Necessary and sufficient conditions for macrorealism using two- and three-time Leggett-Garg inequalities. (September 2019)

• Record Type: Journal Article
• Authors: Halliwell, J J
• Is Part Of: Journal of physics. Volume 1275(2019)
• Publication Date: 2019-09
• Subjects: Physics -- Congresses; 530.5
• DOI: 10.1088/1742-6596/1275/1/012008
• Languages: English
• ISSNs: 1742-6588

Abstract

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.