Advertising Entanglement Capabilities in Quantum Networks
Juniper Networks, Inc.1133 Innovation WaySunnyvaleCA94089USAkireeti.kompella@gmail.comJuniper Networks, Inc.Boeing Avenue 240Schipol-RijkPZ1119The Netherlandsmelchior@aelmans.euQuTechVan der Waalsweg 122DelftLC2611The Netherlandss.d.c.wehner@tudelft.nlRedbit NetworksDublinRepublic of Irelandcristian@redbit.network
Routing
QIRGQuantum InternetEPR pairentanglementfidelitymulti-hop entangled pair
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.
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 .
Quantum networking is an emerging field using the strange (even
counterintuitive) properties of quantum mechanics to bring new,
useful capabilities to networking. One of these is
“entanglement” , 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, abbreviated here as EP)
of particles can be used for quantum teleportation and for quantum key distribution (QKD) .
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. 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 deterministic 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.
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 (). Also, several pairs of imperfectly entangled
qubits can be “distilled” () 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 (, ). 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.
The following terms are used in this document:
A quantum link is a connection transporting traveling
qubits, typically photons. This could be a physical link.
This document does not describe the usage of this link.
A classical link is a connection transporting packets.
This could be a physical link. The proposed extensions in
this document use these links to exchange capabilities.
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 . 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.
In this document, a quantum end node
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.
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 (, ), Ion Traps () and
Neutral Atoms (). An example of a
communication qubit is the electron spin of the NV in
diamond system (). Entanglement
between a communication qubit and traveling photons can
also be produced by absorption. Examples include atomic
ensemble memories ().
A communication qubit c at CQN A is denoted by c@A, or
simply c (if the node A is understood).
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 .
A storage qubit s at node B is denoted s@B.
An entangled pair is a special state of two qubits, known
as an EPR pair . An entangled pair
of qubits c@A and c@B is denoted [[c@A, c@B]].
The process of entangling two particles c@A and c@B is
denoted as follows:
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.
A measure of the quality of the entanglement of an EP
(xref target='QFid'/>). 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].
Two qubits located in the same CQN can interchange states
(). For example, the states of a
communication qubit and a storage qubit at A can be
swapped as follows:
If c@A was entangled with c@B, the result is that s@A is
now entangled with c@B.
Distillation is the process of turning a large number of
weakly entangled states into a smaller number of highly
entangled states ().
For example, EPs [[c1@A, c1@B]] and [[c2@A, c2@B]] of
fidelities F1 and F2 respectively may be distilled as
follows:
If distillation is successful, the fidelity F3 of [[c3@A,
c3@B]] will be higher than F1 and F2.
Given two EPs [[c@A, c1@B]] and [[c2@B, c@C]], one can perform
an entanglement swap:
to create a new EP between q@A and q@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:
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.
From A's point of view, here are a number of questions:
Is B reachable from A via quantum links that allow EP creation?
If so, along what sequence(s) of quantum nodes?
Can each pair of adjacent CQNs in this sequence form EPs? If
so, how long will it take, and what fidelity can be
expected?
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?
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?
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.
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 ,
, , ). 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 (), and Ion
Traps (). The largest distance for
producing long-lived entanglement is presently 1.3kms (). 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.
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 shared with other application specific control and
data plane traffic.
In the figure above, an example request for an entangled pair
between nodes A and B will be affected by the following
properties:
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.
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.
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:
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:
A and B look at the distillation schemes that both
advertise in common.
If there is none in common, stop. Distillation is not
possible.
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.
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:
Number of communication qubits. The number of
communication qubits determines the number of entangled
pairs that the node can produce simultaneously.
Number of storage qubits
Possible operations, along with their execution time and
probability of success:
Swap between communication and storage qubits
Entanglement swap
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.
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.
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.
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.
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 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.
has examples of "standard" LSAs for
routing; has the so-called Traffic
Engineering LSAs.
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:
Only one link property is listed. It gives the time-fidelity
tradeoffs of an entanglement operation as a list:
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.
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.
The authors would like to thank the following people for their
contributions and support to this document: Vesna Manojlovic
(RIPE NCC) and Axel Dahlberg (QuTech). Kompella would also like
to thank Bruno Rijsman for encouraging him to learn about
Quantum Computing and Networking.
Also:
There are no requests as yet to IANA for this document.
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