a “Q-block”, that provides for the implementation of, and interaction with, one qubit, and an associated optical fabric.

FIG. 4 depicts three varieties of Q-block, respectively referenced 40, 42 and 44.

Q-block variety 40 represents the physical hardware needed to manifest a qubit and carry out the “Capture” interaction of FIG. 1A with that qubit, that is, the controlled sending of a light field through the qubit in a prepared state. This variety of Q-block—herein called “a Capture Q-block” (abbreviated in the drawings to “Q-block (C)”)—comprises a physical implementation of a qubit 10 and a light-field emitter 12, together with appropriate optical plumbing, functionality for putting the qubit in a prepared state and for shuttering it (for example, using an electro-optical shutter) except when a light field is to be admitted, functionality (where appropriate for the qubit implementation concerned) for transferring the qubit state between electron spin and nuclear spin (and vice versa) as needed, and control functionality for coordinating the operation of the Capture Q-block to send a light field through its qubit (and on out of the Q-block) upon receipt of a “Fire” signal 41.

Q-block variety 42 represents the physical hardware needed to manifest a qubit and carry out the “Transfer” interaction of FIG. 1A with that qubit, that is, the passing of a received light field through the qubit in a prepared state followed by measurement of the light field. This variety of Q-block—herein called “a Transfer Q-block” (abbreviated in the drawings to “Q-block (T)”)—comprises a physical implementation of a qubit 10 and a light-field detector 13, together with appropriate optical plumbing, functionality (responsive, for example to a herald light pulse 6) for putting the qubit in a prepared state and for shuttering it except when a light field is to be admitted, functionality (where appropriate for the qubit implementation concerned) for transferring the qubit state between electron spin and nuclear spin (and vice versa) as needed, and control functionality for coordinating the operation of the Transfer Q-block and for outputting the measurement results 43.

Q-block variety 44 is a universal form of Q-block that incorporates the functionality of both of the Capture and Transfer Q-block varieties 40 and 42 and so can be used to effect both Capture and Transfer interactions. For convenience, this Q-Block variety is referred to herein simply as a “Q-block” without any qualifying letter and unless some specific point is being made about the use of a Capture or Transfer Q-block 40, 42, this is the variety of Q-block that will be generally be referred to even though it may not in fact be necessary for the Q-block to include both Capture and Transfer interaction functionality in the context concerned—persons skilled in the art will have no difficulty in recognizing such cases and in discerning whether Capture or Transfer interaction functionality is required by the Q-block in its context. One reason not to be more specific about whether a Q-block is of a Capture or Transfer variety is that often either variety could be used provided that a cooperating Q-block is of the other variety (the direction of travel of light fields between them not being critical).

Regardless of variety, every Q-block will be taken to include functionality for carrying out an X measurement in response to receipt of an Xmeas signal 45 thereby enabling the Q-block to be used in elongate and merge operations; the X measurement result is provided in the Result signal 43, it being appreciated that where the Q-block has Transfer interaction functionality, the X measurement functionality will typically use the detector 2 associated with the Transfer interaction functionality. X measurement functionality is not, of course, needed for an entanglement operation and could therefore be omitted from Q-blocks used only for such operations.

It may be noted that where there are multiple Q-blocks in a node, the opportunity exists to share certain components between Q-blocks (for example, where there are multiple Q-blocks with Capture interaction functionality, a common light-field emitter may be used for all such Q-blocks). Persons skilled in the art will appreciate when such component sharing is possible.

An entanglement operation will involve a Q-block with Capture interaction functionality (either a Transfer Q-block 40 or a universal Q-block 44) optically coupled to a Q-block with Transfer interaction functionality (either a Transfer Q-block 42 or a universal Q-block 44), the entanglement operation being initiated by a Fire signal 41 sent to the Q-block with Capture interaction functionality and the success/failure of the operation being indicated in the result signal 43 output by the Q-block with Transfer interaction functionality.

Where an elongate operation is to be effected, the initial entanglement-operation component of the elongate operation will also involve a Q-block with Capture interaction functionality and a Q-block with Transfer interaction functionality. The provision of X measurement functionality in all varieties of Q-block enables the subsequent removal from entanglement of the intermediate qubit to be effected by sending an Xmeas signal to the Q-block implementing this qubit, the measurement results being provided in the result signals 43 output by this Q-block.

Where a merge operation is to be effected, this will also involve a Q-block with Capture interaction functionality and a Q-block with Transfer interaction functionality. Again, the provision of X measurement functionality in all varieties of Q-block enables the removal from entanglement of the qubit(s) involved in the merge operation. Measurement results are provided in the result signals 43 output by the appropriate Q-blocks.

FIG. 5 depicts the FIG. 2 LLE creation subsystem 25 as implemented using respective Q-blocks 44. A respective Q-block 44 is provided in each node 21 and 22, these Q-blocks 44 being optically coupled through the local link fibre 23. Each Q-block 44 has associated control logic formed by LLE control unit 53 in node 21 and LLE control unit 54 in node 54, 53. Because the Q-blocks 44 depicted in FIG. 5 are of the universal variety, the direction of travel along the local link fibre 23 of light fields involved in entanglement creation is not tied down; thus, the Q-block 44 of the node 21 could serve as a Capture Q-block and that of node 22 as a Transfer Q-block or the Q-block 44 of the node 21 could serve as a Transfer Q-block and that of node 51 as a Capture Q-block.

