Imperial College London
Alternate

Professor Halliwell

Faculty of Natural Sciences, Department of Physics

Professor in Theoretical Physics
 
 
 
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Contact

 

+44 (0)20 7594 7831j.halliwell

 
 
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Assistant

 

Mrs Graziela De Nadai-Sowrey +44 (0)20 7594 7843

 
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Location

 

521Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Halliwell:2019:10.1103/PhysRevA.100.042103,
author = {Halliwell, JJ and Mawby, C},
doi = {10.1103/PhysRevA.100.042103},
journal = {Physical Review A: Atomic, Molecular and Optical Physics},
pages = {042103  1--042103  12},
title = {Fine's theorem for Leggett-Garg tests with an arbitrary number of measurement times},
url = {http://dx.doi.org/10.1103/PhysRevA.100.042103},
volume = {100},
year = {2019}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - 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.
AU  - Halliwell,JJ
AU  - Mawby,C
DO  - 10.1103/PhysRevA.100.042103
EP  - 1
PY  - 2019///
SN  - 1050-2947
SP  - 042103
TI  - Fine's theorem for Leggett-Garg tests with an arbitrary number of measurement times
T2  - Physical Review A: Atomic, Molecular and Optical Physics
UR  - http://dx.doi.org/10.1103/PhysRevA.100.042103
UR  - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000488502500003&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
UR  - https://journals.aps.org/pra/abstract/10.1103/PhysRevA.100.042103
UR  - http://hdl.handle.net/10044/1/81728
VL  - 100
ER  -
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