Quantum Internet Research Group AD. Dahlberg
Internet-Draft MS. Skrzypczyk
Intended status: Experimental SW. Wehner
Expires: September 12, 2019 QuTech, Delft University of Technology
March 11, 2019

The Link Layer service in a Quantum Internet
draft-dahlberg-ll-quantum-00

Abstract

In a classical network the link layer is responsible for transferring a datagram between two nodes that are connected by a single link, possibly including switches. In a quantum network however, the link layer will need to provide a robust entanglement generation service between two quantum nodes which are connected by a quantum link, possibly including quantum repeaters. This service can be used by higher layers to produce entanglement between distant nodes or to perform other operations such as qubit transmission, without full knowledge of the underlying hardware and its parameters. This draft defines what can be expected from the service provided by a link layer for a Quantum Network and defines an interface between higher layers and the link layer.

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Table of Contents

1. Introduction

The most important fundamental operation in a quantum network is the generation of entanglement between nodes. Short-distance entanglement can be used to generate long-distance entanglement with the use of an operation called entanglement swap [1] (also formalised in [2]). If nodes A and B share an entangled pair and similarly for B and C, B can perform a so called Bell measurement [3] and send the measurement outcome (2 bits) over a classical channel to A or C such that in the end A and C share an entangled pair. Furthermore, long-distance entanglement in turn enable long-distance qubit transmission by the use of quantum teleportation [3] (also formalised in [2]). Node A can teleport an unknown qubit state to B by consuming an entangled pair between A and B and sending two classical bits to B.

Entanglement between distant nodes of up to 1.3 km have been demonstrated [4], in a proof-of-principle experiment. The next step towards a quantum network is to turn such an experiment to a reliable service. This is the role of the link layer, which turns an ad-hoc physical setup to a reliable entanglement generation service. Since entanglement generation is typically a probabilistic process, one of the main tasks of the link layer is to manage re-tries performed by the physical layer and with high confidence provide entanglement to higher layers within a requested time window. Once an entangled pair has been generated, the nodes need to be able to agree on which qubits are involved in which entangled pair to be able to use it, thus another main task of the link layer is to provide an entanglement identifier.

2. Scope

This draft is meant to define the service and interface of an link layer of a quantum network. It does not present a protocol realising this service. However a protocol that indeed does this have been proposed by us in the paper [5].

3. Desired service

This section definces the service that a link layer provides in a quantum network. The interface and header specification is defined in the next section.

A link layer between two nodes A and B of a quantum network must provide the following features:

4. Interface

This section describes the interface between higher layers and the link layer in a quantum network, along with header specifications for the type of messages. The interface consists of a single type of message from the higher layers to the link layer, which is the CREATE message for requesting entanglement generation. Response messages from the link layer to the higher layers take either the form of an ACK, an OK message or one of many error messages. The ACK is sent back directly upon receiving a CREATE if the link layer supports the request and contains a CREATE ID such that the higher layer can associated the subsequent OK messages to the correct request. It is assumed that the nodes in the network are assigned a unique ID in the network, which is used in the Remote Node ID parameters of the messages below.

4.1. Higher layers to link layer

The higher layers can send a CREATE message to the link layer to request the generation of entanglement. Along with other parameters, as specified below the higher layers can specify a minimum fidelity, a maximum waiting time and the number of entangled pairs to be produced.

4.1.1. Header specification

The CREATE message contains the following parameters:

The complete header specification of the CREATE message is given in Figure 1.

 0                   1                   2                   3
 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
|                        Remote Node ID                         |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
|       Minimum Fidelity        |          Max Time             |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
|           Purpose ID          |           Number              |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Prio  |T|A|C|                                                 |
| rity  |P|T|O|                 Unused                          |
|       |E|O|N|                                                 |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
           

Figure 1: CREATE message header format

4.2. Link layer to higher layers

When receiving a CREATE message from higher layers the link layer will directly respond and notify the higher layer whether requests will be scheduled for generation. If so the link layer responds with an ACK containing a CREATE ID. The higher layer can use this CREATE ID together with the ID of the requesting node to associate OK messages it receives from the link layer to the correct request. Note that the ID of the requesting node is needed since the ACK is returned directly and the CREATE ID is thus not unique for requests from different nodes. If the link layer does not support the given request an error message is instead returned.

