Internet DRAFT - draft-kaws-qirg-advent
draft-kaws-qirg-advent
QIRG K. Kompella
Internet-Draft M. Aelmans
Intended status: Standards Track Juniper Networks, Inc.
Expires: September 28, 2019 S. Wehner
QuTech
C. Sirbu
Redbit Networks
A. Dahlberg
QuTech
March 27, 2019
Advertising Entanglement Capabilities in Quantum Networks
draft-kaws-qirg-advent-03
Abstract
This document describes the use of link-state routing protocols on
classical links in Quantum Networks. It contains proposals for
additions to the IS-IS and OSPF protocols in order for them to
transport relevant information for a Quantum Network, specifically,
for the creation and manipulation of entangled pairs. The document
will describe some of the necessary attributes and some suggestions
of how this information may be used.
No Schrodinger's cats were harmed in the creation of this document.
Requirements Language
The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
"SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this
document are to be interpreted as described in RFC2119 [2].
Status of This Memo
This Internet-Draft is submitted in full conformance with the
provisions of BCP 78 and BCP 79.
Internet-Drafts are working documents of the Internet Engineering
Task Force (IETF). Note that other groups may also distribute
working documents as Internet-Drafts. The list of current Internet-
Drafts is at https://datatracker.ietf.org/drafts/current/.
Internet-Drafts are draft documents valid for a maximum of six months
and may be updated, replaced, or obsoleted by other documents at any
time. It is inappropriate to use Internet-Drafts as reference
material or to cite them other than as "work in progress."
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This Internet-Draft will expire on September 28, 2019.
Copyright Notice
Copyright (c) 2019 IETF Trust and the persons identified as the
document authors. All rights reserved.
This document is subject to BCP 78 and the IETF Trust's Legal
Provisions Relating to IETF Documents
(https://trustee.ietf.org/license-info) in effect on the date of
publication of this document. Please review these documents
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the Trust Legal Provisions and are provided without warranty as
described in the Simplified BSD License.
Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1. Definitions and Notation . . . . . . . . . . . . . . . . 4
2. Motivation . . . . . . . . . . . . . . . . . . . . . . . . . 6
3. Theory of Operation . . . . . . . . . . . . . . . . . . . . . 7
3.1. Multihop Entanglement . . . . . . . . . . . . . . . . . . 8
3.2. Distillation . . . . . . . . . . . . . . . . . . . . . . 9
3.3. Node Properties . . . . . . . . . . . . . . . . . . . . . 9
3.4. Link Properties . . . . . . . . . . . . . . . . . . . . . 10
4. The (Ab)use of Protocols . . . . . . . . . . . . . . . . . . 10
4.1. A Brief Primer on Link-state Protocols . . . . . . . . . 10
4.2. Node Properties . . . . . . . . . . . . . . . . . . . . . 12
4.3. Link Properties . . . . . . . . . . . . . . . . . . . . . 12
5. Security Considerations . . . . . . . . . . . . . . . . . . . 13
6. Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . 13
7. Editorial Comments . . . . . . . . . . . . . . . . . . . . . 13
8. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 13
9. References . . . . . . . . . . . . . . . . . . . . . . . . . 14
9.1. Normative References . . . . . . . . . . . . . . . . . . 14
9.2. Informative References . . . . . . . . . . . . . . . . . 14
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 15
1. Introduction
Quantum networking is an emerging field using the strange (even
counterintuitive) properties of quantum mechanics to bring new,
useful capabilities to computing and networking. One of these is
"entanglement" [8], where the state of a group of particles must be
described as a unit -- it cannot be decomposed to the state of each
particle independently. Entangled pairs (often called EPR pairs,
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abbreviated here as EP) of particles can be used for quantum
teleportation [10] and for quantum key distribution (QKD) [14].
