Entangled Husimi distribution and Complex Wavelet transformation

TL;DR

This paper extends the connection between wavelet transforms and Husimi distribution to entangled quantum states, showing that complex wavelet transforms can effectively analyze entangled phase space distributions.

Contribution

It introduces a novel method linking complex wavelet transformation with entangled Husimi distribution functions in quantum optics.

Findings

Entangled Husimi distribution is the squared modulus of a complex wavelet transform.

The method provides a new tool for analyzing entangled quantum states.

The approach simplifies the study of phase space distributions in quantum optics.

Abstract

Based on the proceding Letter [Int. J. Theor. Phys. 48, 1539 (2009)], we expand the relation between wavelet transformation and Husimi distribution function to the entangled case. We find that the optical complex wavelet transformation can be used to study the entangled Husimi distribution function in phase space theory of quantum optics. We prove that the entangled Husimi distribution function of a two-mode quantum state |phi> is just the modulus square of the complex wavelet transform of exp{-(|eta|^2)/2} with phi(eta)being the mother wavelet up to a Gaussian function.