When a request is satisfied an OK message is sent to the higher layer. The OK message contains different fields depending on whether the request was of type K or M. For K the OK contains a logical qubit identifier (LQID) such that the higher layer can know which qubit holds the generated entanglement. For M the OK contains the basis which the qubit was measured and the measurement outcome.

Both during and after an entanglement generation, the link layer can return error messages to the higher layers, as further described below. For example if something happens to the qubit or another error occurs such that the entanglement is not valid anymore, the link layer can issue an ERR_EXPIRE message.

4.2.1. Header specification

To distinguish the different types of messages that the link layer can return to the higher layer, the first part of the header is a 4 bit field which specifies the type of message using the following mapping:

The complete header specification for these four types of messages are shown below in Figure 2 to Figure 5.

The ACK message contains the following parameters:

 0                   1                   2                   3
 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Type  |          Create ID            |         Unused        |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
           

Figure 2: ACK message header format

The type K OK message contains the following parameters:

 0                   1                   2                   3
 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Type  |          Create ID            | LQID  |D|   Unused    |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
|        Sequence Number        |          Purpose ID           |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
|                        Remote Node ID                         |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
|           Goodness            |      Time of Goodness         |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
           

Figure 3: Type K OK message header format

The type M OK message contains the following parameters:

Note: Time of Goodness is not needed here since there is no decoherence on the measurement outcomes.

 0                   1                   2                   3
 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Type  |          Create ID            |M|Basis|D|   Unused    |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
|        Sequence Number        |          Purpose ID           |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
|                        Remote Node ID                         |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
|           Goodness            |            Unused             |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
           

Figure 4: Type M OK message header format

The ERR message contains the following parameters:

 0                   1                   2                   3
 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Type  |          Create ID            |  ERR  |S|   Unused    |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
|    Sequence number low        |    Sequence number high       |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
|                         Origin Node                           |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
           

Figure 5: Error message header format

The different error codes using in an error message are the following:

5. IANA Considerations

This memo includes no request to IANA.

6. Acknowledgements

The authors would like to acknowledge funding received the Quantum Internet Alliance.

The authors would further like to acknowledge Wojciech Kozlowski for useful feedback on this draft.

7. Informative References

[1] Briegel, H., Dur, W., Cirac, J. and P. Zoller, "Quantum repeates: The Role of Imperfect Local Operations in Quantum Communication", Physical Review Letters 81, 26, 1998.
[2] Kompella, K., Aelmans, M., Wehner, S., Sirbu, C. and A. Dahlberg, "Advertising Entanglement Capabilities in Quantum Networks", QIRG Internet-Draft, 2018.
[3] Nielsen, M. and I. Chuang, "Quantum Computation and Quantum Information", QIRG Internet-Draft, 2018.
[4] Hensen, B., Bernien, H., Dreau, A., Reiserer, A., Kalb, N., Blok, M., Ruitenberg, J., Vermeulen, R., Schouten, R., Abellan, C., Amaya, W., Pruneri, V., Mitchell, M., Markham, M., Twitchen, D., Elkouss, D., Wehner, S., Taminiau, T. and R. Hanson, "Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres", Nature 526, 682-686, 2015.
[5] Dahlberg, A., Skrzypczyk, M., Coopmans, T., Wubben, L., Rozpedek, F., Pompili, M., Stolk, A., Pawelczak, P., Knegjens, R., de Oliveira Filho, J., Hanson, R. and S. Wehner, "A Link Layer Protocol for Quantum Networks", arXiv pre-print (in preparation) arXiv:1903.XXXXX, 2019.
[6] IEEE, "754-1985 - IEEE Standard for Binary Floating-Point Arithmetic", IEEE standard 10.1109/IEEESTD.1985.82928, 1990.

Authors' Addresses

Axel Dahlberg QuTech, Delft University of Technology Lorentzweg 1 Delft, 2628 CJ Netherlands Phone: +31 (0)65 8966821 EMail: e.a.dahlberg@tudelft.nl
Matthew Skrzypczyk QuTech, Delft University of Technology Lorentzweg 1 Delft, 2628 CJ Netherlands EMail: m.d.skrzypczyk@student.tudelft.nl
Stephanie Wehner QuTech, Delft University of Technology Lorentzweg 1 Delft, 2628 CJ Netherlands