Efficient simulation scheme for a class of quantum optics experiments with non-negative Wigner representation

TL;DR

This paper introduces an efficient simulation method for certain quantum optics experiments, demonstrating that many non-Gaussian states are not resources for exponential quantum speed-up and clarifying negativity as a non-classicality indicator.

Contribution

It extends the Gottesman-Knill theorem to non-Gaussian mixed states, providing a new perspective on non-classicality and resource states in quantum computation.

Findings

Efficient simulation scheme for a broad class of quantum optics experiments.

Many non-Gaussian states with positive Wigner functions are not useful for quantum speed-up.

Negativity is interpreted as a measure of non-classicality.

Abstract

We provide a scheme for efficient simulation of a broad class of quantum optics experiments. Our efficient simulation extends the continuous variable Gottesman-Knill theorem to a large class of non-Gaussian mixed states, thereby identifying that these non-Gaussian states are not an enabling resource for exponential quantum speed-up. Our results also provide an operationally motivated interpretation of negativity as non-classicality. We apply our scheme to the case of noisy single-photon-added-thermal-states to show that this class admits states with positive Wigner function but negative P -function that are not useful resource states for quantum computation.