Poisson stochastic master equation unravellings and the measurement problem: a quantum stochastic calculus perspective

TL;DR

This paper explores quantum stochastic differential equations using Poisson processes, revealing a classical representation of quantum noise, and introduces a quantum object acting as an observer to analyze state reduction and measurement in quantum systems.

Contribution

It provides a novel perspective by representing quantum noise through classical Poisson processes and introduces a quantum norm process as an observer for measurement analysis.

Findings

Discontinuous dynamical state reduction modeled via Poisson processes.

Identification of a quantum norm process acting as an observer.

Numerical solution algorithm for quantum master equations interpreted as unravellings.

Abstract

The paper studies a class of quantum stochastic differential equations, modeling an interaction of a system with its environment in the quantum noise approximation. The space representing quantum noise is the symmetric Fock space over L^2(R_+). Using the isomorphism of this space with the space of square-integrable functionals of the Poisson process, the equations can be represented as classical stochastic differential equations, driven by Poisson processes. This leads to a discontinuous dynamical state reduction which we compare to the Ghirardi-Rimini-Weber model. A purely quantum object, the norm process, is found which plays the role of an observer (in the sense of Everett [H. Everett III, Reviews of modern physics, 29.3, 454, (1957)]), encoding all events occurring in the system space. An algorithm introduced by Dalibard et al [J. Dalibard, Y. Castin, and K. M{\o}lmer, Physical review letters, 68.5, 580 (1992)] to numerically solve quantum master equations is interpreted in the context of unravellings and the trajectories of expected values of system observables are calculated.