Convex combinations of bosonic pure-loss channels

TL;DR

This paper explores the quantum information capacities of convex combinations of bosonic pure-loss channels, revealing that non-Gaussian states outperform Gaussian ones and that positive quantum communication rates are achievable despite fading noise.

Contribution

It provides the first comprehensive quantum Shannon theory analysis of fading channels, demonstrating the advantages of non-Gaussian states and developing optimization algorithms.

Findings

Entanglement and quantum key distribution are possible at positive rates over any fading channel.

Non-Gaussian Fock-diagonal states outperform Gaussian states in achieving channel capacities.

Analytical capacity results for binary fading models and iterative algorithms for general fading distributions.

Abstract

The pure-loss channel is a fundamental model for describing noise in bosonic quantum platforms. It is characterised by a single parameter, the transmissivity, which quantifies the fraction of the input energy that reaches the output of the channel. In realistic scenarios, however, such as free-space quantum communication, the transmissivity is not fixed but fluctuates from one channel use to another. In this setting, the overall channel is effectively described as a convex combination of pure-loss channels, known as a fading channel. Despite its practical relevance, the quantum Shannon theory of the fading channel has remained largely unexplored. Here, we address this gap, specifically investigating degradability, anti-degradability, entanglement breakingness, and capacities of the fading channel. Of particular relevance to practical quantum-internet applications, we prove that entanglement distribution and quantum key distribution can always be achieved at a strictly positive rate over any fading channel, no matter how noisy it is or how strongly the transmissivity fluctuates, provided the channel is not completely noisy. Moreover, we prove that thermal states, which are optimal for a broad class of static bosonic Gaussian channels, fail to achieve the entanglement-assisted classical capacity of fading channels: non-Gaussian Fock-diagonal states strictly outperform all Gaussian encodings. Most strikingly, we identify regimes where the coherent information of thermal inputs vanishes, while optimized non-Gaussian states achieve strictly positive values, thereby activating the channel for quantum communication. For a paradigmatic binary fading model we establish this result analytically, deriving the exact capacity-achieving state in closed form. For general fading distributions, we design an iterative variational algorithm to optimize the coherent and mutual information.