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Leggett Garg Inequalities: a Quasi-probability Approach to No-Signalling in Time and New Measurement Protocols

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The Leggett-Garg (LG) inequalities were proposed in order to assess whether sets of pairs of sequential measurements on a single quantum system can be consistent with an underlying notion of macroscopic realism (MR) at three, four or more times. I review the LG formalism and note that the LG inequalities alone are a necessary condition for MR, but not a sufficient one, the shortfall lying in the description of the system at two times, the key point at which LG systems differ from the analogous CHSH inequalities for an EPRB pair. I argue that this shortfall can be addressed by describing the two-time measurement situation in terms of a simple, measurable quasi-probability, which provides a measure of macrorealism at two times. It is closely related to the no-signalling in time condition of Kofler and Brukner. This measure, when combined with the LG inequalities, provides a characterization of macrorealism more detailed than that provided by the LG inequalities alone. In particular, when the quasi-probability is non-negative, the LG system has a natural parallel with the EPRB system and Fine’s theorem, and this augmented LG system is then both a necessary and sufficient condition for macrorealism. In all experiments measuring such systems, the measurements have to be carried out non-invasively in order to evade alternative classical explanations. Two simple protocols are proposed to achieve this.

The Leggett-Garg Inequalities and No-Signalling in Time: A Quasi-Probability Approach. J. J. Halliwell Phys. Rev. A 93 , 022123 (2016)

Decoherent Histories and Measurement of Temporal Correlation Functions for Leggett-Garg Inequalities. J.J.Halliwell Phys. Rev. A 94 , 052131 (2016)

Leggett-Garg Correlation Functions from Non-Invasive Velocity Measurement Continuous in Time. J.J. Halliwell Phys. Rev. A 94 , 052114 (2016)

This talk is part of the CQIF Seminar series.

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