In the LLE creation subsystem 25 of FIG. 5, the single Q-blocks 44 are simply coupled directly to the local link fibre 23. However, in many cases there will be a need to provide a controllable optical fabric in a node to appropriately guide light fields to/from the Q-block(s) of the node depending on its current operational requirements. For example, where there are multiple Q-blocks in a node sharing the same external fibre, an optical fabric may be required to merge outgoing light fields onto the common fibre or direct incoming light fields from the fibre to selected Q-blocks; in another example, an optical fabric may be required in a quantum repeater node (such as node 30 in FIG. 3A) to switch a L-side Q-block and a R-side Q-block from optically interfacing with respective left and right local link fibres for LLE creation, to optically interfacing with each other for a local merge operation.

In general terms, therefore, the quantum physical hardware of a node, that is, the physical elements that implement and support qubits and their interaction through light fields, comprises not only one or more Q-blocks but also an optical fabric in which the Q-block(s) are effectively embedded. By way of example, FIG. 6 depicts such a representation for a quantum repeater node; thus, quantum physical hardware 60 is shown as comprising an optical fabric 61 for guiding light fields to/from the Q-blocks 44 and the Q-blocks 44 are depicted as existing within the optical fabric 61 with the local link fibres 62, 63 coupling directly to the optical fabric. One L-side and one R-side Q-block are shown in solid outline and possible further L-side and R-side Q-blocks are indicated by respective dashed-outline Q-blocks.

As employed herein, any instance of the above-described generalized quantum physical hardware representation (such as the instance shown in FIG. 6 in respect of a quantum repeater), is intended to embrace all possible implementations of the quantum physical hardware concerned, appropriate for the number and varieties of Q-blocks involved and their intended roles. (It may be noted that although FIG. 6 shows the Q-blocks as Q-blocks 44—that is, of the Universal variety—this is simply to embrace all possible implementations and is not a requirement of the role being played by the Q-blocks in the quantum repeater; a particular implementation may use other varieties of Q-blocks as appropriate to their roles. This use of Q-blocks 44 in the above-described generalized quantum physical hardware representation is not limited to the FIG. 6 representation of quantum physical hardware for a quantum repeater).

Depending on the quantum operations to be performed by the quantum physical hardware, the latter is arranged to receive various control signals and to output result signals, In the case of the FIG. 6 quantum physical hardware block 60 appropriate for a quantum repeater, the quantum physical hardware is arranged to receive “Firing Control” and “Target Control” signals 64, 65 for controlling entanglement creation operations, to receive “Merge” signals 67 for controlling merge operations, and to output “Result” signals 66 indicative of the outcome of these operations. The signals 64-67 may be parameterized to indicate particular Q-blocks. Target Control signals are not needed in some quantum repeater embodiments as will become apparent hereinafter. In one implementation of the FIG. 6 quantum physical hardware 60, the Firing Control signals 64 comprise both:

- set-up signals for appropriately configuring the optical fabric 61 (if not already so configured) to optically couple one or more Q-block(s) with Capture interaction functionality to one of the local link fibres, and
- the previously-mentioned “Fire” signal(s) for triggering light-field generation by one or more of the Q-block(s) with Capture interaction functionality;
  
  and the Target Control signals 65 comprise:
- set-up signals for appropriately configuring the optical fabric 61 (if not already so configured) to optically couple a Q-block with Transfer interaction functionality to one of the local link fibres.

Furthermore, in this implementation, the Merge signals 66 comprise both:

- set-up signals for appropriately configuring the optical fabric 61 (if not already so configured) to effect a merge operation involving a L-side and R-side Q-block of the repeater,
- a “Fire” signal for triggering the first merge-operation process, and
- where the FIG. 1C form of merge operation is being carried out, one or more Xmeas signals to instigate the X measurements that form the second merge-operation process.

For quantum physical hardware intended to perform elongate operations, the quantum physical hardware, as well as being arranged to receive Firing Control signals (for performing the entanglement creation component of the elongate operation) and to output Result signals, is also arranged to receive Xmeas signals for instigating X measurements whereby to complete the elongate operation.

The optical fabric of a node may have a default configuration. For example, where the FIG. 6 quantum physical hardware 60 only includes one L-side and one R-side Q-block, the optical fabric 61 may be arranged to default to an LLE creation configuration optically coupling the Q-blocks to respective ones of the local link fibres. In this case, the merge signals 66 are arranged to only temporarily optically couple the two Q-blocks to each other for the time needed to carry out a merge operation. In cases such as this, the Target Control signals 65 can be dispensed with entirely and the Firing Control signals 64 simply comprise Fire signals sent to the appropriate Q-block.

“Firing Squad” LLE Creation Subsystem

Consideration will now be given to local link entanglement (LLE) creation subsystems embodying the invention.

