Gaussian classical-quantum channels: gain of entanglement-assistance

TL;DR

This paper introduces Bosonic Gaussian classical-quantum channels, analyzes their entanglement-assisted capacity, and demonstrates conditions where this capacity equals or exceeds the unassisted capacity.

Contribution

It establishes the conditions under which the entanglement-assisted capacity equals the unassisted capacity for Gaussian c-q channels and provides explicit examples where they differ.

Findings

C_{ea} equals C under certain energy constraints

Explicit examples show C < C_{ea} is possible

Entropy increase property for weak complementary channels

Abstract

In the present paper we introduce and study Bosonic Gaussian classical-quantum (c-q) channels; the embedding of the classical input into quantum is always possible and therefore the classical entanglement-assisted capacity C_{ea} under appropriate input constraint is well defined. We prove a general property of entropy increase for weak complementary channel, that implies the equality C_{ea}=C (where C is the unassisted capacity) for certain class of c-q Gaussian channel under appropriate energy-type constraint. On the other hand, we show by explicit example that the inequality C<C_{ea} is not unusual for constrained c-q Gaussian channel.