"Enough" Wigner negativity implies genuine multipartite entanglement

TL;DR

This paper establishes fundamental links between Wigner negativity and genuine multipartite entanglement in continuous-variable quantum systems, providing practical criteria for certifying GME using phase-space measurements.

Contribution

It proves that sufficient Wigner negativity certifies GME and offers practical measurement-based criteria for GME detection in various quantum platforms.

Findings

Large Wigner negativity volume certifies GME.

Violations of nonclassicality depth bounds indicate GME.

Criteria are implementable with phase-space measurements in experimental systems.

Abstract

Wigner negativity and genuine multipartite entanglement (GME) are key nonclassical resources that enable computational advantages and broader quantum-information tasks. In this work, we prove two theorems for multimode continuous-variable systems that relate these nonclassical resources. Both theorems show that "enough" Wigner negativity -- either a large-enough Wigner negativity volume along a suitably-chosen two-dimensional slice, or a large-enough nonclassicality depth of the centre-of-mass of a system -- certifies the presence of GME. Moreover, violations of the latter inequality provide lower bounds of the trace distance to the set of non-GME states. Our results also provide sufficient conditions for generating GME by interfering a state with the vacuum through a multiport interferometer, complementing long-known necessary conditions. Beyond these fundamental connections, our methods have practical advantages for systems with native phase-space measurements: they require only measuring the Wigner function over a finite region, or measuring a finite number of characteristic function points. Such measurements are frequently performed with readouts common in circuit/cavity quantum electrodynamic systems, trapped ions and atoms, and circuit quantum acoustodynamic systems. As such, our GME criteria are readily implementable in these platforms.