Fundamental limitation on quantum broadcast networks

Bäuml, Stefan; Azuma, Koji

doi:10.1088/2058-9565/aa6d3c

Cited by 40 publications

(53 citation statements)

References 59 publications

(108 reference statements)

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“…We have just begun to grasp full implications of our bound (1): for instance, its tighter version for specific channels like Pirandola's one37 or with deriving a better bound52 for the squashed entanglement of the channel, its applications to the many-body quantum physics in any spacetime topology regarded as a quantum network1 and to a more complicated quantum communication channel network—such as a multi-party protocol with broadcasting channels535455—will be in a fair way to appear.…”

Section: Discussionmentioning

confidence: 99%

Fundamental rate-loss trade-off for the quantum internet

2016

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The quantum internet holds promise for achieving quantum communication—such as quantum teleportation and quantum key distribution (QKD)—freely between any clients all over the globe, as well as for the simulation of the evolution of quantum many-body systems. The most primitive function of the quantum internet is to provide quantum entanglement or a secret key to two points efficiently, by using intermediate nodes connected by optical channels with each other. Here we derive a fundamental rate-loss trade-off for a quantum internet protocol, by generalizing the Takeoka–Guha–Wilde bound to be applicable to any network topology. This trade-off has essentially no scaling gap with the quantum communication efficiencies of protocols known to be indispensable to long-distance quantum communication, such as intercity QKD and quantum repeaters. Our result—putting a practical but general limitation on the quantum internet—enables us to grasp the potential of the future quantum internet.

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Section: Discussionmentioning

confidence: 99%

Fundamental rate-loss trade-off for the quantum internet

2016

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“…where the last equality is due to the separability of the initial state 1 r ( ) and to the definition of m l á ñ ( ) given in equation (22). At this point, the thesis of theorem 2 follows directly from the inequality given in equation (36). ,…”

Section: Proofs For Theorems 1 Andmentioning

confidence: 95%

“…For this reason, every choice made by the parties at a certain stage of the protocol may depend on all previously obtained LOCC outcomes. In the remainder of this section we formally describe any protocol of this kind, similarly to what has been done in [24,32,36]. For the sake of simplicity, we will drop the subscript ABC C M 1 ¼ from states spread over the whole network.…”

Section: Adaptive Strategy Over Quantum Networkmentioning

confidence: 99%

“…This issue has been addressed in [32] and [24], where the authors obtained network versions of equation (2), by respectively using E R or E sq as measures of entanglement. The possibility of dealing with quantum broadcast channels [33] has also been considered in [34][35][36][37][38][39]. When multiple channels are involved, a typical approach consists in splitting the whole network into two parts, and then in using the maximum amount of entanglement generated by the channels connecting them in order to bound the number of ebits (pbits) produced by a communication protocol.…”

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confidence: 99%

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Versatile relative entropy bounds for quantum networks

Rigovacca¹,

Kato²,

Bäuml³

et al. 2018

New J. Phys.

