Local extrema of entropy functions under tensor products

TL;DR

This paper investigates the behavior of entropy functions in quantum channels, demonstrating local additivity of von-Neumann entropy under specific conditions and stability of 2-norm entropy minima in low-dimensional subspaces.

Contribution

It introduces conditions for local additivity of von-Neumann entropy and shows stability of 2-norm entropy minima in tensor products with low-dimensional subspaces.

Findings

Von-Neumann entropy minimum is locally additive under local commutativity.

Local minima of 2-norm entropy are closed under tensor products when one subspace has dimension 2.

Provides conditions for entropy function behavior in quantum channels.

Abstract

We show that under a certain condition of local commutativity the minimum von-Neumann entropy output of a quantum channel is locally additive. We also show that local minima of the 2-norm entropy functions are closed under tensor products if one of the subspaces has dimension 2.