A complete criterion for separability detection

TL;DR

This paper introduces a comprehensive, efficiently computable criterion for detecting separability in bosonic quantum systems, advancing the understanding and characterization of entanglement with practical algorithms.

Contribution

It presents a new complete separability criterion based on semidefinite programs, improving detection capabilities and applications in quantum state estimation and entanglement robustness analysis.

Findings

Effective approximation of optimal measurement strategies

Enhanced detection of entanglement in complex states

Compatibility with existing entanglement criteria

Abstract

Using new results on the separability properties of bosonic systems, we provide a new complete criterion for separability. This criterion aims at characterizing the set of separable states from the inside by means of a sequence of efficiently solvable semidefinite programs. We apply this method to derive arbitrarily good approximations to the optimal measure-and-prepare strategy in generic state estimation problems. Finally, we report its performance in combination with the criterion developed by Doherty et al. [1] for the calculation of the entanglement robustness of a relevant family of quantum states whose separability properties were unknown.