Objectivity of classical quantum stochastic processes

Abstract

We investigate what can be concluded about a quantum system when sequential quantum measurements of its observable -- a prominent example of the so-called quantum stochastic process -- fulfill the Kolmogorov consistency condition and thus appear to an observer as a sampling of a classical trajectory. We identify a set of physical conditions imposed on the system dynamics, that when satisfied, lead to the aforementioned trajectory interpretation of the measurement results. We then show that when another quantum system is coupled to the observable, the operator representing it can be replaced by external noise. Crucially, the realizations of this surrogate (classical) stochastic process follow the same trajectories as those measured by the observer. Therefore, it can be said that the trajectory interpretation suggested by the Kolmogorov consistent measurements also applies in contexts other than sequential measurements.

12 pages + 8 pages of appendices. Accepted in Quantum

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• A perturbation theory for multi-time correlation functions in open quantum systems
• Temporal nonclassicality in continuous-time quantum walks
• Emergence of non-Markovian Decoherent Histories in Integrable Environment: A "Tape Recorder" Model for Local Quantum Observables
• Phenomenological quantum mechanics: I. Phenomenology of quantum observables