A Quantum Network consists of quantum nodes and links. Here, we will
be concerned with controllable quantum nodes (CQN) that allow control
decisions. We posit a classical network parallel to the quantum
network, with classical nodes (CN) and links. A classical node is
colocated with a quantum node; a classical link may be a fiber or
wavelength parallel to the corresponding quantum link. The existence
of such a classical link is required by most quantum methods to
create EPs deterministically or in a heralded fashion, where the
creation of EPs is conditioned on a specific signal. To make useful
decisions, it is desirable to augment this data to describe the
capabilities and states of quantum nodes and links. At current time
there is a need for classical links besides quantum links. In the
future this might change into a situation where classical links will
perhaps become obsolete.
This document proposes to carry entanglement capability data as Type
Length Values (TLVs) over IS-IS or OSPF link-state advertisements
over the corresponding classical network. A subset of the CQNs may
run quantum applications such as QKD; these nodes may want to
initiate multihop EPs.
Once an EP is created, the state of one particle ("quantum bit" or
qubit) of an EP can be transferred to another qubit within the same
QN by a process known as swapping or a SWAP gate ([12]). Also,
several pairs of imperfectly entangled qubits can be "distilled"
([13]) to fewer but "better entangled" qubits.
Long distance entanglement can be produced from piecewise short
distance entanglement: Given an EP between CQN A and CQN B, and
another EP between CQN B and CQN C, one can create an EP between CQN
A and CQN C by a process known as an "entanglement swap". These
operations can be used to manipulate EPs to improve their lifetimes
or their quality, or to create multihop EPs. Physically, qubits can
be realized in many ways. For example, they can be represented by
the energy levels of Nitrogen Vacancy (NV) Centers in diamond ([16],
[17]). Logically, a qubit can be classified as a "communication
qubit", a "traveling qubit" or a "storage qubit".
This document primarily discusses the exchange of quantum
capabilities over a classical network. Some illustrative examples of
how these capabilities can be used in a quantum network may be given,
but this document should not be considered authoritative on these
procedures.
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1.1. Definitions and Notation
The following terms are used in this document:
Quantum link: A quantum link is a connection transporting traveling
qubits, typically photons. This could be a physical link, or by
means of teleportation over pre-established entanglement amongst
distant network nodes. Such pre-shared entanglement effectively
forms a shortcut - a virtual quantum link - which can be used
exactly once. This document does not describe the usage of these
links itself.
Classical link: A classical link is a connection transporting
packets. This could be a physical or virtual link carried over a
(MPLS) network. The proposed extensions in this document use
these links to exchange capabilities.
Controllable Quantum Node (CQN): A controllable quantum node is a
quantum device consisting of at least one qubit, capable of
performing (a subset of) the following operations described in
detail below: storing qubits for some amount of time, performing
quantum operations such as entanglement distillation and
entanglement swapping, and producing entanglement between the
nodes and traveling qubits. The latter are generally realized
using photons over fibers or through free space.
The term controllable refers to the fact that external control in
software is capable of selecting the desired operations and qubits
to use. Such nodes can be quantum repeaters that allow choices of
operations to be made, as well as quantum end nodes capable of
executing complex application protocols [14]. Quantum repeaters
that merely allow timing control, such as automatic entanglement
swapping whenever qubits arrive in a specific timing interval,
will not be referred to as CQN. Such automated repeaters can be
seen as lying at the quantum physical layer and do not enter
routing or other decision making, apart from being switched on or
off, and hence are not relevant to advertisement protocols like
the ones considered here.
Quantum end node (QEN): In this document, a quantum end node [14] is
one of a pair of quantum nodes forming a entanglement via a
sequence of zero or more CQNs. Quantum end nodes typically run a
higher-layer quantum application such as QKD.
Entangled Pair (EP): An entangled pair is a special state of two
qubits, known as an EPR pair [8]. An entangled pair of qubits c@A
and c@B is denoted [[c@A, c@B]].
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The process of entangling two particles c@A and c@B is denoted as
follows:
ent(c@A, c@B) -> [[c@A, c@B]]
ent(c@A, c@B) may take time T and succeed with probability P, and
yield an entangled pair [[c@A, c@B]] of fidelity F.
Fidelity: A measure of the quality of the entanglement of an EP QFid
[11]). Fidelity lies in the interval [0, 1] where a higher value
indicates better quality; usable fidelity values lie in the half-
open interval (0.5, 1].
