Quantum Internet Research Group AD. Dahlberg
Internet-Draft MS. Skrzypczyk
Intended status: Experimental SW. Wehner, Ed.
Expires: April 12, 2020 QuTech, Delft University of Technology
October 10, 2019
The Link Layer service in a Quantum Internet
draft-dahlberg-ll-quantum-03
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.
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.
Status of This Memo
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provisions of BCP 78 and BCP 79.
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This Internet-Draft will expire on April 12, 2020.
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Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 2
2. Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
3. Desired service . . . . . . . . . . . . . . . . . . . . . . . 3
4. Interface . . . . . . . . . . . . . . . . . . . . . . . . . . 4
4.1. Higher layers to link layer . . . . . . . . . . . . . . . 4
4.1.1. Header specification . . . . . . . . . . . . . . . . 4
4.2. Link layer to higher layers . . . . . . . . . . . . . . . 7
4.2.1. Header specification . . . . . . . . . . . . . . . . 8
5. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 12
6. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . 13
7. Informative References . . . . . . . . . . . . . . . . . . . 13
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 14
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 does 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. For an overview of quantum networking and its
applications we refer to [5].
Long lived entanglement between distant nodes capable of storing such
entanglement has been demonstrated over a distance of up to 1.3 km
[4], in a proof-of-principle experiment. This entanglement was also
heralded, that is, there exits a so-called heralding signal that
indicates success in entanglement production without consuming such
entanglement. Short lived and non-heralded entanglement has been
observed from a satellite over a distance of 1200 km [6] in a proof
of principle experiment. The next step towards a quantum network is
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to turn ad-hoc experiments that produce entanglement into a reliable
service. This is the role of the link layer, which turns an ad-hoc
physical setup to a reliable entanglement generation service.
Reliable here means that the higher layers can (unless a timeout or
other critical failures occur) rely in deterministic entanglement
production. In particular, this means that since the underlying
physical process is often probabilistic but entanglement generation
can be confirmed using the heralding signal, one of the main tasks of
the link layer is to manage re-tries in producing entanglement at the
the physical layer. Once an entangled pair has been generated, the
nodes need to be able to agree on which qubits are involved in which
entangled pair in order 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. Further considerations that motivate
this definition can be found in [7]. It does not present a protocol
realising this service. However a protocol that indeed does this
have been proposed in [7], together with more details on use cases
and design decisions in forming a quantum network stack.
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 minimal features (see [7] for an extended
feature set):
o Allow both node A and B to initialize entanglement generation.
o Allow the initializing node to specify a desired minimum
fidelity[3] and maximum waiting time.
o Notify both nodes of success or failure of entanglement generation
before the requested maximum waiting time has passed since the
request was initialized.
o If success is notified, the generated entangled pair has with high
confidence higher (or equal) fidelity than the desired minimum
fidelity.
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o For a successful request, provide an entanglement identifier to
allow higher layers to use identify the entangled pair in the
network without the need for further communication.
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:
o Remote Node ID (32 bits): Used if the node is directly connected
to multiple nodes. Indicates which node to generate entanglement
with.
o Minimum fidelity (16 bits): The desired minimum fidelity, between
0 and 1, of the generated entangled pair. A binary value encoding
the integer 'n' represents the fidelity 'n' divided by (2^16-1).
o Time Unit (TU) (2 bits): The time units used for specifying Max
Time, where (00, 01, 10) each indicate (micro-seconds,
milliseconds, seconds) respectively and 11 is unused.
o Max Time (14 bits): The maximum time in the time units specified
above that the higher layer is willing to wait for the request to
be fulfilled. A binary value encoding the integer 'n'
representing the time in the specified time units.
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o Purpose ID (16 bits): Allows the higher layer to tag the request
for a specific purpose. If the request is from an application
this can be thought of as a port number. The purpose ID can also
be used by a network layer to specify that this entanglement
request is part of long-distance entanglement generation over a
specific path.
o Number (16 bits): The number of entangled pairs to generate.
o Priority (3 bits): Can be used to indicate if this request is of
high priority and should ideally be fulfilled early. Higher means
faster service.
o Type of request (TPE) (1 bit): Either create and keep (K) or
measure directly (M), where K stores the generated entanglement in
memory and M measures the entanglement directly.
o Atomic (ATO) (1 bit): A flag that indicates that the request
should be satisfied as a whole without interuption by other
requests.
o Consecutive (CON) (1 bit): A flag indicating an OK is returned for
each pair made for a request. Otherwise, an OK is sent only when
the entire request is completed (more common in application use
cases). For K type requests, this means all pair should be in
memory at the same time.
o Random basis choice for measure directly
* (RL) (2 bits): Choose to measure the local qubit randomly in
either
* (RR) (2 bits): Choose to measure the remote qubit randomly in
either
Using the following encoding:
* 00: No random choice
* 01: X or Z basis (BB84)
* 10: X, Y or Z basis (six state)
* 11: CHSH rotated bases, Z basis rotated by angles +/- pi/4
around Y axis.
