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arXiv · 1811.10408

Necessary and sufficient conditions for macrorealism using two and three-time Leggett-Garg inequalities

J. J. Halliwell
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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.

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J. J. Halliwell. 2018-11-21. Necessary and sufficient conditions for macrorealism using two and three-time Leggett-Garg inequalities. https://doi.org/10.1088/1742-6596%2F1275%2F1%2F012008

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