A Quantum Stochastic Approach to Poisson Master Equation Unravellings and Ghirardi-Rimini-Weber Theory

Abstract

The theory of quantum stochastic calculus is used to expand the traditional Ghirardi-Rimini-Weber theory to a fully quantum theory, where the noise can be then be interpreted as a new field interacting with quantum systems. A derivation of a stochastic unravellling of the GKSL master equation is first presented from the standpoint of a purely quantum theory, which is then specialized to the case of the GRW master equation. Reverse engineering this procedure gives rise to a new nonlinear quantum stochastic wave equation which preserves a generalized system norm and is an unravelling of the GKSL master equation. Comments on how this particular interpretation can be tested are given.