Non-Markovian continuous quantum measurement of retarded observables

Abstract

We reconsider the non-Markovian time-continuous measurement of a Heisenberg observable x and show for the first time that it can be realized by an infinite set of entangled von Neumann detectors. The concept of continuous read-out is introduced and used to re-derive the non-Markovian stochastic Schrodinger equation. We can prove that, contrary to recent doubts, the resulting non-Markovian quantum trajectories are true single system trajectories and correspond to the continuous measurement of a retarded functional of x. However, the generic non-Markovian trajectories are mixed state trajectories. This version merges an Erratum [PRL, in print] with my Letter [PRL 100, 080401 (2008)], some corrections follow directly from the recent criticism by Wiseman and Gambetta, further corrections restore the validity of my Letter. Contrary to my suggestion there, the given continuous measurement schemes cannot yield pure state trajectories but mixed-state ones. Yet, it is possible to retain my claim that the non-Markovian stochastic Schrodinger equation describes true time-continuous measurement - with delay and retrodiction.