New lower bounds to the output entropy of multi-mode quantum Gaussian channels

TL;DR

This paper establishes that thermal Gaussian states minimize output entropy in multi-mode quantum Gaussian channels, leading to new bounds on communication rates for quantum information tasks.

Contribution

It proves the minimal output entropy property for multi-mode Gaussian channels without input restrictions, a first in the field.

Findings

Thermal Gaussian states minimize output entropy for certain multi-mode channels.

Derived new lower bounds on output entropy based on input entropy.

Applied bounds to improve limits on quantum communication rates.

Abstract

We prove that quantum thermal Gaussian input states minimize the output entropy of the multi-mode quantum Gaussian attenuators and amplifiers that are entanglement breaking and of the multi-mode quantum Gaussian phase contravariant channels among all the input states with a given entropy. This is the first time that this property is proven for a multi-mode channel without restrictions on the input states. A striking consequence of this result is a new lower bound on the output entropy of all the multi-mode quantum Gaussian attenuators and amplifiers in terms of the input entropy. We apply this bound to determine new upper bounds to the communication rates in two different scenarios. The first is classical communication to two receivers with the quantum degraded Gaussian broadcast channel. The second is the simultaneous classical communication, quantum communication and entanglement generation or the simultaneous public classical communication, private classical communication and quantum key distribution with the Gaussian quantum-limited attenuator.