Entanglement and entropy in multipartite systems: a useful approach

TL;DR

This paper introduces a new approach using the concurrence vector to analyze entanglement and entropy in multipartite quantum systems, providing computational tools, new relations, and conditions for genuine entanglement, applicable to both pure and mixed states.

Contribution

It presents a novel form of the concurrence vector that simplifies analysis and derives new relations and conditions for entanglement and entropy properties in multipartite systems.

Findings

Provides polynomial-time computable conditions for genuine entanglement.

Proves subadditivity and a modified strong subadditivity of Tsallis-2 entropy.

Simplifies derivation of known relations and introduces new inequalities.

Abstract

Quantum entanglement and quantum entropy are crucial concepts in the study of multipartite quantum systems. In this work we show how the notion of concurrence vector, re-expressed in a particularly useful form, provides new insights and computational tools for the analysis of both. In particular, using this approach for a general multipartite pure state, one can easily prove known relations in an easy way and to build up new relations between the concurrences associated with the different bipartitions. The approach is also useful to derive sufficient conditions for genuine entanglement in generic multipartite systems that are computable in polynomial time. From an entropy-of-entanglement perspective, the approach is powerful to prove properties of the Tsallis-$2$ entropy, such as the subadditivity, and to derive new ones, e.g. a modified version of the strong subadditivity which is always fulfilled; thanks to the purification theorem these results hold for any multipartite state, whether pure or mixed.