Communication qubit: A qubit is called a communication qubit if it
is possible to produce entanglement between this qubit and a
traveling photon. This can be done by emission from the quantum
node, that is, entanglement is produced between the qubit and the
photon which is emitted from the quantum node. This process has
been demonstrated in a number of physical systems that can be used
as quantum nodes such as NV in diamond ([16], [17]), Ion Traps
([18]) and Neutral Atoms ([19]). An example of a communication
qubit is the electron spin of the NV in diamond system ([15]).
Entanglement between a communication qubit and traveling photons
can also be produced by absorption. Examples include atomic
ensemble memories ([20]).
A communication qubit c at CQN A is denoted by c@A, or simply c
(if the node A is understood).
Storage qubit: A qubit is called a storage qubit if the node has the
capability to use this qubit as a (temporary) quantum memory, but
the qubit cannot serve as a communication qubit. To make storage
qubits useful a node is required to possess the ability to
transfer the state of a communication qubit to a storage qubit.
An example of a storage qubit is the nuclear spin in the NV in
diamond system [16].
A storage qubit s at node B is denoted s@B.
Swap: Two qubits located in the same CQN can interchange states
([13]). For example, the states of a communication qubit and a
storage qubit at A can be swapped as follows:
swap(c@A, s@A)
If c@A was entangled with c@B, the result is that s@A is now
entangled with c@B.
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Distillation: Distillation is the process of turning a large number
of weakly entangled states into a smaller number of highly
entangled states ([13]).
For example, EPs [[c1@A, c1@B]] and [[c2@A, c2@B]] of fidelities
F1 and F2 respectively may be distilled as follows:
dist([[c1@A, c1@B]], [[c2@A, c2@B]]) -> [[c3@A, c3@B]]
If distillation is successful, the fidelity F3 of [[c3@A, c3@B]]
will be higher than F1 and F2.
Entanglement Swap: Given two EPs [[c@A, c1@B]] and [[c2@B, c@C]],
one can perform an entanglement swap:
entSwap([[c@A, c1@B]], [[c2@B, c@C]]) -> [[c@A, c@C]]
to create a new EP between c@A and c@C. This is how "multihop"
EPs are created from a sequence of "single-hop" EPs.
The swap operation can also be used within a CQN. A possible use
case is when there aren't enough communication qubits to create
the needed EPs. If, in the above example, B doesn't have two
communication qubits c1 and c2, the following can be done:
ent(c@A, c@B) -> [[c@A, c@B]] # entangle
swap(c@B, s@B) -> [[c@A, s@B]] # swap EP to storage qubit
ent(c@B, c@C) -> [[c@B, c@C]] # use freed up qubit c@B
entSwap(c@A, c@B) -> [[s@B, c@C]] # create multihop EP
2. Motivation
Consider the following (very simple) quantum network consisting of
QENs A and B, and CQNs X, Y, Z, U, V. The goal is to create an EP
between qubits at A and at B, perhaps for the high-level task of QKD
between A and B.
X - Y - Z
. .
A B A, B: QEN
. .
U --- V X, Y, Z, U, V: CQNs
From A's point of view, here are a number of questions:
1. Is B reachable from A via quantum links that allow EP creation?
2. If so, along what sequence(s) of quantum nodes?
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3. Can each pair of adjacent CQNs in this sequence form EPs? If so,
how long will it take, and what fidelity can be expected?
4. If each pair of adjacent CQNs successfully forms EPs of
sufficient fidelity, can these be swapped to form a multihop EP
between A and B?
5. If a multihop EP between A and B were to be formed, would it be
of good enough fidelity, or should a second multihop EP be formed
and the two EPs distilled into one high fidelity EP? How many
times should this process be repeated?
6. If the overall answer is Yes, should A proceed via sequence A, X,
Y, Z, B, or sequence A, U, V, B?
This document aims to provide all CQNs in a quantum network with the
information they need to answer such questions, and to create EPs at
their desired fidelity and speed.
