Entanglement and impropriety

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