Forward-Backward Squeezing Propagator

TL;DR

This paper introduces a forward-backward propagator for pseudo-diffusion equations of Q-functions, generalizing the Cahill-Glauber operator with squeezing parameters, and provides an algorithm for direct Q-function squeezing.

Contribution

It defines a novel forward-backward propagator for pseudo-diffusion equations and generalizes the Cahill-Glauber operator with squeezing parameters.

Findings

A forward-backward propagator for pseudo-diffusion equations is established.

The generalized operator depends on two squeezing parameters and obeys a generalized diffusion equation.

An algorithm for directly squeezing Q functions using diffusion propagators is provided.

Abstract

I show that a usual propagator cannot be defined for the pseudo-diffusion equation of the Q-functions. Instead, a forward-backward propagator is defined, which motivated a generalization of Cahill-Glauber interpolating operator. Our generalized operator ${\bf Q}(p,q;\sigma_p^{-1},\sigma_q)$ depends on two squeezing parameters $\sigma_p$ and $\sigma_q$, and is shown to obey a generalized pseudo-diffusion equation or a diffusion equation, depending on the curve $(\sigma_p(\mu),\sigma_q(\mu))$ along which one moves in the $(\sigma_p,\sigma_q)$ plane. An algorithm is also given for squeezing Q functions directly, using one-dimensional diffusion propagators.