More particularly, FIG. 7 depicts a “firing squad” form of LLE creation subsystem 70 formed between two nodes 71 and 72 that are optically coupled by local link fibre 75.

The node 71 comprises an LLE control unit 171, and quantum physical hardware formed by f Q-blocks 73 (with respective IDs 1 to f) that have Capture interaction functionality, and an optical merge unit 76. The Q-blocks 73 (herein “fusilier” Q-blocks) collectively form a “firing squad” 77. The node 72 comprises an LLE control unit 172, and quantum physical hardware formed by a single Q-block 74 with Transfer interaction functionality. The fusilier Q-blocks 73 of the firing squad 77 of node 71 are optically coupled through the optical merge unit 76 and the local link optical fibre 75 to the single target Q-block 74 of node 72. Thus, as can be seen, all the Q-blocks 73 of the firing squad 77 are aimed to fire at the same target Q-block 74.

When the LLE control unit 171 of node 71 outputs a Fire signal to its quantum physical hardware to trigger an LLE creation attempt, the fusilier Q-blocks 73 of the firing squad 77 are sequentially fired and the emitted light fields pass through the merge unit 76 and onto the fibre 75 as a light-field train 78. It may be noted that there will be an orderly known relationship between the fusilier Q-block IDs and the order in which the light fields appear in the train. Rather than each light field being preceded by its own herald, a single herald 79 preferably precedes the light-field train 78 to warn the target Q-block 74 of the imminent arrival of the train 78, this herald 79 being generated by emitter 179 in response to the Fire signal and in advance of the firing of the fusilier Q-blocks 73.

As each light field arrives in sequence at the target Q-block 74 of node 72, the shutter of the target Q-block is briefly opened to allow the light field to pass through the qubit of the target Q-block to potentially interact with the qubit, the light field thereafter being measured to determine whether an entanglement has been created. If no entanglement has been created, the qubit of target Q-block 74 is reset and the shutter is opened again at a timing appropriate to let through the next light field of the train 78. However, if an entanglement has been created by passage of a light field of train 78, the shutter of the target Q-block is kept shut and no more light fields from the train 78 are allowed to interact with the qubit of target Q-block 74. The measurement-result dependent control of the Q-block shutter is logically part of the LLE control unit 172 associated with the target Q-block 74 though, in practice, this control may be best performed by low-level control elements integrated with the quantum physical hardware.

It will be appreciated that the spacing of the light fields in the train 78 should be such as to allow sufficient time for a determination to be made as to whether or not a light field has successfully entangled the target qubit, for the target qubit to be reset, and for the Q-block shutter to be opened, before the next light field arrives.

In fact, rather than using an explicit shutter to prevent disruptive interaction with the target qubit of light fields subsequent to the one responsible for entangling the target qubit, it is possible to achieve the same effect by transferring the qubit state from electron spin to nuclear spin immediately following entanglement whereby the passage of subsequent light fields does not disturb the captured entangled state (the target qubit having been stabilized against light-field interaction). It may still be appropriate to provide a shutter to exclude extraneous light input prior to entanglement but as the qubit is not set into its prepared state until the herald is detected, such a shutter can generally be omitted.

The LLE control unit 172 is also responsible for identifying which light field of the train successfully entangled the target qubit of Q-block 74 and thereby permit identification of the fusilier Q-block 73 (and thus the qubit) entangled with the target Q-block qubit (as already noted, there is a known relationship between the fusilier Q-block IDs and the order in which the light fields appear in the train). For example, the light fields admitted to the target Q-block may simply be counted and this number passed back by the LLE control unit 172 to the node 71 in a ‘success’ form of a message 173, the LLE control unit 171 of node 71 performing any needed conversion of this number to the ID number of the successful fusilier Q-block 73 before storing the latter, for example in a register, for later reference (alternatively, the fusilier ID may be passed on immediately). Of course, if none of the light fields of train 78 is successful in creating an entanglement, a ‘fail’ form of message 173 is returned.

With regard to the parity information contained in the measurement result in respect of the successful entanglement of the target qubit, this parity information is passed to the control unit 172 which may either store it for later use (for example in a register) or pass it on, for example to node 71 in the message 173.

Rather than sequentially firing the fusilier Q-blocks 73 of node 71 to produce the train of light fields 78, an equivalent result can be achieved by firing them all together but using different lengths of fibre to connect each fusilier Q-block to the optical merge unit 76, thereby introducing different delays and creating the light-field train 78.

The number of fusilier Q-blocks 73 in the firing squad 77 is preferably chosen to give a very high probability of successfully entangling target Q-block 74 at each firing of the firing squad, for example 99% or greater. More particularly, if the probability of successfully creating an entanglement with a single firing of a single fusilier Q-block is s, then the probability of success for a firing squad of f fusilier Q-blocks will be:

Firing squad success probability=1−(1−s)^f

whereby for s=0.25, 16 fusilier Q-blocks will give a 99% success rate and 32 fusilier Q-blocks a 99.99% success rate. Typically one would start with a desired probability P_successof successfully entangling the target qubit with a single firing (i.e. a single light-field train) and then determine the required number f of fusilier qubits according to the inequality:

P
_success≦1−(1−s)^f

The time interval between adjacent light fields in the train 78 is advantageously kept as small as possible consistent with giving enough time for the earlier light field to be measured, the target qubit reset and its shutter opened before the later light field arrives. By way of example, the light fields are spaced by 1-10 nanoseconds.

