Measured quantum probability distribution functions for Brownian motion

TL;DR

This paper introduces a quantum analog of classical joint probability distributions for stochastic processes, providing a method to construct quantum distributions for measurement sequences, exemplified with quantum Brownian motion and Wigner functions.

Contribution

It presents a novel framework for quantum joint probability distributions and extends it to quantum Brownian motion and entangled systems with heat baths.

Findings

Explicit examples of quantum distributions for Brownian motion

A general formula for the Wigner function of an entangled Brownian particle

Extension of the prescription to systems interacting with heat baths

Abstract

The quantum analog of the joint probability distributions describing a classical stochastic process is introduced. A prescription is given for constructing the quantum distribution associated with a sequence of measurements. For the case of quantum Brownian motion this prescription is illustrated with a number of explicit examples. In particular it is shown how the prescription can be extended in the form of a general formula for the Wigner function of a Brownian particle entangled with a heat bath.