3. Theory of Operation
A CQN contains one or more communication qubits and one or more
storage qubits. Many proposals exist for producing EPs between
remote quantum nodes (see for example [16], [17], [18], [20]).
Abstractly, these result in the generation of EPs with fidelity F
after an expected time t. To give an example, we describe the
generation of EPs that has been implemented in NV in diamond ([16]),
and Ion Traps ([18]). The largest distance for producing long-lived
entanglement is presently 1.3kms ([17]). To entangle a pair of
communication qubits, the QNs send carefully timed photons towards
the HS. If the process is successful, HS sends an OK message to both
QNs.
+----------+ +----------+
| | c-chan +------------+ c-chan | |
| Control- | <-------> | Heralding | <-------> | Control-|
| lable | | Station | | lable |
| Quantum | *~~~~~~~> | | <~~~~~~~* | Quantum |
| Node | q-chan +------------+ q-chan | Node |
| A | | B |
| | <----------------------------------> | |
+----------+ classical network control plane +----------+
The classical network control plane is of particular interest here as
it would be used by the proposed protocol to advertise and exchange
information about the capabilities of the CQNs to generate
entanglement. This classical channel exists between all CQNs and is
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shared with other application specific control and data plane
traffic.
3.1. Multihop Entanglement
resulting entanglement
*~~~~~~~~~~~~~~~~~~~~~~~~~~~~*
+-+ +-+ +-+
|A+----------------------------+B+----------------------------+C|
+-+ A-B Link properties +-+ +-+
[(F1,t1), (F2,t2)] Node B properties:
- Number of Communication Qubits
- Number of Storage Qubits
Node capabilities (operations):
- Swap comm <-> storage
- Entanglement swap
- [(Distillation scheme, time)...]
In the figure above, an example request for an entangled pair between
nodes A and B will be affected by the following properties:
o A chosen combination of F(idelity) and t(ime) duration to produce
an entanglement at the respective Fidelity. These parameters
roughly equate to the quality of the link, the accuracy with which
the nodes can use the link, and the delay in classical networking.
o The actual capability of nodes A and B to make use of the
communication qubits.
A new EP creation between CQNs B and C will similarly be affected by
the same parameters as above.
resulting entanglement
*~~~~~~~~~~~~~~~~~~~~~~~~~~~~* *~~~~~~~~~~~~~~~~~~~~~~~~~~~~*
+-+ +-+ +-+
|A+----------------------------+B+----------------------------+C|
+-+ +-+ B-C Link properties +-+
[(F1,t1), (F2,t2)]
And finally, with an entanglement swap operation at node B (which is
a node specific capability and has a specific duration) we end up
with an A-C EP:
*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*
+-+ +-+ +-+
|A+----------------------------+B+----------------------------+C|
+-+ +-+ +-+
Node B entanglement swap operation
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3.2. Distillation
If a pair of CQNs A and B share a number of EPs of insufficient
quality, they may be combined into a single EP of higher quality by
distillation. To do so, these CQNs need to agree on which
distillation scheme to use before distillation can proceed. This
does not necessarily need to be via communication between A and B, if
one agrees upon a deterministic procedure of selecting one. This
document suggests the following procedure:
1. A and B look at the distillation schemes that both advertise in
common.
2. If there is none in common, stop. Distillation is not possible.
3. If there is a non-trivial subset in common, the first scheme in
the node with the lower router ID is to be used by A and B.
Given a chosen distillation scheme (S,t,p), an additional time delay
will be added for the actual operation: For a 2:1 distillation scheme
between nodes A and B, 2 EPs need to be produced followed by an
operation on A and B that produces 1 EP. This operation will take
time some expected time t, and succeed with probability p.
2:1 distillation (S,t,p)
*~~~~~~~~~~~~~~~~~~~~~~~~~~~~*
*~~~~~~~~~~~~~~~~~~~~~~~~~~~~*
+-+ +-+ +-+
|A+----------------------------+B+----------------------------+C|
+-+ A-B Link properties +-+ +-+
[(F1,t1), (F2,t2)]
3.3. Node Properties
We are interested in exposing the properties of CQNs (including QENs)
to allow sophisticated decision making, for example in the creation
of entanglement. These properties include:
1. Number of communication qubits. The number of communication
qubits determines the number of entangled pairs that the node can
produce simultaneously.
