Non-Gaussian pure states and positive Wigner functions

TL;DR

This paper evaluates the accuracy of the truncated Wigner method in capturing non-Gaussian, non-classical features of quantum states, specifically in the single mode anharmonic oscillator, and compares it with the positive-P method.

Contribution

It benchmarks the truncated Wigner approach against the positive-P method for non-Gaussian states, demonstrating its reliability and stability in certain regimes.

Findings

Truncated Wigner reliably predicts non-Gaussian statistics.

Positive-P can suffer from divergences.

Truncated Wigner reproduces non-Gaussian correlations and maintains purity.

Abstract

Non-Gaussian correlations in a pure state are inextricably linked with non-classical features, such as a non positive-definite Wigner function. In a commonly used simulation technique in ultracold atoms and quantum optics, known as the truncated Wigner method, the quantum dynamics is mapped to stochastic trajectories in phase space, governed by a positive approximation to the true Wigner distribution. The question thus arises: how accurate is this approach in predicting truly non-classical behaviour? In this article, we benchmark the ability of the truncated Wigner phase-space method to reproduce the non-Gaussian statistics of the single mode anharmonic oscillator. We find that the this method can reliably predict departures from Gaussian statistics over a wide range of particle numbers, whereas the positive-P representation method, which is in principle exact, can suffer from divergent instabilities. The truncated Wigner function, furthermore, is able to reproduce the non-Gaussian correlations while satisfying the condition for purity.