It will be appreciated that with the FIG. 7 form of LLE creation sub-system 70, because there is only one target Q-block 74, the firing squad 77 cannot in practice be re-triggered until the whole sub-system is freed up by the most recently created entanglement being consumed or timing out (or otherwise ceasing to be of use). The minimum time between triggering of the firing squad 77 is thus the round trip time between the nodes (that is, the minimum time for the light train 78 to reach node 72 and for message 173 to be returned to node 71) plus a time for consuming the entanglement (for example, in a merge operation). FIG. 8 shows a modified form of the FIG. 7 LLE creation subsystem 70 in which more than one target Q-block is provided.

More particularly, in the FIG. 8 LLE creation subsystem 80 the basic arrangement of the quantum physical hardware (firing squad 77 and optical merge unit 76) in node 71 is the same as for the FIG. 7 subsystem; the LLE control unit 181 of the FIG. 8 subsystem does, however, differ in certain respects from the control unit 171 of FIG. 7 as will be explained below. The main difference between the FIG. 7 and FIG. 8 subsystems, is to be found in node 72 where the quantum physical hardware now comprises multiple (p in total) target Q-blocks 74 with respective IDs 1 to p, and an optical switch 183 for directing light fields received over the local link 75 to a selected one of the target Q-blocks 74. The optical switch 183 is controlled by LLE control unit 182 of node 72 such that all the incoming light fields are directed by the optical switch 183 to the same target Q-block 74 until a successful entanglement is created whereupon the optical switch 183 is switched to pass the incoming light fields to a new, available (un-entangled), target Q-block 74. The optical switch thus effectively performs the role of shuttering an entangled target qubit from subsequent light fields and thereby preventing interaction of these light fields with that qubit. Each successful entanglement is reported to the node 71 in a ‘success’ message 173 which may now also include (in addition to information permitting identification of the involved fusilier Q-block 73. and parity information) the ID of the target Q-block 74 concerned.

Of course, the control unit 182 must keep track of the availability status of each of the target Q-blocks 74 since the control unit 182 is tasked with ensuring that the optical switch 183 only passes the incoming light fields to a target Q-block with an un-entangled qubit. This availability status can be readily tracked by the control unit 182 using a status register 186 arranged to store a respective entry for each target Q-block 74. Each register entry not only records the availability of the corresponding target Q-block but may also record, in the case where the Q-block is unavailable (because its qubit is entangled with the qubit of a fusilier Q-block), identity information on the involved fusilier Q-block and/or parity information.

Operating node 72 in this way ensures an efficient use of the light fields fired by the firing squad 77 as they are all used to attempt entanglement creation.

The control unit 181 of node 71 also includes a status register 185, this register being arranged to store a respective entry for each fusilier Q-block 73. Each register entry records the availability of the corresponding fusilier Q-block 73; a fusilier Q-block is ‘unavailable’ between when its qubit is entangled with the qubit of a target Q-block 74 (as indicated by a message 173) and when the entanglement concerned is consumed, times out, or otherwise ceases to be useful. All fusilier Q-blocks 74 are, of course, effectively ‘unavailable’ for the round trip time between when the firing squad is triggered and a message is received back from node 72 since it is not known whether any particular fusilier Q-block is, or is about to become, involved in an entanglement; such ‘unavailability’ may be specifically logged to the status register 185 for each fusilier Q-block or treated more generally by the control unit 181. Each entry of register 185 may also record, in the case where the corresponding Q-block is unavailable because its qubit is entangled, identity information on the involved target Q-block and/or parity information where such information has been provided in the related message 173.

As already noted, the firing squad 77 of the FIG. 7 LLE creation subsystem 70 can only be re-triggered once the previous entanglement has been consumed or timed out (or otherwise ceased to be of use). It is also possible to operate the FIG. 8 LLE creation subsystem 80 in a similar manner, waiting for the one or more entanglements created by the last triggering of the firing squad 77 to be consumed, timed out, or otherwise ceasing to be of use, before re-triggering the firing squad 77.

However, because there are multiple target Q-blocks at least some of which are likely to be un-entangled, it is alternatively possible to re-trigger the firing squad 77 as soon as the fate of the light-field fusillade of previous triggering of the firing squad 77 is known through the message(s) 173. Such a re-triggering of the firing squad 77 must take account of the availability status of each of the fusilier Q-blocks as indicated by the corresponding entry in the status register 185—unavailable fusilier Q-blocks 73 are not fired but are skipped over (either leaving a gap in the light-field train 78 or shortening it—leaving a gap is generally preferred). The probability of an entanglement being produced by such a triggering of the firing squad 77 is, of course, reduced due to the lesser number of fusilier Q-blocks being fired. Nevertheless, re-triggering the firing squad 77 without waiting for all its fusilier Q-blocks 73 to become available, gives rise to an overall increase in the rate of LLE creation. Also, the triggering of the firing squad is de-coupled from the LLE-consumer process using the created LLEs (such as a local merge process in the case of a quantum repeater) thereby enabling the firing squad 77 to be fired at regular (or irregular) intervals unrelated to LLE-consumer process need.

