Probing Kirkwood-Dirac nonpositivity and its operational implications via moments

TL;DR

This paper introduces a practical method to detect nonclassical features in the Kirkwood-Dirac distribution using moments, with implications for quantum coherence and work extraction, facilitating experimental applications.

Contribution

It presents a new criterion based on moments for identifying nonclassicality in the KD distribution, extending to other quantum resources.

Findings

Effective detection of nonclassical signatures via moments.

Extension of the method to quantum coherence and work.

Efficient criteria suitable for experimental implementation.

Abstract

The Kirkwood-Dirac (KD) distribution has recently emerged as a powerful quasiprobability framework with wide-ranging applications in quantum information processing tasks. In this work, we introduce an experimentally motivated criterion for detecting nonclassical signatures of the KD distribution using its statistical moments and demonstrate its effectiveness through explicit examples. We further show that this approach extends naturally to identifying other quantum resources, such as quantum coherence and nonclassical extractable work -- that are intrinsically connected to the KD distribution. Our criteria involves the evaluation of simple functionals, making it well-suited for efficient experimental implementation.