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Physical Review A

Capacity of a continuously distributed quantum network

Xiangzhen Zhou, Xutao Yu, Zaichen Zhang

Published Jul 13, 2018• 1 citation
Publisher

Abstract

This paper investigates the capacity of a continuously distributed quantum network. A mathematical model of a multihop quantum communication process is given for capacity analysis. Our model assumes $n$ nodes in a unit square, and both a capacity upper bound for arbitrarily distributed quantum networks and a constructed capacity lower bound for randomly distributed quantum networks are obtained as $n\ensuremath{\rightarrow}\ensuremath{\infty}$. According to our results, the capacity in arbitrarily distributed networks is proportional to $n$ while capacity in randomly distributed networks is independent of $n$. Moreover, our findings exhibit the bounds on quantum network capacity and could open a door to performance analysis for future quantum networking.

DOI
10.1103/physreva.98.012316

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This paper investigates the capacity of a continuously distributed quantum network. A mathematical model of a multihop quantum communication process is given for capacity analysis. Our model assumes nnn nodes in a unit square, and both a capacity upper bound for arbitrarily distributed quantum networks and a constructed capacity lower bound for randomly distributed quantum networks are obtained as n\ensuremath→\ensuremath∞n\ensuremath{\rightarrow}\ensuremath{\infty}n\ensuremath→\ensuremath∞. According to our results, the capacity in arbitrarily distributed networks is proportional to nnn while capacity in randomly distributed networks is independent of nnn. Moreover, our findings exhibit the bounds on quantum network capacity and could open a door to performance analysis for future quantum networking.
Quantum network is the key to enable distributed quantum information processing. As the single-link communication rate decays exponentially with the distance, to enable reliable end-to-end quantum communication, the number of nodes needs to grow with the network scale. For highly connected networks, we identify a threshold transition in the capacity as the density of network nodes increases: below a critical density the rate is almost zero, while above the threshold the rate increases linearly with the density. Surprisingly, above the threshold the typical communication capacity between two nodes is independent of the distance between them, due to multipath routing enabled by the quantum network. In contrast, for less connected networks such as scale-free networks, the end-to-end capacity saturates to constants as the number of nodes increases, and always decays with the distance. Our results are based on capacity evaluations, therefore the minimum density requirement for an appreciable capacity applies to any general protocols of quantum networks.
Quantum communication channels and quantum memories are the fundamental building blocks of large-scale quantum communication networks. Estimating their capacity to transmit and store quantum information is crucial in order to assess the performance of quantum communication systems and to detect useful communication paths among the nodes of future quantum networks. However, the estimation of quantum capacities is a challenging task for continuous-variable systems, such as the radiation field, for which a complete characterization via quantum tomography is practically unfeasible. Here we introduce a method for detecting the quantum capacity of continuous-variable communication channels and memories without performing a full process tomography. Our method works in the general scenario where the devices are used a finite number of times, can exhibit correlations across multiple uses, and can change dynamically under the control of a malicious adversary. The method is experimentally friendly and can be implemented using only finitely squeezed states and homodyne measurements.
Abstract The optimal performance of a communication network is limited not only by the quality of point-to-point channels, but by the efficacy of its constituent technologies. Understanding the limits of quantum networks requires an understanding of both the ultimate capacities of quantum channels and the efficiency of imperfect quantum repeaters. In this work, using a recently developed node-splitting technique which introduces internal losses and noise into repeater devices, we present achievable end-to-end rates for noisy-repeater quantum networks. These are obtained by extending the coherent and reverse coherent information (single channel capacity lower bounds) into end-to-end capacity lower bounds, both in the context of single-path and multi-path routing. These achievable rates are completely general, and apply to networks composed of arbitrary channels arranged in general topologies. Through this general formalism, we show how tight upper-bounds can also be derived by supplementing appropriate single-edge capacity bounds. As a result, we develop tools which provide tight performance bounds for quantum networks constituent of channels whose capacities are not exactly known, and reveal critical network properties which are necessary for high-rate quantum communications. This permits the investigation of pertinent classes of quantum networks with realistic technologies; qubit amplitude damping networks and bosonic thermal-loss networks.
Abstract In quantum mechanics, a fundamental law prevents quantum communications to simultaneously achieve high rates and long distances. This limitation is well known for point-to-point protocols, where two parties are directly connected by a quantum channel, but not yet fully understood in protocols with quantum repeaters. Here we solve this problem bounding the ultimate rates for transmitting quantum information, entanglement and secret keys via quantum repeaters. We derive single-letter upper bounds for the end-to-end capacities achievable by the most general (adaptive) protocols of quantum and private communication, from a single repeater chain to an arbitrarily complex quantum network, where systems may be routed through single or multiple paths. We analytically establish these capacities under fundamental noise models, including bosonic loss which is the most important for optical communications. In this way, our results provide the ultimate benchmarks for testing the optimal performance of repeater-assisted quantum communications.
In quantum mechanics, a fundamental law prevents quantum communications to simultaneously achieve high rates and long distances. This limitation is well known for point-to-point protocols, where two parties are directly connected by a quantum channel, but not yet fully understood in protocols with quantum repeaters. Here we solve this problem bounding the ultimate rates for transmitting quantum information, entanglement and secret keys via quantum repeaters. We derive single-letter upper bounds for the end-to-end capacities achievable by the most general (adaptive) protocols of quantum and private communication, from a single repeater chain to an arbitrarily complex quantum network, where systems may be routed through single or multiple paths. We analytically establish these capacities under fundamental noise models, including bosonic loss which is the most important for optical communications. In this way, our results provide the ultimate benchmarks for testing the optimal performance of repeater-assisted quantum communications.