Negativity volume of the generalized Wigner function as an entanglement witness for hybrid bipartite states

TL;DR

This paper shows that the negativity volume of a generalized Wigner function can serve as an effective entanglement witness for hybrid bipartite states, simplifying experimental detection compared to full state tomography.

Contribution

It introduces the negativity volume of the generalized Wigner function as a new entanglement witness for hybrid states, with practical advantages for experimental detection.

Findings

Negativity volume exceeds a critical value for entangled states.

Demonstrated approach on hybrid qubit-bosonic states.

Provided example with a qubit-Schrodinger cat state.

Abstract

In a recent paper, Tilma, Everitt {\it et al.} derived a generalized Wigner function that can characterize both the discrete and continuous variable states, i.e., hybrid states. As such, one can expect that the negativity of the generalized Wigner function applied to the hybrid states can reveal their nonclassicality, in analogy with the well-known Wigner function defined for the continuous variable states. In this work, we demonstrate that, indeed, the negativity volume of the generalized Wigner function of the hybrid bipartite states can be used as an entanglement witness for such states, provided that it exceeds a certain critical value. In particular, we study hybrid bipartite qubit-bosonic states and provide a qubit-Schr\"{o}dinger cat state as an example. Since the detection of the generalized Wigner function of hybrid bipartite states in phase space can be experimentally simpler than the tomographic reconstruction of the corresponding density matrix, our results, therefore, present a convenient tool in the entanglement identification of such states.