Efficient detection of nonclassicality using moments of the Wigner function

TL;DR

This paper introduces a practical method to detect nonclassical quantum states with negative Wigner functions by evaluating moments directly, avoiding full state tomography, and proposes an experimental implementation using the mode SWAP operator.

Contribution

It presents a novel criterion for detecting negative Wigner functions through moments, enabling efficient experimental detection of nonclassicality without full state reconstruction.

Findings

The method can be implemented in real experiments.

Explicit examples demonstrate the detection scheme.

An experimental approach using the mode SWAP operator is proposed.

Abstract

States with a negative Wigner function, a significant subclass of nonclassical states, serve as a valuable resource for various quantum information processing tasks. Here, we provide a criterion for detecting such quantum states characterized by a negative Wigner function. Our method relies on evaluating moments of the Wigner function, which involves computing simple functionals and can be implemented in a real experiment without the need for full state tomography or Wigner function reconstruction. We provide explicit examples to support our detection scheme. Further, we propose an experimental method utilizing the mode SWAP operator to realize these moments in a real experiment.