Entropic characterization of quantum operations

TL;DR

This paper explores the entropic properties of quantum channels, proving additivity of map entropy for all q and characterizing channels with minimal output entropy, advancing understanding of quantum decoherence.

Contribution

It introduces the concept of map entropy for quantum channels, proves its additivity for all q, and characterizes channels with minimal output entropy, including the depolarizing channel.

Findings

Proved additivity of map entropy for all q values.

Identified depolarizing channel as having minimal map entropy for given conditions.

Conjectured existence of channels close to unitaries where additivity holds.

Abstract

We investigate decoherence induced by a quantum channel in terms of minimal output entropy and of map entropy. The latter is the von Neumann entropy of the Jamiolkowski state of the channel. Both quantities admit q-Renyi versions. We prove additivity of the map entropy for all q. For the case q = 2, we show that the depolarizing channel has the smallest map entropy among all channels with a given minimal output Renyi entropy of order two. This allows us to characterize pairs of channels such that the output entropy of their tensor product acting on a maximally entangled input state is larger than the sum of the minimal output entropies of the individual channels. We conjecture that for any channel {\Phi}1 acting on a finite dimensional system there exists a class of channels {\Phi}2 sufficiently close to a unitary map such that additivity of minimal output entropy for {\Psi}1 x {\Psi}2 holds.