Detection of quantum imaginarity using moments and its interferometric realization

TL;DR

This paper introduces a practical method to detect quantum imaginarity using moments of the Kirkwood-Dirac distribution, enabling scalable, low-overhead identification in complex quantum systems with an interferometric measurement scheme.

Contribution

It proposes a novel, experimentally feasible approach to detect quantum imaginarity via moments, reducing the need for full state tomography in high-dimensional systems.

Findings

Method successfully detects quantum imaginarity in simulated examples.

Interferometric scheme enables practical measurement of moments.

Approach scalable to many-body quantum systems.

Abstract

Complex numbers, intrinsic to the formulation of quantum theory, play a pivotal role in enabling advantages across a broad range of quantum information-processing tasks. Despite their fundamental importance, practical and scalable criteria for detecting quantum imaginarity remain relatively underexplored, particularly methods that enable its identification with reduced experimental overhead. In this work, we propose a realistic and experimentally feasible method to detect quantum imaginarity using moment-based approach. Our framework relies on experimentally accessible moments of the Kirkwood-Dirac quasiprobability distribution, enabling scalable detection in many-body and high-dimensional systems without requiring full state tomography. We then present an illustrative example to support our detection scheme. Finally, we present an interferometric scheme for measuring these moments, paving the way for experimental implementation of our detection protocol.