Operator extension of strong subadditivity of entropy

TL;DR

This paper proves an operator inequality that generalizes the strong subadditivity of entropy, providing a broader mathematical framework that reduces to the known entropy inequality upon taking a trace.

Contribution

The authors introduce an operator extension of the strong subadditivity of entropy, advancing the theoretical understanding of entropy inequalities in quantum information theory.

Findings

Established an operator inequality extending strong subadditivity

Showed the operator inequality reduces to classical entropy inequality after tracing

Contributed to the mathematical foundation of quantum entropy inequalities

Abstract

We prove an operator inequality that extends strong subadditivity of entropy: after taking a trace, the operator inequality becomes the strong subadditivity of entropy.