Leggett-Garg inequalities and no-signaling in time: A quasiprobability approach
File(s)1508.02271.pdf (211.41 KB)
Accepted version
Author(s)
Halliwell, JJ
Type
Journal Article
Abstract
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 macrorealism. Here, the LG inequalities are explored using a simple quasiprobability linear in the projection operators to describe the properties of the system at two times. We show that this quasiprobability is measurable, has the same correlation function as the usual two-time measurement probability (for the bivalent variables considered here) and has the key property that the probabilities for the later time are independent of whether an earlier measurement was made, a generalization of the no-signaling in time condition of Kofler and Brukner. We argue that this quasiprobability, appropriately measured, provides a noninvasive measure of macrorealism per se at the two-time level. This measure, when combined with the LG inequalities, provides a characterization of macrorealism more detailed than that provided by the LG inequalities alone. When the quasiprobability is non-negative, the LG system has a natural parallel with the Einstein-Podolsky-Rosen-Bohm system and Fine's theorem. A simple spin model illustrating key features of the approach is exhibited.
Date Issued
2016-02-26
Date Acceptance
2015-12-16
Citation
Physical Review A, 2016, 93 (2)
ISSN
1050-2947
Publisher
American Physical Society
Journal / Book Title
Physical Review A
Volume
93
Issue
2
Copyright Statement
©2016 American Physical Society. Leggett-Garg inequalities and no-signaling in time: A quasiprobability approach. J. J. Halliwell
Phys. Rev. A 93, 022123 – Published 26 February 2016
Phys. Rev. A 93, 022123 – Published 26 February 2016
Sponsor
Engineering & Physical Science Research Council (EPSRC)
Grant Number
EP/J008060/1
Subjects
Science & Technology
Physical Sciences
Optics
Physics, Atomic, Molecular & Chemical
Physics
QUANTUM-MECHANICS
LOGICAL REFORMULATION
CONSISTENT HISTORIES
HIDDEN-VARIABLES
MAGNETIC-FLUX
HILBERT-SPACE
THEOREM
SYSTEMS
REALISM
MACROREALISM
Publication Status
Published
Article Number
022123