Entropy Uncertainty Relations and Strong Sub-additivity of Quantum Channels

TL;DR

This paper establishes an entropic uncertainty relation for quantum channels, extending previous measurement-based results, and introduces generalized strong sub-additivity inequalities that improve understanding of quantum entropy and data processing.

Contribution

It presents a novel entropic uncertainty relation for quantum channels and generalizes strong sub-additivity of quantum entropy, including an improved data processing inequality.

Findings

Proved an entropic uncertainty relation for two quantum channels.

Derived a generalized strong super-additivity of quantum entropy.

Established an improved data processing inequality.

Abstract

We prove an entropic uncertainty relation for two quantum channels, extending the work of Frank and Lieb for quantum measurements. This is obtained via a generalized strong super-additivity (SSA) of quantum entropy. Motivated by Petz's algebraic SSA inequality, we also obtain a generalized SSA for quantum relative entropy. As a special case, it gives an improved data processing inequality.