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Fine's theorem for Leggett-Garg tests with an arbitrary number of measurement times

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Title: Fine's theorem for Leggett-Garg tests with an arbitrary number of measurement times
Authors: Halliwell, JJ
Mawby, C
Item Type: Journal Article
Abstract: If the time evolution of a quantum system can be understood classically, then there must exist an underlying probability distribution for the variables describing the system at a sequence of times. It is well known that for systems described by a single time-evolving dichotomic variable Q and for which a given set of temporal correlation functions are specified, a necessary set of conditions for the existence of such a probability are provided by the Leggett-Garg (LG) inequalities. Fine's theorem in this context is the nontrivial result that a suitably augmented set of LG inequalities are both necessary and sufficient conditions for the existence of an underlying probability. We present a proof of Fine's theorem for the case of measurements on a dichotomic variable at an arbitrary number of times, thereby generalizing the familiar proofs for three and four times. We demonstrate how the LG framework and Fine's theorem can be extended to the case in which all possible two-time correlation functions are measured (instead of the partial set of two-time correlators normally studied). We examine the limit of a large number of measurements for both of the above cases.
Issue Date: 1-Oct-2019
Date of Acceptance: 1-Oct-2019
URI: http://hdl.handle.net/10044/1/81728
DOI: 10.1103/PhysRevA.100.042103
ISSN: 1050-2947
Publisher: American Physical Society
Start Page: 042103 – 1
End Page: 042103 – 12
Journal / Book Title: Physical Review A: Atomic, Molecular and Optical Physics
Volume: 100
Issue: 4
Copyright Statement: ©2019 American Physical Society
Keywords: Science & Technology
Physical Sciences
Optics
Physics, Atomic, Molecular & Chemical
Physics
BELLS THEOREM
QUANTUM
Science & Technology
Physical Sciences
Optics
Physics, Atomic, Molecular & Chemical
Physics
BELLS THEOREM
QUANTUM
Publication Status: Published
Open Access location: https://arxiv.org/pdf/1906.04865.pdf
Article Number: ARTN 042103
Online Publication Date: 2019-10-01
Appears in Collections:Physics
Theoretical Physics