Nonclassical time correlation functions in continuous quantum measurement

TL;DR

This paper investigates the properties of nonclassical time correlation functions in continuous quantum measurements, revealing how weak measurements and quasi-probabilities can violate classical macrorealism.

Contribution

It introduces a method to separate system-dependent uncertainty from detector noise and analyzes the properties of quasi-probabilities in continuous quantum measurement.

Findings

Quasi-probability satisfies a weak positivity condition.

Violation of classical macrorealism demonstrated with fourth-order correlations.

Analysis of time correlation functions in weak measurement regimes.

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 carried out. Such a measurement is parameterized by its strength parameter that can interpolate continuously between the ideal strong measurement with no dynamics-the strict Zeno effect, and a 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 quasi-probability, which, despite its weaker properties, is shown to satisfy a weak positivity condition. We discuss the basic properties of this quasi-probability 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 quasi-probability in the twolevel system.