Representation of entanglement by negative quasi-probabilities

TL;DR

This paper discusses how negative quasi-probabilities can represent entanglement in bipartite quantum states, with an optimization method to clearly distinguish entangled from separable states.

Contribution

It introduces an optimization procedure to derive minimal-negativity quasi-probabilities that unambiguously identify entanglement.

Findings

Optimized quasi-probabilities with minimal negativity prove entanglement.

Positivity of quasi-probabilities indicates separability.

Reconstruction from experimental data is feasible.

Abstract

Any bipartite quantum state has quasi-probability representations in terms of separable states. For entangled states these quasi-probabilities necessarily exhibit negativities. Based on the general structure of composite quantum states, one may reconstruct such quasi-propabilities from experimental data. Because of ambiguity, the quasi-probabilities obtained by the bare reconstruction are insufficient to identify entanglement. An optimization procedure is introduced to derive quasi-probabilities with a minimal amount of negativity. Negativities of optimized quasi-probabilities unambiguously prove entanglement, their positivity proves separability.