Fine's theorem for Leggett-Garg tests with an arbitrary number of measurement times
File(s)
Accepted version
OA Location
Author(s)
Halliwell, JJ
Mawby, C
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.
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.
Date Issued
2019-10-01
Date Acceptance
2019-10-01
Citation
Physical Review A: Atomic, Molecular and Optical Physics, 2019, 100 (4), pp.042103 – 1-042103 – 12
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
Identifier
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000488502500003&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
Subjects
Science & Technology
Physical Sciences
Optics
Physics, Atomic, Molecular & Chemical
Physics
BELLS THEOREM
QUANTUM
Publication Status
Published
Article Number
ARTN 042103
Date Publish Online
2019-10-01