End-to-End Capacities of Imperfect-Repeater Quantum Networks

TL;DR

This paper develops a general framework to determine the ultimate and achievable capacities of noisy quantum networks with imperfect repeaters, providing bounds and insights for realistic quantum communication technologies.

Contribution

It introduces a node-splitting technique to incorporate losses and noise, extending capacity bounds to complex quantum networks with arbitrary topologies.

Findings

Achievable end-to-end rates for noisy-repeater quantum networks are derived.

Tight upper bounds on network capacities are established using capacity bounds of individual channels.

The framework applies to various network topologies and realistic quantum technologies.

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.