o Probability distributions used to sample random basis for measure
directly:
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* (PL1) (8 bits): Parameter for local probability distribution
used to sample basis if RL is not 00
* (PL2) (8 bits): Parameter for local probability distribution
used to sample basis if RL is not 00
* (PR1) (8 bits): Parameter for remote probability distribution
used to sample basis if RR is not 00
* (PR2) (8 bits): Parameter for remote probability distribution
used to sample basis if RR is not 00
Each value is seen as the integer representing of the binary
value. Probability distributions are used as follows
* If the specified random basis has 2 elements then the
distribution obeys the probabilities (PL(R)1 / 255, 1 - PL(R)1
/ 255)
* If the specified random basis has 3 elements then the
distribution obeys the probabilities (PL(R)1 / 255, PL(R)2 /
255, 1 - PL(R)1 / 255 - PL(R)2 / 255)
o Rotation of measurement basis in the case of M types of requests
for both the local and remote measurement. Three rotations from
the defaults Z basis are performed, first a rotation around the
X-axis (ROTX1L(R)), then a rotation around the Y-axis (ROTYL(R))
and finally a rotation again around the X-axis. Note that
arbitrary rotations can be composed as these three rotations, see
<https://en.wikipedia.org/wiki/Euler_angles>. If all three fields
are 00000000, the qubits are measured in the Z basis. If RL(R) is
not 00, these three fields (ROTX1L(R), ROTYL(R) and ROTX2L(R)) are
ignored.
* Measurement rotation around X for local (remote) node
(ROTX1L(R)) (8 bits): Measurement to be performed in the case
of M types of request. Default is Z measurement. Specified
measurement to be rotated around the X axis by angle of 2
pi/256 * ROTX1
* Measurement rotation around Y for local (remote) node
(ROTYL(R)) (8 bits): Measurement to be performed in the case of
M types of request. Default is Z measurement. Specified
measurement to be rotated around the Y axis by an angle of 2
pi/256 * ROTY
* Measurement rotation around X for local (remote) node
(ROTX2L(R)) (8 bits): Measurement to be performed in the case
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of M types of request. Default is Z measurement. Specified
measurement to be rotated around the X axis by an angle of 2
pi/256 * ROTX2
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 |TU | Max Time |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Purpose ID | Number |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
|Prio |T|A|C| | | | | |
|rity |P|T|O|RL |RR | reserved | PL1 | PL2 |
| |E|O|N| | | | | |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| | | | |
| PR1 | PR2 | ROTX1L | ROTXYL |
| | | | |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| | | | |
| ROTX2L | ROTX1R | ROTYR | ROTX2R |
| | | | |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
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 may choose to 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 (keep) or M (measure directly). For K the
OK contains a logical qubit identifier (LQID) such that the higher
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layer can know which logical 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 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:
o 0001: ACK
o 0010: Type K OK
o 0011: Type M OK
o 0100: ERR
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:
o Create ID (16 bits): A Create ID that the higher layer can use to
associate subsequent OK messages to the request.
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:
o Create ID (16 bits): Must be the same Create ID that was given in
the ACK of the corresponding request.
o Logical Qubit ID (LQID) (4 bits): A logical ID of the qubit which
is part of the entangled pair.
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o Directionality flag (D) (1 bit): Specifies if the request came
from this node (D=0) or from the remote node (D=1).
o Sequence number (16 bits): A sequence number for identifying the
entangled pair. It is assumed to be unique for entangled pairs
between the given nodes. Thus together with the IDs of the nodes
between which the entanglement is produced, one can create an
entanglement identifier which is unique in the network.
o Purpose ID (16 bits): The purpose ID of the request (only used by
the node which did not initiate the request)
o Remote Node ID (32 bits): Used if the node is directly connected
to multiple nodes.
o Goodness (16 bits): An estimate of the fidelity of the generated
entangled pair. Should not be seen as a guarantee.
o Time of Goodness (ToG) (16 bits): The time of the goodness
estimate. Not necessarily the time when the estimate is performed
but rather the time for which the estimate is for. Can be used to
make an updated estimate based on decoherence times of the qubits.
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:
o Create ID (16 bits): The same Create ID that was given in the ACK
of the corresponding request.
o Measurement outcome (M) (1 bit): The outcome of the measurement
performed on the entangled pair.
o Basis (3 bits): Which basis the entangled pair was measured in,
used if the basis is random, i.e. if RBC is not 00 in the CREATE.
