Estimating the output entropy of a tensor product of two quantum channels

TL;DR

This paper establishes lower bounds on the output entropy of tensor products of quantum channels, specifically focusing on dephasing channels, and characterizes phase-damping channels as special cases.

Contribution

It introduces a nontrivial lower bound on entropy gain for bipartite quantum states under tensor product channels and characterizes phase-damping channels within dephasing channels.

Findings

Lower bounds on entropy gain for bipartite states

Estimated output entropy for tensor products involving dephasing channels

Characterization of phase-damping channels as special cases

Abstract

In this paper we find, for a class of bipartite quantum states, a nontrivial lower bound on the entropy gain resulting from the action of a tensor product of identity channel with an arbitrary channel. By means of that we then estimate (from below) the output entropy of the tensor product of dephasing channel with an arbitrary channel. Finally, we provide a characterization of all phase-damping channels resulting as particular cases of dephasing channels.