2. Number of storage qubits
3. Possible operations, along with their execution time and
probability of success:
1. Swap between communication and storage qubits
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2. Entanglement swap
3. List of supported distillation schemes (in order of
preference).
Note that several other parameters can be advertised, such as the T1
and T2 times for a qubit's decoherence. These are omitted for now,
instead just giving the decay of the fidelity of an EP. If deemed
useful, T1 and T2 times can additionally be advertised.
3.4. Link Properties
A list of (Fn,tn) pairs describing the tradeoffs of a possible
entanglement produced by two nodes (the ends of said link): tn is the
time to produce an entangled pair with fidelity Fn.
4. The (Ab)use of Protocols
The routing protocols IS-IS and/or OSPF could be used in order to
advertise entanglement capabilities. This section describes the
additional data fields needed in order to facilitate the objective.
4.1. A Brief Primer on Link-state Protocols
This document suggests the use of a link-state protocol to distribute
the capabilities of CQNs to create entanglement. This section offers
a short introduction to link-state protocols for those not familiar
with them.
Consider a directed graph G=(V, E) with vertices (nodes) V and edges
(links) E. Consider also G'=(V', E'); there is a 1-1 mapping from V'
to V and from E' to E such that e1' = (v1', v2') is in E' iff e1 =
(v1, v2) is in E and v1' maps to v1 and v2' maps to v2. G'
represents the quantum network; V' represents the set of CQNs, and E'
the set of quantum links between pairs of CQNs; G represents a
classical network parallel to G'; that is, each CQN v' has a
corresponding classical node v. v plays a dual role: it is the
control node for v', and proxies on behalf of v' in the link-state
protocol.
The basic objective of a link-state protocol is to "flood" properties
of nodes and (directed) links to all nodes in the network. This is
accomplished by means of "link-state advertisements" (LSAs) that each
node originates and sends to its immediate neighbors. The neighbors
in turn send received LSAs to their own neighbors; this process
repeats until every node receives every LSA (hence the term
"flooding"). The focus of LSAs is the link properties (hence _link-
state_ advertisements), although node properties are also advertised.
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There are mechanisms to prevent looping of LSAs, and for reliable
flooding. There is also a sequence number by which a more recent
update of an LSA can be identified as such, and a mechanism for
"aging out" LSAs belonging to nodes no longer in the network. In
what follows, quantum node and link properties are added to the link-
state advertisements of the corresponding classical node. Note that
link properties need not be symmetric; that is, the link properties
of (v, w) need not be the same as those of (w, v).
The net result of flooding is that every node has the same picture of
the network (modulo LSAs in flight); in particular, each node knows
the overall topology and connectivity of the network, and can use
this information to make decisions. In a classical network, such a
decision could be to compute a shortest path; for the quantum
network, it could be choosing a feasible path (i.e., sequence of
CQNs) for a multihop entanglement. Note that a node doesn't really
know when it has complete and up-to-date information about the
network; LSA updates may be originated at any time. Usually, this is
okay: for example, if a node v learns enough of the network to have a
path to another node w, it can compute a multihop entanglement to w.
Subsequent updates may provide a more optimal (or higher probability)
entanglement path. There are heuristics one can apply to guess that
the link-state database (LSDB) (i.e., the union of all LSAs) is
complete-ish; however, as nodes (and links) can fail or disconnect,
there really is no such thing as "the full LSDB".
Each node v is identified by a "router ID" (an IP address uniquely
allocated to v), denoted by rid(v). A link L = (v, w) is identified
by (rid(v), i) where i is an index allocated by v for L unique for
each link emanating from v. (L may also be identified by IP
addresses, but we'll ignore that for now.) It is generally expected
that a directed link (v, w) is matched by a link (w, v); if not, (v,
w) is ignored from subsequent consideration; in particular, no link
properties are advertised for this link by v. Note that a pair of
nodes may have multiple links between them; for simplicity, the
notation will not be extended to indicate this. We'll assume rid(v')
= rid(v) and the index allocated to a quantum link e' is the same as
that of the corresponding classical link e.
