Poisson stochastic master equation unravelings and the measurement problem: A quantum stochastic calculus perspective

Abstract

This 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 L2. 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, Rev. Mod. Phys. 29(3), 454 (1957)]}, encoding all events occurring in the system space. An algorithm introduced by Dalibard et al. [Phys. Rev. Lett. 68(5), 580 (1992)] to numerically solve quantum master equations is interpreted in the context of unraveling, and the trajectories of expected values of system observables are calculated.