Necessary and sufficient conditions for macrorealism using two and three-time Leggett-Garg inequalities
Abstract
The Leggett-Garg (LG) inequalities were introduced, as a temporal parallel of the Bell inequalities, to test macroscopic realism -- the view that a macroscopic system evolving in time possesses definite properties which can be determined without disturbing the future or past state. The original LG inequalities are only a necessary condition for macrorealism, and are therefore not a decisive test. We argue, for the case of measurements of a single dichotomic variable Q, that when the original four three-time LG inequalities are augmented with a set of twelve two-time inequalities also of the LG form, Fine's theorem applies and these augmented conditions are then both necessary and sufficient. A comparison is carried out with the alternative necessary and sufficient conditions for macrorealism based on no-signaling in time conditions which ensure that all probabilities for Q at one and two times are independent of whether earlier or intermediate measurements are made. We argue that the two tests differ in their implementation of the key requirement of non-invasive measurability so are testing different notions of macrorealism, and these notions are elucidated.
Keywords
Cite
@article{arxiv.1811.10408,
title = {Necessary and sufficient conditions for macrorealism using two and three-time Leggett-Garg inequalities},
author = {J. J. Halliwell},
journal= {arXiv preprint arXiv:1811.10408},
year = {2020}
}
Comments
12 pages. Latex. To appear in proceedings of the conference, Decoherence, Information, Complexity, Entropy (DICE), Castiglioncello, Italy, September 2018, edited by T.Elze et al. arXiv admin note: substantial text overlap with arXiv:1704.01485