On unified-entropy characterization of quantum channels

TL;DR

This paper explores the properties of quantum channels using unified entropies, extending concepts like map entropy, deriving inequalities, and analyzing additivity, with implications for understanding quantum information processing.

Contribution

It introduces a unified $(q,s)$-entropy for quantum channels, extends the map entropy concept, and derives new inequalities and bounds for quantum channel analysis.

Findings

Defined the map $(q,s)$-entropy as the unified entropy of the dynamical matrix.

Derived Fannes-type inequalities for these entropies.

Provided bounds on output entropy for tensor product channels with maximally entangled inputs.

Abstract

We consider properties of quantum channels with use of unified entropies. Extremal unravelings of quantum channel with respect to these entropies are examined. The concept of map entropy is extended in terms of the unified entropies. The map $(q,s)$-entropy is naturally defined as the unified $(q,s)$-entropy of rescaled dynamical matrix of given quantum channel. Inequalities of Fannes type are obtained for introduced entropies in terms of both the trace and Frobenius norms of difference between corresponding dynamical matrices. Additivity properties of introduced map entropies are discussed. The known inequality of Lindblad with the entropy exchange is generalized to many of the unified entropies. For tensor product of a pair of quantum channels, we derive two-sided estimating of the output entropy of a maximally entangled input state.