Let v, w be a pair of neighboring nodes, and let L1 = (v, w) and L2 =
(w, v) in E be directed links in opposite directions between v and w
with identifiers (rid(v), i1) and (rid(w), i2) respectively (where i1
is the index allocated for L1 by v, and similarly for i2)). As a
first step in running a link-state protocol, v runs a "hello
protocol" all its links; in particular, over L1. Similarly, w will
run the hello protocol over L2. The hello protocol serves to
exchange the indices i1 and i2, and thus identify (rid(v), i1) as the
reverse link of (rid(w), i2). This allows both v and w to correlate
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the link properties of L1 and L2. If the hello protocol fails
between v and w, neither node includes link properties for the link
in their LSAs.
Once the hello protocol has been run on all links, v starts the
process of generating and sending its own LSA over all its links, and
of receiving the current LSDB from its neighbors. Note that an LSA
originated by v must propagate unchanged across the network; only v
is allowed to change it (and such a change must be accompanied by
updating the LSA's sequence number). Such an update is triggered by
a new link coming up, an existing link going down, or a node or link
property changing.
IS-IS and OSPF are in principle similar, although the details of the
protocol mechanisms and encodings vary. In both protocols, a Type-
Length-Value (TLV) is used to encode most node and link properties.
In IS-IS, TLVs are used for all properties, and a single type of LSA
is used; in OSPF, there are several types of LSAs, and many (but not
all) properties are encoded as TLVs.
[1] has examples of "standard" LSAs for routing; [4] has the so-
called Traffic Engineering LSAs.
4.2. Node Properties
Here, we give a protocol-independent description of quantum node
properties; later documents will specify the encoding specifically
for IS-IS and OSPF.
Note that the following list of node properties is a strawman; all
details are subject to change, and other properties may be added as
needed.
The following node properties are added to the appropriate LSA:
<Qubit-TLV><NCQ><NSQ>
<CS-Swap><Prob><ExecTime>
<Ent-Swap><Prob><ExecTime>
<Measure><Prob><ExecTime>
<NDistSch><DistScheme1><DistScheme2>
4.3. Link Properties
Only one link property is listed. It gives the time-fidelity
tradeoffs of an entanglement operation as a list:
<N-Ent-TO><time1><fid1><time2><fid2>...
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This is interpreted as follows: an entanglement operation may be
initiated between nodes v and w over link (v, w). Depending on how
fast one wants to complete (time-i), the list gives the corresponding
fidelity of the resulting entanglement (fid-i). time-i is given in
nanoseconds; fid-i as a number between 0 and 999999. THe denominator
is 1000000.
Note that this link property is symmetric, as entanglement is
initiated simultaneously at v and w.
5. Security Considerations
It is not anticipated that adding these extensions to IS-IS and OSPF
will present new security hazards to those protocols. Since however
a common application of entangled pairs is for security purposes
(such as QKD), it is worth investigating whether this application
places a higher burden of security on the underlying protocols.
6. Acknowledgments
The authors would like to thank the following people for their
contributions and support to this document: Vesna Manojlovic,
Marcello Caleffi and Rodney Van Meter. Kompella would also like to
thank Bruno Rijsman for encouraging him to learn about Quantum
Computing and Networking.
Also:
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/_ \'. __..-' , ,--...--'''
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`-';' ; ; ;
__...--'' ___...--_..' .;.'
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7. Editorial Comments
It could be worth investigating the use of a distance-vector routing
protocol to limit flooding.
8. IANA Considerations
There are no requests as yet to IANA for this document.
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9. References
9.1. Normative References
[1] Callon, R., "Use of OSI IS-IS for routing in TCP/IP and
dual environments", RFC 1195, DOI 10.17487/RFC1195,
December 1990, <https://www.rfc-editor.org/info/rfc1195>.
