Generalized non-additive entropies and quantum entanglement

TL;DR

This paper explores how generalized non-additive entropies can be used to infer quantum states from incomplete data, improving entanglement detection and avoiding false positives in bipartite spin systems.

Contribution

It introduces a formalism based on non-additive entropies for quantum state inference, addressing issues like fake entanglement and extending thermodynamic relations.

Findings

Avoids fake entanglement in Bell-CHSH data

Demonstrates effectiveness of Tsallis and exponential entropies

Provides extended thermodynamic relations for quantum systems

Abstract

We examine the inference of quantum density operators from incomplete information by means of the maximization of general non-additive entropic forms. Extended thermodynamic relations are given. When applied to a bipartite spin 1/2 system, the formalism allows to avoid fake entanglement for data based on the Bell-CHSH observable, and, in general, on any set of Bell constraints. Particular results obtained with the Tsallis entropy and with an introduced exponential entropic form are also discussed.