Macrorealistic inequalities stronger than the standard Leggett-Garg inequalities

TL;DR

This paper introduces new macrorealistic inequalities that are stronger than standard Leggett-Garg inequalities, revealing incompatibilities with quantum theory in scenarios where traditional inequalities fail.

Contribution

The authors formulate three classes of macrorealistic inequalities, including stronger versions that detect macrorealism violations missed by standard Leggett-Garg inequalities.

Findings

New inequalities reveal macrorealism violations in cases where standard inequalities do not.

Extension of inequalities to four-time and two-time measurement scenarios.

Discussion of an alternative macrorealism formulation based on no-signaling in time.

Abstract

In two-party, two-input and two-output measurement scenario only relevant Bell's inequality is the Clauser-Horne-Shimony-Holt (CHSH) form. They also provide the necessary and sufficient conditions for local realism. Any other form, such as, Clauser-Horne and Wigner forms reduce to the CHSH one. Standard Leggett-Garg inequalities are often considered to be the temporal analog of CHSH inequalities. But, they do not provide the necessary and sufficient conditions for macrorealism. There is thus scope of formulating new macrorealist inequalities different and stronger than the standard Leggett-Garg inequalities for testing compatibility between the macrorealism and quantum theory. In this paper, we propose three different classes of macrorealistic inequalities in three-time scenario; (i) The ones equivalent to standard Leggett-Garg inequalities in both macrorealist model and in quantum theory. (ii) A class of inequalities which are equivalent to the standard ones in macrorealist model but inequivalent and stronger in quantum theory (iii) Another class of inequalities which are inquivalent to the all formulations of Leggett-Garg inequalities both in macrorealist model and in quantum theory. This class of macrorealist inequalities reveals the incompatibility between macrorealism and quantum theory for specific cases even when any other formulation of Leggett-Garg inequalities fail to do so. We extend the formulations of the class (ii) inequalities to the four-time and two-time measurement scenario. Further, we provide a brief discussion about the alternate formulation of macrorealism which was derived based on the no-signaling in time conditions.