On Quantum Steering and Wigner Negativity

TL;DR

This paper explores the relationship between quantum steering and Wigner negativity in continuous-variable systems, demonstrating that steering can enable remote creation of Wigner negativity, but is not always necessary for it.

Contribution

It generalizes previous results from Gaussian states to non-Gaussian states, showing steering's sufficiency but not necessity for Wigner negativity generation.

Findings

Steering enables remote Wigner negativity creation in non-Gaussian states.

Quantum correlations are not always necessary for Wigner negativity.

Steering is sufficient but not necessary for conditional Wigner negativity.

Abstract

Quantum correlations and Wigner negativity are two important signatures of nonclassicality in continuous-variable quantum systems. In this work, we investigate how both are intertwined in the context of the conditional generation of Wigner negativity. It was previously shown that when Alice and Bob share a Gaussian state, Bob can perform some measurement on his system to create Wigner negativity on Alice's side if and only if there is Gaussian steering from Alice to Bob. In this work, we attempt to generalise these findings to a much broader class of scenarios on which Alice and Bob share a non-Gaussian state. We show that if Alice can initially steer Bob's system with Wigner-positive measurements, Bob can remotely create Wigner negativity in Alice's subsystem. Even though this shows that quantum steering is sufficient, we also show that quantum correlations are in general not necessary for the conditional generation of Wigner negativity.