Use of “Firing Squad” LLE Subsystem in a Quantum Repeater

FIG. 9 depicts the general form of a quantum repeater implementation based upon LLE creation subsystems of the FIG. 7 form.

More particularly, quantum repeater 90 is optically coupled by left and right local link fibres 62, 63 to left and right neighbour nodes respectively (not illustrated). The quantum repeater 90 includes quantum physical hardware 60 depicted in the generalized manner explained with respect to FIG. 6 and comprising:

- a L-side (left-side) target Q-block 74 that forms part of a left LLE creation subsystem 70L;
- multiple R-side fusilier Q-blocks 73 that form the firing squad 77 of a right LLE creation subsystem 70R; and
- an optical fabric 61 coupled to left and right local link fibres 62, 63 via respective optical interfaces 91L, 91R.

The left and right LLE creation subsystems 70L, 70R are substantially of the form illustrated in FIG. 7. As graphically depicted in FIG. 10, the left LLE creation subsystem 70L comprises:

- (a) in repeater 90, the above-mentioned L-side elements of the quantum physical hardware 60 (in particular, the target Q-block 74, depicted in FIG. 10 by a box with the letter ‘T’ inside), and a left LLE (L-LLE) control unit 92;
- (b) the left local link fibre 62; and
- (c) in a left neighbour node 100L, a firing squad of fusilier Q-blocks 73 (depicted in FIG. 10 by a box with the letters ‘FS’ inside) and its associated optical fabric and LLE control unit.

The right LLE creation subsystem 70R comprises:

- (a) in repeater 90, the above-mentioned R-side elements of the quantum physical hardware 60 (in particular, the firing squad 77 depicted as box ‘FS’), and a right LLE (R-LLE) control unit 93;
- (b) the right local link fibre 63; and
- (c) in a right neighbour node 100R, a target Q-block (box ‘T’) and its associated optical fabric and LLE control unit.

Thus, although the quantum repeater 90 does not itself incorporate a complete operative LLE creation subsystem 70 of the FIG. 7 form, its R-side and L-side respectively comprise complementary firing squad and target portions of a FIG. 7 LLE creation subsystem 70, albeit that these portions relate to oppositely directed LLE creation subsystems.

With this arrangement of complementary firing squad and target portions of an LLE creation subsystem 70, multiple quantum repeaters 90 can be optically coupled in series such as to form an LLE creation subsystem between neighbouring repeaters as is illustrated in FIG. 11 for quantum repeaters j−1, j, j+1 (the quantum repeater j forming an LLE creation subsystem 111 with its left neighbour repeater j−1 and an LLE creation subsystem 112 with its right neighbour repeater j+1).

The optical fabric 61 of the quantum repeater 90, as well as coupling the L-side and R-side Q-blocks to the left and right local link fibres 62, 63 respectively for LLE creation, also provides for the selective optical coupling of the L-side target Q-block 74 to a selected one of the R-side fusilier Q-blocks 73 for the purpose of effecting a local merge operation on the qubits of these Q-blocks.

During LLE creation, the quantum physical hardware 60 receives firing control signals from the R-LLE control unit 93 for controlling the R-side elements (in particular, the triggering of the firing squad 77), and outputs result signals (success/failure; parity; fusilier-identifying information) from the L-side target Q-block 74 to the L-LLE control unit 92. For a local merge operation, the quantum physical hardware 60 receives merge control signals from a merge control unit 97 (these signals selecting the fusilier Q-block 73 that is to participate in the merge, and triggering the merge itself), and outputs back to the unit 97 results signal (success/failure; parity) regarding the outcome of the merge operation.

FIGS. 12A and 12B illustrated two possible implementations of the optical fabric 61 depending on the nature of the Q-blocks 73 and 74.

The FIG. 12A optical fabric implementation is applicable to the case where the fusilier and target Q-blocks 73, 74 are universal Q-blocks 44 (c.f. FIG. 4). In this case, the left local link fibre 62 interfaces directly with the optical input of the target universal Q-block 74, and the optical output of this universal Q-block is optically coupled to an intermediate optical fibre 121. An active optical switch 122 interfaces the intermediate fibre 121 with the inputs of the fusilier universal Q-blocks 73 and a passive optical merge unit 123 puts the outputs of the fusilier Q-blocks 73 onto the right local link fibre 63. During LLE creation operation, the target Q-block 74 is set up for Transfer interaction and light fields coming in over the left link fibre 62 are fed to the target Q-block; the fusilier Q-blocks 73 are set up for Capture interaction and the optical merge unit 123 couples the fusilier Q-blocks 73 to the right local link fibre 63. For a merge operation, the target Q-block 74 is set up for Capture interaction and the fusilier Q-block involved in the merge is set up for Transfer interaction (the fusilier Q-block concerned will have been indicated in the merge set-up signals fed to the quantum physical hardware 60); the optical switch 122 is also set by the merge set up signals to optically couple the target Q block 74 to the fusilier Q-blocks 93 involved in the merge.

