Optical fibres with memory effects and their quantum communication capacities

TL;DR

This paper introduces a model of optical fibres with memory effects, demonstrating that quantum communication is possible over longer distances and higher noise levels than previously thought, by analyzing capacities under memory influence.

Contribution

It provides an exact solution for the quantum capacities of optical fibres with memory effects, challenging the memoryless assumption limitations in quantum communication.

Findings

Quantum capacities are enhanced by memory effects due to cross-talk.

Reliable quantum communication is achievable in noisy regimes with memory effects.

Identifies critical time intervals for effective quantum communication.

Abstract

The development of quantum repeaters poses significant challenges in terms of cost and maintenance, prompting the exploration of alternative approaches for achieving long-distance quantum communication. In the absence of quantum repeaters and under the memoryless (iid) approximation, it has been established that some fundamental quantum communication tasks are impossible if the transmissivity of an optical fibre falls below a known critical value, resulting in a severe constraint on the achievable distance for quantum communication. However, if the memoryless assumption does not hold -- e.g. when input signals are separated by a sufficiently short time interval -- the validity of this limitation is put into question. In this paper we introduce a model of optical fibre that can describe memory effects for long transmission lines. We then solve its quantum capacity, two-way quantum capacity, and secret-key capacity exactly. By doing so, we show that -- due to the memory cross-talk between the transmitted signals -- reliable quantum communication is attainable even for highly noisy regimes where it was previously considered impossible. As part of our solution, we find the critical time interval between subsequent signals below which quantum communication, two-way entanglement distribution, and quantum key distribution become achievable.