Capacities of lossy bosonic memory channels

TL;DR

This paper introduces a model for lossy bosonic memory channels, calculates their capacities, and demonstrates that coherent state encoding is optimal, revealing that the channel behaves like a product of single-mode channels.

Contribution

It provides a general model for bosonic memory channels and proves the optimality of coherent state encoding, simplifying their analysis.

Findings

Classical and quantum capacities are calculated.

Memory channels are unitarily equivalent to product of single-mode channels.

Coherent state encoding is proven to be optimal.

Abstract

We introduce a general model for a lossy bosonic memory channel and calculate the classical and the quantum capacity, proving that coherent state encoding is optimal. The use of a proper set of collective field variables allows to unravel the memory, showing that the n-fold concatenation of the memory channel is unitarily equivalent to the direct product of n single-mode lossy bosonic channels.