Objectivity of classical quantum stochastic processes

TL;DR

This paper explores conditions under which quantum measurement sequences can be interpreted as classical trajectories, showing that under certain dynamics, quantum systems exhibit classical-like stochastic behavior.

Contribution

It identifies physical conditions that ensure quantum measurement processes can be viewed as classical trajectories and demonstrates the classical noise surrogate's validity in coupled systems.

Findings

Sequential quantum measurements can be interpreted as classical trajectories under specific conditions.

Quantum systems coupled to an observable can be modeled with external noise reproducing measurement trajectories.

The trajectory interpretation extends beyond sequential measurements to other quantum contexts.

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.