The FIG. 12B optical fabric implementation is applicable to the case where the target Q-block 94 is a Transfer Q-block 42 (c.f. FIG. 4) and the fusilier Q-blocks 73 are Capture Q-blocks 40. In this case, a passive optical merge unit 125 puts the outputs of the fusilier Capture Q-blocks 74 onto a single fibre which is then switched by an active optical switch 126 either to the right local link fibre 63 or to a loop-back optical fibre 127. A passive optical merge unit 124 fronts the target Transfer Q-block 73, the optical merge unit 124 being coupled on its input side to the left local link fibre 62 and the loop-back optical fibre 127. For an LLE creation operation, the optical switch 125 is set to feed the light fields output by the fusilier Capture Q-blocks 73 to the right local link fibre 63. For a merge operation, the optical switch 125 is set to feed the light field output by a selected one of the fusilier Capture Q-blocks 73 to the loop-back fibre 127 (the Q-block concerned will have been indicated in the merge set-up signals fed to the quantum physical hardware 60).

Returning to FIG. 9 and the general form of the quantum repeater 90, the repeater is arranged to be linked by logical control channels to its left and right neighbour nodes as is more fully described below.

An LLE control (“LLEC”) classical communication channel 94 inter-communicates the L-LLE control unit 92 with the R-LLE control unit of the left neighbour node (that is, the R-LLE control unit associated with the same LLE creation subsystem 70L as the L-LLE control unit 92); the L-LLE control unit 92 uses the LLEC channel 94 to pass LLE creation success/failure messages (message 173 in FIG. 7) to the R-LLE control unit of the left neighbour node.

An LLE control (“LLEC”) classical communication channel 95 inter-communicates the R-LLE control unit 93 with the L-LLE control unit of the right neighbour node (that is, the L-LLE control unit associated with the same LLE creation subsystem 70R as the R-LLE control unit 93); the R-LLE control unit 93 receives LLE creation success/failure messages (message 173 in FIG. 7) over the LLEC channel 95 from the L-LLE control unit of the right neighbour node.

A merge control (“MC”) classical communication channel 98, 99 inter-communicates the MC unit 97 with corresponding units of its left and right neighbour nodes to enable the passing of success/failure and parity information concerning merge operations. As noted above, the passing of success/failure information may be omitted in appropriate cases.

The LLEC communication channel 94, 95 and the MC communication channel 98, 99 can be provided over any suitable high-speed communication connections (such as radio) but are preferably carried as optical signals over optical fibres. More particularly, the LLEC communication channel 94, 95 and the MC communication channel 98, 99 can be carried over respective dedicated optical fibres or multiplexed onto the same fibre (which could be the fibre used for the local links optically coupling Q-blocks in neighbouring nodes—for example, the MC communication channel can be implemented as intensity modulations of the herald signal 79, particularly where only parity information is being sent on this channel). More generally, the LLEC and MC communication channels can be combined into a single duplex classical communications channel.

It will be appreciated from the foregoing that initiation of right-side LLE creation is effectively under the control of the R-LLE control unit 93 (as this unit 93 is responsible for triggering the firing squad 77); initiation of left-side LLE creation is effectively under the control of the R-LLE control unit in the left neighbour node; and initiation of a local merge operation is under the control of the merge control unit 97. Of course, a merge operation can only be effected once the target Q-block 74 is entangled to the left and one of the fusilier Q-blocks is entangled to the right.

There are a number of different strategies that can be adopted for building an end-to-end (“E2E”) entanglement between two end nodes linked by a chain of quantum repeaters 90; the strategy used will generally be embedded in the operational logic of one or more of the control units of each repeater.

One strategy (herein called “Extend-from-End”) involves an iterative process, starting with an LLE between the left end node and the neighbouring quantum repeater, of extending an entanglement existing between the left end node and a quantum repeater of the chain of nodes by merging that entanglement with an LLE formed between that repeater and its right neighbour node. For each iteration, the operative quantum repeater (the one effecting the entanglement-extending merge) shifts rightwards by one along the chain of nodes (that is, away from the end node anchoring the entanglement being extended).With this strategy, a current operative repeater, once it has successfully carried out an entanglement-extending merge, passes on its ‘operative repeater’ mantle to its right neighbour. This neighbour, now the operative repeater, knows that it is entangled leftwards (because its left neighbour would only have passed on its ‘operative repeater’ mantle after successfully merging the LLE between them with the entanglement anchored at the left end node) and so can carry out its own merge operation whenever a right-side LLE exists. By appropriate choice of the number of fusilier Q-blocks 73 in the firing squad 77, it is possible to achieve a high probability of successfully creating a right-side LLE from a single triggering of the firing squad. Therefore, if a right-side LLE does not already exist when a repeater becomes the operative repeater, such an LLE can be created rapidly; as a result, building of an E2E entanglement proceeds quickly. From the foregoing, it will be appreciated that the “Extend-from-End” strategy is effectively embodied by having the merge control unit of each repeater only becoming active when it becomes the operative repeater, and then passing on the ‘operative repeater’ mantle to its right neighbour after successfully carrying out an entanglement-extending merge.