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We provide a versatile upper bound on the number of maximally entangled qubits, or private bits, shared by two parties via a generic adaptive communication protocol over a quantum network when the use of classical communication is not restricted. Although our result follows the idea of Azuma et al (2016 Nat. Commun. 7 13523) of splitting the network into two parts, our approach relaxes their strong restriction, consisting of the use of a single entanglement measure in the quantification of the maximum amount of entanglement generated by the channels. In particular, in our bound the measure can be chosen on a channel-by-channel basis, in order to make it as tight as possible. This enables us to apply the relative entropy of entanglement, which often gives a state-of-the-art upper bound, on every Choi-simulable channel in the network, even when the other channels do not satisfy this property. We also develop tools to compute, or bound, the max-relative entropy of entanglement for channels that are invariant under phase rotations. In particular, we present an analytical formula for the max-relative entropy of entanglement of the qubit amplitude damping channel. IntroductionWhenever two parties, say Alice and Bob, want to communicate by using a quantum channel, its noise unavoidably limits their communication efficiency [1]. In the limit of many channel uses, their asymptotic optimal performance can be quantified by the channel capacity, which represents the supremum of the number of qubits/bits that can be faithfully transmitted per channel use. Obtaining an exact expression for this quantity is typically far from trivial. Indeed, in addition to the difficulty of studying the asymptotic behaviour of the channel, the value of the capacity also depends on the task Alice and Bob want to perform, as well as on the free resources available to them [1]. Two representative tasks, which will be considered in our paper, involve the generation and distribution of a string of shared private bits (pbits) [2,3] or of maximally entangled states (ebits) [4]. These are known to be fundamental resources for more complex protocols, such as secure classsical communication [5,6], quantum teleportation [7], and quantum state merging [8]. An example of free resource involves the possibility of exchanging classical information over a public classical channel, such as a telephone line or over the internet. Depending on the restrictions on this, the capacity is said to be assisted by zero, forward, backward, or two-way classical communication [1]. In this paper we will focus on the last option, that is, no restriction will be imposed on the use of classical communication.Although the capacity of a quantum channel is by definition an abstract and theoretical quantity, it is also practically useful in that it can be compared with the performance of known transmission schemes. This comparison could then give an indication on the extent of improvements that could be expected in the future. From this perspective, similar conclusions could be obt...

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“…[48]) and the algorithm for determining a Steiner tree approximation as discussed in section 2.2. We remark that Steiner trees have also been used in [95] for deriving fundamental limitations on quantum broadcast channels. These algorithms require the definition of a cost function C for the edges of the graph.…”

Section: Region Routingmentioning

confidence: 99%

A quantum network stack and protocols for reliable entanglement-based networks

Pirker

Dür

2019

New J. Phys.

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We present a stack model for breaking down the complexity of entanglement-based quantum networks. More specifically, we focus on the structures and architectures of quantum networks and not on concrete physical implementations of network elements. We construct the quantum network stack in a hierarchical manner comprising several layers, similar to the classical network stack, and identify quantum networking devices operating on each of these layers. The layers responsibilities range from establishing point-to-point connectivity, over intra-network graph state generation, to inter-network routing of entanglement. In addition we propose several protocols operating on these layers. In particular, we extend the existing intra-network protocols for generating arbitrary graph states to ensure reliability inside a quantum network, where here reliability refers to the capability to compensate for devices failures. Furthermore, we propose a routing protocol for quantum routers which enables the generation of arbitrary graph states across network boundaries. This protocol, in correspondence with classical routing protocols, can compensate dynamically for failures of routers, or even complete networks, by simply re-routing the given entanglement over alternative paths. We also consider how to connect quantum routers in a hierarchical manner to reduce complexity, as well as reliability issues arising in connecting these quantum networking devices. quantum network shall not be limited to the generation of Bell-pairs only [50][51][52][53], because many interesting applications require multipartite entangled quantum states. Therefore, the ultimate goal of quantum networks should be to enable their clients to share arbitrary entangled states to perform distributed quantum computational tasks. An important subclass of multipartite entangled states are so-called graph states [54], and many protocols in quantum information theory rely on this class of states.Here we consider entanglement-based quantum networks utilizing multipartite entangled states [51-53, 55-57] which are capable of generating arbitrary graph states among clients. In general, we identify three successive phases in entanglement-based quantum networks: dynamic, static, and adaptive. In the dynamic phase, which is the first phase, the quantum network devices utilize the quantum channels to distribute entangled states among each other. Once this phase completes, the quantum network devices share certain entangled quantum states, which results in the static phase. In this phase, the quantum network devices store these entangled states for future requests locally. Finally, in the adaptive phase, the network devices manipulate and adapt the entangled states of the static phase. This might be caused either due to requests of clients in networks, but also due to failures of devices in a quantum network.We follow the approach of [51] where a certain network state is stored in the static phase, and client requests to establish certain target (graph) states in the network ar...

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Fundamental limitation on quantum broadcast networks

Cited by 40 publications

References 59 publications

Fundamental rate-loss trade-off for the quantum internet

Fundamental rate-loss trade-off for the quantum internet

Versatile relative entropy bounds for quantum networks

A quantum network stack and protocols for reliable entanglement-based networks

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