Equivalence Relations for the Classical Capacity of Single-Mode Gaussian Quantum channels

TL;DR

This paper establishes a method to compute the classical capacity of any single-mode Gaussian quantum channel by reducing it to a fiducial channel, which simplifies analysis and implementation.

Contribution

It introduces a new equivalence between arbitrary single-mode Gaussian channels and a specific fiducial channel, enabling easier capacity calculation.

Findings

Classical capacity can be computed from the fiducial channel.

Analytical expression for Gaussian classical capacity is provided.

Classical capacity cannot exceed the derived bound by more than 1/ln2 bits.

Abstract

We prove the equivalence of an arbitrary single-mode Gaussian quantum channel and a newly defined fiducial channel preceded by a phase shift and followed by a Gaussian unitary operation. This equivalence implies that the energy-constrained classical capacity of any single-mode Gaussian channel can be calculated based on this fiducial channel, which is furthermore simply realizable with a beam splitter, two identical single-mode squeezers, and a two-mode squeezer. In a large domain of parameters, we also provide an analytical expression for the Gaussian classical capacity, exploiting its additivity, and prove that the classical capacity cannot exceed it by more than 1/ln2 bits.