Non-classicality and entanglement criteria for bipartite optical fields characterized by quadratic detectors II: Criteria based on probabilities

TL;DR

This paper develops and analyzes various non-classicality criteria for bipartite optical fields based on photocount and photon-number distributions, revealing their relations, grouping, and effectiveness in quantifying non-classicality.

Contribution

It introduces new criteria based on probabilities, relates them, and discusses their ability to detect non-classicality, including the impact of modes and noise.

Findings

Criteria effectively identify non-classicality in experimental data.

Number of modes influences non-classicality detection results.

Linear transformation into s-ordered form aids quantification.

Abstract

Numerous non-classicality criteria based on the probabilities of experimental photocount or theoretical photon-number distributions are derived using several approaches. Relations among the derived criteria are revealed and the fundamental criteria are identified. They are grouped into parametric systems that allow the analysis of the non-classicality from different points of view ('local' non-classicality, pairwise character of photon correlations, etc.). Considering their structure, the criteria may be divided into groups that differ in the power to resolve the non-classicality. Quantification of the non-classicality using the Lee non-classicality depth and the non-classicality counting parameter is discussed. The used number of field's modes is identified as an important parameter that may cause unexpected results. An appropriate linear transformation of a photocount (photon-number) distribution into its s-ordered form, needed for the determination of the non-classicality depth, is derived. For comparison, the derived criteria are applied both to an experimental photocount histogram of a twin beam and the reconstructed photon-number distributions with different levels of the noise.