Nonclassical time correlation functions in continuous quantum measurement

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A continuous projective measurement of a quantum system often leads to a suppression of the dynamics, known as the Zeno effect. Alternatively, generalized non projective, 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 (back action) 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 macro realism using the fourth order time correlation functions with respect to the quasi-probability in the two level system.

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ISO 690BEDNORZ, Adam, Wolfgang BELZIG, Abraham NITZAN, 2012. Nonclassical time correlation functions in continuous quantum measurement. In: New Journal of Physics. 2012, 14(1), 013009. ISSN 1367-2630. eISSN 1367-2630. Available under: doi: 10.1088/1367-2630/14/1/013009
BibTex
@article{Bednorz2012Noncl-22489,
  year={2012},
  doi={10.1088/1367-2630/14/1/013009},
  title={Nonclassical time correlation functions in continuous quantum measurement},
  number={1},
  volume={14},
  issn={1367-2630},
  journal={New Journal of Physics},
  author={Bednorz, Adam and Belzig, Wolfgang and Nitzan, Abraham},
  note={Article Number: 013009}
}
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