End-to-end capacities of a quantum communication network

Stefano Pirandola

doi:10.1038/s42005-019-0147-3

Stefano Pirandola

Open Access

https://doi.org/10.1038/s42005-019-0147-3

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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.

Highlights

In quantum mechanics, a fundamental law prevents quantum communications to simultaneously achieve high rates and long distances
Under the assistance of twoway CCs, the optimal transmission of quantum information is related to the optimal distribution of entanglement followed by teleportation, so that it does not depend on the physical direction of the quantum channel but rather on the direction of the teleportation protocol
This work establishes the ultimate boundaries of quantum and private communications assisted by repeaters, from the case of a single repeater chain to an arbitrary quantum network under single- or multi-path routing

Summary

Introduction

A fundamental law prevents quantum communications to simultaneously achieve high rates and long distances. 15 showed that the maximum rate at which two remote parties can distribute quantum bits (qubits), entanglement bits (ebits), or secret bits over a lossy channel (e.g., an optical fiber) is equal to −log2(1 − η), where η is the channel’s transmissivity This limit is the Pirandola–Laurenza–Ottaviani–Banchi (PLOB) bound[15] and cannot be surpassed even by the most powerful strategies that exploit arbitrary local operations (LOs) assisted by two-way classical communication (CC), known as adaptive LOCCs16. In all the ideal repeater-assisted scenarios, where we can beat the PLOB bound, it is fundamental to determine the maximum rates that are achievable by two end-users, i.e., to determine their end-to-end capacities for transmitting qubits, distributing ebits, and generating secret keys Finding these capacities is important to establish the boundaries of quantum network communications and to benchmark practical implementations, so as to check how far prototypes of quantum repeaters are from the ultimate theoretical performance

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