Robustness of negativity of the Wigner function to dissipation

TL;DR

This paper proves that the negativity of the Wigner function in non-Gaussian quantum states persists as long as the quantum efficiency exceeds 50%, but for bright states, this negativity is highly sensitive to losses, complicating detection.

Contribution

It establishes that the 50% efficiency threshold is both necessary and sufficient for Wigner negativity, and analyzes the non-linear dependence in bright non-Gaussian states.

Findings

Negativity persists if quantum efficiency > 50%.

Negativity drops sharply with photon loss in bright states.

Detection of negativity becomes challenging with photon loss.

Abstract

Non-Gaussian quantum states, described by negative valued Wigner functions, are important both for fundamental tests of quantum physics and for emerging quantum information technologies. However, they are vulnerable to dissipation. It is known, that the Wigner functions negativity could exist only if the overall quantum efficiency $\eta$ of the setup is higher than 1/2. Here we prove that this condition is not only necessary but also a sufficient one: the negativity always persists while this condition is fulfilled. At the same time, in the case of bright (multi-photon) non-Gaussian quantum states, the negativity dependence on $\eta$ is highly non-linear. With the loss of several photons, it drops by orders of magnitude, hampering its experimental detection.