In fact, the high probability of successfully creating a right-side LLE from a single triggering of the firing squad of the repeater 90 permits a number of other strategies for building an end-to-end (“E2E”) entanglement that would otherwise be impracticable. For example, a “Synchronized” strategy can be used in the case where all repeaters in a chain of quantum repeaters 90 can be time synchronized (for example, by timing taken from a GPS constellation or by phase lock looping clocks in the repeaters by signals sent between them). Now, during each successive synchronized operating cycle of the repeaters, each repeater creates a right-side LLE by the triggering of its firing squad (whereby LLEs are brought into existence between all repeaters), and then all the repeaters substantially simultaneously carry out a merge operation—provided all the merges are successful, the effect is to create an E2E entanglement. The overall process of creating an E2E entanglement is thus even quicker than for the “Extend-from-End” strategy because the repeaters are effectively operating in parallel. It will be appreciated that the “Synchronized” strategy is effectively embodied by having the merge control unit 97 and R-LLE control unit 93 of each repeater operate under the control of the synchronized clock.

Another strategy that takes advantage of the high probability of successfully creating a right-side LLE, but which does not call for synchronized operation of the quantum repeaters in the chain, has the quantum repeaters operating on a “Quasi Asynchronous” basis to build an end-to-end (E2E) entanglement. Building an E2E entanglement on the “Quasi Asynchronous” basis involves a cycle-trigger signal being propagated over the MC channel along the chain of nodes from one end node thereby to enable each repeater along the chain to carry out one top-level cycle of operation in which it initiates a local merge operation when left and right qubits of the repeater are known to be, or are expected to be, leftward and rightward entangled respectively. Typically, each repeater is responsible for initiating creation of right side LLEs either in response to receiving the cycle-trigger signal or independently thereof. In due course, every repeater will have effected a single merge and this results in an E2E entanglement being created, the whole process constituting an E2E operating cycle. The order in which the repeaters carry out their respective merge operations in an E2E operating cycle is not necessarily the same as the order in which the repeaters receive the cycle-trigger signal but will depend on a number of factors, most notably the spacing between nodes. Further E2E operating cycles can be initiated by the sending out of further cycle-trigger signals. While the top-level operating cycles of any one repeater do not overlap, the E2E operating cycles may do so.

The FIG. 7 LLE creation subsystem 70 can thus be usefully employed in a quantum repeater regardless of the strategy implemented by the repeater for building an end-to-end (“E2E”) entanglement. Of course, the FIG. 8 LLE creation subsystem 80 can also be employed in a quantum repeater in a similar manner to the FIG. 7 subsystem but with appropriate changes to take into account the possibility of the simultaneous existence of multiple right/left LLEs (the main requirement in this respect is to ensure that the merge control unit knows which left-side and right-side Q-blocks it is to merge, such information being available in the status registers 185 and 186 of the LLE control units 181, 182).

It may be noted that the end nodes linked by a chain of quantum repeaters will each contain functionality for inter-working with the facing side (L or R) of the neighbouring quantum repeater. Thus, the left end node will include functionality similar to that of the R-side of a quantum repeater thereby enabling the left end node to inter-work with the L-side of the neighbouring repeater, and the right end node will include functionality similar to that of the L-side of a quantum repeater to enable the right end node to inter-work with the R-side of the neighbouring repeater.

Entanglement parity can be handled either by standardizing the parity of entanglements by qubit state flipping, or by storing LLE parity information and subsequently combining it with merge parity information for passing on along cumulatively to an end node thereby to enable the latter to determine the parity of end-to-end entanglements.

As described above, the merging of leftward and rightward entanglements by a quantum repeater is done by carrying out a merge operation (c.f. FIG. 1C and related text) directly on the relevant repeater L-side and R-side qubit. However, it may be desirable in certain cases to arrange for this merging to be carried out through the intermediary of one or more local qubits ('intermediate qubits'). As an example, where one intermediate qubit is provided, the leftward and rightward entanglements can be separately extended to the intermediate qubit by respective elongate operations involving the entangled L-side/R-side qubit (as appropriate) and the intermediate qubit; thereafter, the intermediate qubit is removed from entanglement by performing an X measurement operation upon it. It will be appreciated that the details of how the local merging of a repeater's leftward and rightward entanglements is effected is not critical to the general manner of operation of the quantum repeater.

It will be appreciated that many variants are possible to the above described embodiments of the invention.

Although in the foregoing neighbouring nodes have been described as optically coupled through local link optical fibres, it is to be understood that in appropriate circumstances these local links can be established over optical channels other than optical fibres. For example, the optical channel can simply be free space, particularly in satellite applications of the described LLE creation sub-systems.

With regard to the implementation of the LLE control units (171, 172; 181, 182; 92, 93) and the merge control unit (97), it will be appreciated that typically the described functionality will be provided by a program controlled processor or corresponding dedicated hardware.

