Optimizing detection of continuous variable entanglement for limited data

TL;DR

This paper develops optimized entanglement detection criteria for continuous variable systems using the Husimi Q-distribution, especially effective with limited or coarse data, enhancing detection capabilities.

Contribution

It introduces adaptable entanglement criteria based on the Husimi Q-distribution tailored for sparse and finite-sample experimental data in continuous variable systems.

Findings

Optimized criteria improve entanglement detection in coarse-grained measurements.

Enhanced detection sensitivity with finite sample sizes.

Broader class of entangled states can be identified.

Abstract

We explore the advantages of a class of entanglement criteria for continuous variable systems based on the Husimi $Q$-distribution in scenarios with sparse experimental data. The generality of these criteria allows optimizing them for a given entangled state and experimental setting. We consider the scenario of coarse grained measurements, or finite detector resolution, where the values of the Husimi $Q$-distribution are only known on a grid of points in phase space, and show how the entanglement criteria can be adapted to this case. Further, we examine the scenario where experimental measurements amount to drawing independent samples from the Husimi distribution. Here, we customize our entanglement criteria to maximize the statistical significance of the detection for a given finite number of samples. In both scenarios optimization leads to clear improvements enlarging the class of detected states and the signal-to-noise ratio of the detection, respectively.