Monogamy of correlations and entropy inequalities in the Bloch picture

TL;DR

This paper explores the relationships between correlations and entropy in quantum states using the Bloch representation, introducing a new basis and deriving stronger entropy inequalities for finite-dimensional systems.

Contribution

It introduces the split Bloch basis for better representation of low-dimensional quantum states and derives new, stronger entropy inequalities for Tsallis 2-entropy.

Findings

Dimension-dependent entropy inequalities established

Introduction of the split Bloch basis for quantum state representation

Stronger entropy relations than subadditivity for finite dimensions

Abstract

We investigate monogamy of correlations and entropy inequalities in the Bloch representation. Here, both can be understood as direct relations between different correlation tensor elements and thus appear intimately related. To that end we introduce the split Bloch basis, that is particularly useful for representing quantum states with low dimensional support and thus amenable to purification arguments. Furthermore, we find dimension dependent entropy inequalities for the Tsallis 2-entropy. In particular, we present an analogue of the strong subadditivity and a quadratic entropy inequality. These relations are shown to be stronger than subadditivity for finite dimensional cases.