Entanglement and Impropriety

TL;DR

This paper explores how improper Gaussian variables in multi-modal squeezed states can mimic entangled photon pairs, revealing a classical analogy to quantum entanglement through threshold detection models.

Contribution

It introduces a model showing that improper Gaussian variables can replicate entanglement-like correlations in classical light states, bridging quantum and classical optics.

Findings

Improper Gaussian variables can mimic entanglement in classical light.

Coincidence detection can produce entanglement-like correlations from classical states.

The model demonstrates classical analogs to quantum entanglement phenomena.

Abstract

The relationship between quantum entanglement and classical impropriety is considered in the context of multi-modal squeezed states of light. Replacing operators with complex Gaussian random variables in the Bogoliubov transformations for squeezed states, we find that the resulting transformed variables are not only correlated but also improper. A simple threshold exceedance model of photon detection is considered and used to demonstrate how the behavior of improper Gaussian random variables can mimic that of entangled photon pairs when coincidence post-selection is performed.