Multiple parallel LLE creation subsystems of the FIG. 7 or FIG. 8 form can be used in parallel between neighbouring nodes. For example, in a chain of quantum repeaters of the FIG. 9 form, each repeater can be provided with multiple complementary firing squad and target portions of a FIG. 7 LLE creation subsystem 70; this permits the setting up of multiple LLE creation subsystems between adjacent repeaters, these subsystems typically being operated in a staggered manner to multiple up the rate of LLE creation. With such an arrangement, the same local link fibre can be used for all the LLE creation subsystems.

Rather than providing a quantum repeater 90 with complementary firing squad and target portions of the FIG. 7 LLE creation subsystem, it would alternatively be possible to provide two distinct varieties of quantum repeater, one containing two oppositely-directed firing squad portions and the other two oppositely-directed target portions.

FIG. 13A depicts for the quantum repeater variety 130 with two oppositely-directed firing squad portions, how left and right LLE creation subsystems 132L and 132R are formed (the representation used in FIG. 13 for the firing squad and target elements is the same as used in FIG. 10). The left LLE creation subsystem 132L comprises:

- (a) in repeater 130, a firing squad ‘FS’ and its associated optical fabric and left LLE (L-LLE) control unit;
- (b) the left local link fibre 62; and
- (c) in a left neighbour node 131L, a target Q-block and its associated optical fabric and LLE control unit.

The right LLE creation subsystem 132R comprises:

- (a) in repeater 130, a firing squad ‘FS’ and its associated optical fabric and right LLE (R-LLE) control unit;
- (b) the right local link fibre 63; and
- (c) in a right neighbour node 131R, a target Q-block ‘T’ and its associated optical fabric and LLE control unit.

FIG. 13B depicts for the quantum repeater variety 135 with two oppositely-directed target portions, how left and right LLE creation subsystems 137L and 137R are formed. The left LLE creation subsystem 137L comprises:

- (a) in repeater 135, a target Q-block ‘T’ and its associated optical fabric and left LLE (L-LLE) control unit;
- (b) the left local link fibre 62; and
- (c) in a left neighbour node 136L, a firing squad ‘FS’ of fusilier Q-blocks, and its associated optical fabric and LLE control unit.

The right LLE creation subsystem 137R comprises:

- (a) in repeater 135, a target Q-block ‘T’ and its associated optical fabric and right LLE (R-LLE) control unit;
- (b) the right local link fibre 63; and
- (c) in a right neighbour node 136R, a firing squad ‘FS’ and its associated optical fabric and LLE control unit.

The two quantum repeater varieties 130, 135 can be optically coupled in series such as to form an LLE creation subsystem between neighbouring repeaters by alternating the varieties as is illustrated in FIG. 11 for quantum repeaters j−1, j, j+1. The quantum repeater j is of variety 130 and forms an LLE creation subsystem 138 with its left neighbour repeater j−1 of variety 135, and an LLE creation subsystem 139 with its right neighbour repeater j+/of variety 135.

Although in the foregoing description light fields have generally been described as being sent over optical fibres both between nodes and between components of the quantum physical hardware of a node, it will be appreciated that light fields can be sent over any suitable optical channel whether guided (as with an optical waveguide) or unguided (straight line) and whether through free space or a physical medium. Thus, for example, the optical fabric of the quantum physical hardware of a node may comprise silicon channels interfacing with a qubit provided by a nitrogen atom in a diamond lattice located within an optical cavity.

As already indicated, persons skilled in the art will understand how the Q-blocks can be physically implemented and relevant example implementation details can be found in the following papers, herein incorporated by reference:

“Fault-tolerant quantum repeaters with minimal physical resources, and implementations based on single photon emitters” L. Childress, J. M. Taylor, A. S. Sørensen, and M. D. Lukin; Physics Review A 72, 052330 (2005).
“Fault-Tolerant Quantum Communication Based on Solid-State Photon Emitters” L. Childress, J. M. Taylor, A. S. Sørensen, and M. D. Lukin Physical Review Letters 96, 070504 (2006).
“Hybrid quantum repeater based on dispersive CQED interactions between matter qubits and bright coherent light” T D Ladd, P van Loock, K Nemoto, W J Munro, and Y Yamamoto; New Journal of Physics 8 (2006) 184, Published 8 Sep. 2006.
“Hybrid Quantum Repeater Using Bright Coherent Light” P. van Loock, T. D. Ladd, K. Sanaka, F. Yamaguchi, Kae Nemoto, W. J. Munro, and Y. Yamamoto; Physical Review Letters 96, 240501 (2006).
“Distributed Quantum Computation Based-on Small Quantum Registers” Liang Jiang, Jacob M. Taylor, Anders S. Sørensen, Mikhail D. Lukin; Physics Review. A 76, 062323 (2007).

Number	Date	Country	Kind
0907936.9	May 2009	GB	national
0911276.4	Jun 2009	GB	national

Method And Apparatus For Creating Entanglements And Quantum Repeater Utilising The Same

Information

Publication Number

Date Filed

Date Published

Inventors

CPC

US Classifications

International Classifications

Abstract

Description

Claims

Priority Claims (2)

PCT Information