Non-Markovian Stochastic Schrodinger equations: generalization to real-valued noise using quantum measurement theory

Preprint
Publisher Website
Google Scholar
  • 20 February 2002
Abstract
Do stochastic Schrodinger equations, also known as unravelings, have a physical interpretation? In the Markovian limit, where the system {\em on average} obeys a master equation, the answer is yes. Markovian stochastic Schrodinger equations generate quantum trajectories for the system state conditioned on continuously monitoring the bath. For a given master equation, there are many different unravelings, corresponding to different sorts of measurement on the bath. In this paper we address the non-Markovian case, and in particular the sort of stochastic Schrodinger equation introduced by Strunz, Di\' osi, and Gisin [Phys. Rev. Lett. {\bf 82}, 1801 (1999)]. Using a quantum measurement theory approach, we rederive their unraveling which involves complex-valued Gaussian noise. We also derive an unraveling involving real-valued Gaussian noise. We show that in the Markovian limit, these two unravelings correspond to heterodyne and homodyne detection respectively. Although we use quantum measurement theory to define these unravelings, we conclude that the stochastic evolution of the system state is not a true quantum trajectory, as the identity of the state through time is a fiction.

This publication has 0 references indexed in Scilit: