Temporal Leggett-Garg-Bell inequalities for sequential multi-time actions in quantum information processing, and a re-definition of Macroscopic Realism

TL;DR

This paper redefines Macrorealism to align with classical physics principles, introduces new temporal Bell inequalities applicable to complex processes, and demonstrates their potential for exponential quantum violations, with historical experimental relevance.

Contribution

It presents a redefinition of Macrorealism, derives new temporal Bell inequalities for multi-step processes, and shows their theoretical exponential violation and experimental relevance.

Findings

Derived a new family of temporal Bell inequalities.

Demonstrated theoretical exponential violation of these inequalities.

Linked the inequalities to a 2005 experimental test.

Abstract

The usual formulation of Macrorealism is recast to make this notion fully concurrent with the basic ideas behind classical physics. The assumption of non-invasiveness of measurements is dropped. Instead, it is assumed that the current state of the system defines full initial conditions for its subsequent evolution. An example of a new family of temporal Bell inequalities is derived which can be applied to processes in which the state of the system undergoes arbitrarily many transformations (which was not the case in the original approach). An exponential (in terms of number of operations) violation of this inequality is demonstrated theoretically. Finally it is shown that such inequalities were indirectly tested in a 2005 experiment by the Weinfurter group.