Nonclassical time correlation functions in continuous quantum measurement

Abstract

A continuous projective measurement of a quantum system often leads to a suppression of the dynamics, known as the Zeno effect. Alternatively generalized nonprojective, so called “weak” measurements can be performed. Such a measurement is parametrized by its strength parameter that can interpolate continuously between ideal strong measurement with no dynamics – strict Zeno effect, and weak measurement characterized by almost free dynamics but blurry observations. Here we analyze the stochastic properties of this uncertainty component in the resulting observation trajectory. The observation uncertainty results from intrinsic quantum uncertainty, the effect of measurement on the system (backaction) and detector noise. It is convenient to separate the latter, system independent contribution from the system dependent uncertainty, and this paper shows how to accomplish this separation. The system dependent uncertainty is found in terms of a quasiprobability, which, despite its weaker properties is shown to satisfy a weak positivity condition. We discuss the basic properties of this quasiprobability with special emphasis on its time correlation functions as well as their relationship to the full correlation functions along the observation trajectory, and illustrate our general results with simple examples. We demonstrate a violation of classical macrorealism using the fourth order time correlation functions with respect to the quasiprobability in the two-level system.