Quasi-probability distributions for observables in dynamic systems
Department of Applied Physics, University of Geneva, 1211 Geneva 4, Switzerland
| Published: | 2017-10-12, volume 1, page 32 |
| Eprint: | arXiv:1702.00998v4 |
| Doi: | https://doi.org/10.22331/q-2017-10-12-32 |
| Citation: | Quantum 1, 32 (2017). |
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Abstract
We develop a general framework to investigate fluctuations of non-commuting observables. To this end, we consider the Keldysh quasi-probability distribution (KQPD). This distribution provides a measurement-independent description of the observables of interest and their time-evolution. Nevertheless, positive probability distributions for measurement outcomes can be obtained from the KQPD by taking into account the effect of measurement back-action and imprecision. Negativity in the KQPD can be linked to an interference effect and acts as an indicator for non-classical behavior. Notable examples of the KQPD are the Wigner function and the full counting statistics, both of which have been used extensively to describe systems in the absence as well as in the presence of a measurement apparatus. Here we discuss the KQPD and its moments in detail and connect it to various time-dependent problems including weak values, fluctuating work, and Leggett-Garg inequalities. Our results are illustrated using the simple example of two subsequent, non-commuting spin measurements.
Featured image: The Keldysh quasi-probability distribution (left) contains all information needed to predict measurement outcomes (right). Negative values in the quasi-probability distribution reflect non-classical behavior and drastically influence the outcomes of weak measurements which can lead to the occurrence of anomalous weak values.
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