# General mapping of multi-qu$d$it entanglement conditions to non-separability indicators for quantum optical fields

## TL;DR

This paper establishes a universal method to translate multi-qudit entanglement witnesses into non-separability indicators for quantum optical fields, enabling new criteria for detecting polarization entanglement and non-classicality in macroscopic systems.

## Contribution

It introduces a general mapping from entanglement witnesses to non-separability indicators for optical fields, including necessary and sufficient conditions and advantages of using intensity rates.

## Key findings

- Derived conditions for polarization entanglement detection.
- Mapped Bell inequalities to optical field scenarios.
- Proposed experimental setups with integrated optics.

## Abstract

We show that any multi-qudit entanglement witness leads to a non-separability indicator for quantum optical fields, which involves intensity correlations. We get, e.g., necessary and sufficient conditions for intensity or intensity-rate correlations to reveal polarization entanglement. We also derive separability conditions for experiments involving multiport interferometers, now feasible with integrated optics. We show advantages of using intensity rates rather than intensities, e.g., a mapping of Bell inequalities to ones for optical fields. The results have implication for studies of non-classicality of "macroscopic" systems of undefined or uncontrollable number of "particles".