Capacity of a bosonic memory channel with Gauss-Markov noise

TL;DR

This paper analyzes the classical capacity of a quantum bosonic memory channel with correlated Gauss-Markov noise, deriving optimal modulation strategies and input states to compute capacity in the many-mode limit.

Contribution

It introduces a quantum water-filling solution and analytically derives optimal input states for bosonic memory channels with Gauss-Markov noise.

Findings

Optimal modulation follows a quantum water-filling solution.

Analytical expression for the optimal multimode input state.

Capacity computed in the limit of infinite modes.

Abstract

We address the classical capacity of a quantum bosonic memory channel with additive noise, subject to an input energy constraint. The memory is modeled by correlated noise emerging from a Gauss-Markov process. Under reasonable assumptions, we show that the optimal modulation results from a "quantum water-filling" solution above a certain input energy threshold, similar to the optimal modulation for parallel classical Gaussian channels. We also derive analytically the optimal multimode input state above this threshold, which enables us to compute the capacity of this memory channel in the limit of an infinite number of modes. The method can also be applied to a more general noise environment which is constructed by a stationary Gauss process. The extension of our results to the case of broadband bosonic channels with colored Gaussian noise should also be straightforward.