TY - JOUR

T1 - Nonclassical time correlation functions in continuous quantum measurement

AU - Bednorz, Adam

AU - Belzig, Wolfgang

AU - Nitzan, Abraham

PY - 2012/1

Y1 - 2012/1

N2 - 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 systemdependent 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 fourthorder time correlation functions with respect to the quasi-probability in the twolevel system.

AB - 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 systemdependent 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 fourthorder time correlation functions with respect to the quasi-probability in the twolevel system.

UR - http://www.scopus.com/inward/record.url?scp=84856433245&partnerID=8YFLogxK

U2 - 10.1088/1367-2630/14/1/013009

DO - 10.1088/1367-2630/14/1/013009

M3 - מאמר

AN - SCOPUS:84856433245

VL - 14

JO - New Journal of Physics

JF - New Journal of Physics

SN - 1367-2630

M1 - 013009

ER -