Revealing entanglement through local features of phase-space distributions

TL;DR

This paper introduces a hierarchy of criteria based on phase-space distributions to detect entanglement, especially non-Gaussian types, using simple measurement schemes that outperform existing methods.

Contribution

It develops a new hierarchy of separability criteria in phase space, connecting to the Peres--Horodecki criterion, and proposes a practical measurement scheme for entanglement detection.

Findings

The lowest-order criterion effectively detects non-Gaussian entanglement.

The proposed measurement scheme uses passive linear transformations and coherent ancillas.

Our method surpasses existing techniques by probing specific phase-space regions.

Abstract

We formulate an infinite hierarchy of continuous-variable separability criteria in terms of quasiprobability distributions and their derivatives evaluated at individual points in phase space. Our approach is equivalent to the Peres--Horodecki criterion and sheds light on how distillable entanglement manifests in the phase-space picture. We demonstrate that already the lowest-order variant constitutes a powerful method for detecting the elusive non-Gaussian entanglement of relevant state families. Further, we devise a simple measurement scheme that relies solely on passive linear transformations and coherent ancillas. By strategically probing specific phase-space regions, our method offers clear advantages over existing techniques that rely on access to the full phase-space distributions.