Efficient Characterization of N-Beam Gaussian Fields Through Photon-Number Measurements: Quantum Universal Invariants

TL;DR

This paper introduces a method to characterize N-beam Gaussian quantum states using intensity moments and photon-number measurements, enabling practical detection of entanglement and quantum correlations.

Contribution

It proposes a novel approach linking quantum invariants to intensity moments, facilitating experimental determination of entanglement in Gaussian states.

Findings

Successfully determined invariants of noisy 3-beam Gaussian states

Reformulated Peres-Horodecki criterion in terms of measurable moments

Demonstrated experimental applicability with photon-number-resolved measurements

Abstract

Quantum universal invariants of general N-beam Gaussian fields are investigated from the point of view of fields' intensity moments. A method that uniquely links these invariants, including the global and marginal fields' purities, to intensity moments is suggested. Determination of these invariants identifies the Gaussian states including their quantum correlations. In particular, the Peres-Horodecki separability criterion is reformulated in terms of quantum universal invariants, and consequently in terms of experimental intensity moments, offering a practical tool for determining the entanglement or separability of these states. The approach is experimentally demonstrated by determining the invariants of noisy symmetric 3-beam Gaussian states using photon-number-resolved measurements. Furthermore, their entanglement properties are analyzed and characterized.