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Conditions for macrorealism for systems described by many-valued variables

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Title: Conditions for macrorealism for systems described by many-valued variables
Authors: Halliwell, JJ
Mawby, C
Item Type: Journal Article
Abstract: Macrorealism (MR) is the view that a system evolving in time possesses definite properties independent of past or future measurements and is traditionally tested for systems described at each time by a single dichotomic variable Q . A number of necessary and sufficient conditions for macrorealism have been derived for a dichotomic variable using sets of Leggett-Garg (LG) inequalities, or the stronger no signaling in time (NSIT) conditions, or a combination thereof. Here we extend this framework by establishing necessary and sufficient conditions for macrorealism for measurements made at two and three times for systems described by variables taking three or more values at each time. Our results include a generalization of Fine's theorem to many-valued variables for measurements at three pairs of times and we derive the corresponding complete set of LG inequalities. We find that LG inequalities and NSIT conditions for many-valued variables do not enjoy the simple hierarchical relationship exhibited by the dichotomic case. This sheds light on some recent experiments on three-level systems which exhibit a LG inequality violation even though certain NSIT conditions are satisfied. Under measurements of dichotomic variables using the Lüders projection rule the three-time LG inequalities cannot be violated beyond the Lüders bound (which coincides numerically with the Tsirelson bound obeyed by correlators in Bell experiments), but this bound can be violated in LG tests using degeneracy-breaking (von Neumann) measurements. We identify precisely which MR conditions are violated under these circumstances.
Issue Date: 8-Jul-2020
Date of Acceptance: 1-Jul-2020
URI: http://hdl.handle.net/10044/1/81473
DOI: 10.1103/PhysRevA.102.012209
ISSN: 1050-2947
Publisher: American Physical Society
Start Page: 012209 – 1
End Page: 012209 – 15
Journal / Book Title: Physical Review A: Atomic, Molecular and Optical Physics
Volume: 102
Issue: 1
Copyright Statement: ©2020 American Physical Society
Keywords: Science & Technology
Physical Sciences
Optics
Physics, Atomic, Molecular & Chemical
Physics
QUANTUM-MECHANICS
LOGICAL REFORMULATION
CONSISTENT HISTORIES
BELLS THEOREM
FAMILY
TESTS
Science & Technology
Physical Sciences
Optics
Physics, Atomic, Molecular & Chemical
Physics
QUANTUM-MECHANICS
LOGICAL REFORMULATION
CONSISTENT HISTORIES
BELLS THEOREM
FAMILY
TESTS
General Physics
01 Mathematical Sciences
02 Physical Sciences
03 Chemical Sciences
Publication Status: Published
Open Access location: https://arxiv.org/abs/2004.05858
Article Number: ARTN 012209
Online Publication Date: 2020-07-08
Appears in Collections:Physics
Theoretical Physics