[2] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", BCP 14, RFC 2119,
DOI 10.17487/RFC2119, March 1997,
<https://www.rfc-editor.org/info/rfc2119>.
[3] Katz, D., Kompella, K., and D. Yeung, "Traffic Engineering
(TE) Extensions to OSPF Version 2", RFC 3630,
DOI 10.17487/RFC3630, September 2003,
<https://www.rfc-editor.org/info/rfc3630>.
[4] Li, T. and H. Smit, "IS-IS Extensions for Traffic
Engineering", RFC 5305, DOI 10.17487/RFC5305, October
2008, <https://www.rfc-editor.org/info/rfc5305>.
[5] Ishiguro, K., Manral, V., Davey, A., and A. Lindem, Ed.,
"Traffic Engineering Extensions to OSPF Version 3",
RFC 5329, DOI 10.17487/RFC5329, September 2008,
<https://www.rfc-editor.org/info/rfc5329>.
[6] Aggarwal, R. and K. Kompella, "Advertising a Router's
Local Addresses in OSPF Traffic Engineering (TE)
Extensions", RFC 5786, DOI 10.17487/RFC5786, March 2010,
<https://www.rfc-editor.org/info/rfc5786>.
9.2. Informative References
[7] "Qubit", <https://en.wikipedia.org/wiki/Qubit>.
[8] "Quantum Entanglement",
<https://en.wikipedia.org/wiki/Quantum_entanglement>.
[9] "Quantum Network",
<https://en.wikipedia.org/wiki/Quantum_network>.
[10] "Quantum Teleportation",
<https://en.wikipedia.org/wiki/Quantum_teleportation>.
[11] "Quantum Fidelity", <https://en.wikipedia.org/wiki/
Fidelity_of_quantum_states>.
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[12] Wehner, S., Elkouss, D., and R. Hanson, "Quantum internet:
A vision for the road ahead", Science 362, 6412, 2018.
[13] Rozpedek, F., Schiet, T., Thinh, L., Elkouss, D., Doherty,
A., and S. Wehner, "Optimizing practical entanglement
distillation", Phys. Rev. A 97, 062333, 2018,
<https://arxiv.org/abs/1803.10111>.
[14] "Quantum Key Distribution",
<https://en.wikipedia.org/wiki/Quantum_key_distribution>.
[15] "Nitrogen-vacancy center",
<https://en.wikipedia.org/wiki/Nitrogen-vacancy_center>.
[16] Humphreys, P., "Deterministic delivery of remote
entanglement on a quantum network", Nature 558, 2018.
[17] Hensen, B. and , "Loophole-free Bell inequality violation
using electron spins separated by 1.3 kilometres",
Nature 526, 2015.
[18] Hucul, D. and , "Modular entanglement of atomic qubits
using photons and phonons", Nature Physics 11(1), 2015.
[19] Noelleke, C. and , "Efficient Teleportation Between Remote
Single-Atom Quantum Memories", Physical Review
Letters 110, 140403, 2013.
[20] Sangouard, N. and , "Quantum repeaters based on atomic
ensembles and linear optics", Reviews of Modern
Physics 83, 33, 2011.
Authors' Addresses
Kireeti Kompella
Juniper Networks, Inc.
1133 Innovation Way
Sunnyvale, CA 94089
USA
Email: kireeti.kompella@gmail.com
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Melchior Aelmans
Juniper Networks, Inc.
Boeing Avenue 240
Schipol-Rijk, PZ 1119
The Netherlands
Email: maelmans@juniper.net
Stephanie Wehner
QuTech
Van der Waalsweg 122
Delft, LC 2611
The Netherlands
Email: s.d.c.wehner@tudelft.nl
Cristian Sirbu
Redbit Networks
Dublin
Republic of Ireland
Email: cristian@redbit.network
Axel Dahlberg
QuTech
Van der Waalsweg 122
Delft, LC 2611
The Netherlands
Email: E.A.Dahlberg@tudelft.nl
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