The following representation is used:
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* 000: Z-basis
* 001: X-basis
* 010: Y-basis
* 011: Z-basis rotated by angle pi/4 around Y-axis
* 100: Z-basis rotated by angle -pi/4 around Y-axis
* 101: Unused
* 110: Unused
* 111: Unused
o Directionality flag (D) (1 bit): Specifies if the request came
from this node (D=0) or from the remote node (D=1).
o Sequence number (16 bits): A sequence number for identifying the
entangled pair. It is assumed to be unique for entangled pairs
between the given nodes. Thus together with the IDs of the nodes,
one can create an entanglement identifier which is unique in the
network.
o Purpose ID (16 bits): The purpose ID of the request (only used by
the node which did not initiate the request)
o Remote Node ID (32 bits): Used if the node is directly connected
to multiple nodes.
o Goodness (16 bits): An estimate of the fidelity of the generated
entangled pair. Should not be seen as a guarantee.
Note: Time of Goodness is not needed here since there is no
decoherence on the measurement outcomes.
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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|D|Basis| 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:
o Create ID (16 bits): The same Create ID that was given in the ACK
of the corresponding request.
o Error code (ERR) (4 bits): Specifies what error occurred. See
below what the error codes mean.
o Expire by sequence numbers (S) (1 bit): Used by ERR_EXPIRE, to
specify whether a range of sequence numbers should be expired
(S=1) or all sequence numbers associated with the given Create ID
and Origin Node (S=0).
o Sequence number low (16 bits): Used by error code ERR_EXPIRE to
identify a range of sequence numbers that needs to be expired.
Numbers above Sequence number low (inclusive) and below Sequence
number high (exclusive) should be expired.
o Sequence number high (16 bits): Used by error code ERR_EXPIRE to
identify a range of sequence numbers that needs to be expired.
Numbers above Sequence number low (inclusive) and below Sequence
number high (exclusive) should be expired.
o Origin Node (32 bits): Used if the node is directly connected to
multiple nodes. Needed here since Create IDs are not unique for
request from different nodes.
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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:
o Error returned directly when a CREATE message is received:
* ERR_UNSUPP (0001): The given request is not supported. For
example if the minimum fidelity is not achievable or if the
request is of type K and the hardware cannot store
entanglement.
* ERR_CREATE (0010): The create message could not be parsed.
* ERR_REJECTED (0011): The request was rejected by this node
based on for example the Purpose ID.
* ERR_OTHER (0100): An unknown error occurred.
o Error returned after a CREATE message is received, before or after
an OK is returned:
* ERR_EXPIRE (0101): One or more already sent OK messages have
expired and the entangled pair is not available anymore. Can
either be specified as a range of sequence numbers or by a
create ID by using the S flag.
* ERR_REJECTED (0011): The request was rejected by the other node
based on for example the Purpose ID.
* ERR_TIMEOUT (0110): The request was not satisfied within the
requested max waiting time.
5. IANA Considerations
This memo includes no request to IANA.
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6. Acknowledgements
The authors would like to acknowledge funding received from the EU
Flagship on Quantum Technologies, Quantum Internet Alliance.
The authors would further like to acknowledge Tim Coopmans, Leon
Wubben, Filip Rozpedek, Matteo Pompili, Arian Stolk, Przemyslaw
Pawelczak, Robert Knegjens, Julio de Oliveria Filho, Sidney Cadot,
Joris van Rantwijk and Ronald Hanson for inputs and discusssion and
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, <https://journals.aps.org/prl/abstract/10.1103/
PhysRevLett.81.5932>.
[2] Kompella, K., Aelmans, M., Wehner, S., Sirbu, C., and A.
Dahlberg, "Advertising Entanglement Capabilities in
Quantum Networks", QIRG Internet-Draft, 2018,
<https://datatracker.ietf.org/doc/draft-kaws-qirg-
advent/>.
[3] Nielsen, M. and I. Chuang, "Quantum Computation and
Quantum Information", Book Cambridge University Press,
2010, <https://doi.org/10.1017/CBO9780511976667>.
[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,
<https://arxiv.org/abs/1508.05949>.
[5] Wehner, S., Elkouss, D., and R. Hanson, "Quantum internet:
A vision for the road ahead", Science 362, 6412, 2018,
<http://science.sciencemag.org/content/362/6412/
eaam9288?intcmp=trendmd-sci>.
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[6] Yin, J., Cao, Y., Li, Y., Liao, S., Zhang, L., Ren, J.,
Cai, W., Liu, W., Li, B., Dai, H., Li, G., Lu, Q., Gong,
Y., Xu, Y., Li, S., Li, F., Yin, Y., Jiang, Z., Li, M.,
Jia, J., Ren, G., He, D., Zhou, Y., Zhang, X., Wang, N.,
Chang, X., Zhu, Z., Liu, N., Chen, Y., Lu, C., Shu, R.,
Peng, C., Wang, J., and J. Pan, "Satellite-based
entanglement distribution over 1200 kilometers",
Science 356, 6343, 2017,
<https://arxiv.org/abs/1707.01339>.
[7] 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 arXiv:1903.09778, 2019,
<https://arxiv.org/abs/1903.09778>.
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 (editor)
QuTech, Delft University of Technology
Lorentzweg 1
Delft 2628 CJ
Netherlands
Email: s.d.c.wehner@tudelft.nl
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