The decreasing property of relative entropy and the strong superadditivity of quantum channels

TL;DR

This paper explores the relationship between the decreasing property of quantum relative entropy and the strong superadditivity of quantum channels, providing new proofs and entropy estimates for various channels.

Contribution

It establishes the strong superadditivity for several quantum channels using the decreasing property of quantum relative entropy, extending previous results without input restrictions.

Findings

Proved strong superadditivity for depolarizing, quantum-classical, and erasure channels.

Provided entropy estimates for phase damping and Weyl quantum channels.

Linked the decreasing property of quantum relative entropy to superadditivity in quantum information.

Abstract

We argue that a fundamental (conjectured) property of memoryless quantum channels, namely the strong superadditivity, is intimately related to the decreasing property of the quantum relative entropy. Using the latter we first give, for a wide class of input states, an estimation of the output entropy for phase damping channels and some Weyl quantum channels. Then we prove, without any input restriction, the strong superadditivity for several quantum channels, including depolarizing quantum channels, quantum-classical channels and quantum erasure channels.