A Family of Continuous Variable Entanglement Criteria using General Entropy Functions

TL;DR

This paper introduces a family of entanglement criteria for continuous variable quantum systems based on generalized entropy functions, which can outperform traditional second-order moment-based tests and Shannon entropy-based criteria.

Contribution

The authors develop new entanglement witnesses using Rénnyi and Tsallis entropies, extending previous methods and demonstrating improved sensitivity for detecting entanglement.

Findings

Criteria outperform second-order moment-based tests

Criteria outperform Shannon entropy-based tests

Effective in identifying entanglement in experimental states

Abstract

We derive a family of entanglement criteria for continuous variable systems based on the R\'enyi entropy of complementary distributions. We show that these entanglement witnesses can be more sensitive than those based on second-order moments, as well as previous tests involving the Shannon entropy [Phys. Rev. Lett. \textbf{103}, 160505 (2009)]. We extend our results to include the case of discrete sampling, and develop another set of entanglement tests using the discrete Tsallis entropy. We provide several numerical results which show that our criteria can be used to identify entanglement in a number of experimentally relevant quantum states.