Certifiable randomness from temporal correlations

TL;DR

This paper derives Leggett-Garg inequalities under new assumptions and demonstrates their use in certifying randomness in a device-independent manner, expanding the foundational understanding of temporal correlations.

Contribution

It introduces a novel derivation of LGI based on predictability and no signaling in time, enabling device-independent randomness certification.

Findings

LGI can certify randomness without macroscopic realism assumptions

New derivation based on predictability and no signaling in time

Supports device-independent randomness generation

Abstract

Leggett-Garg inequalities (LGI) are constrains on certain combinations of temporal correlations obtained by measuring one and the same system at two different instants of time. The usual derivations of LGI assume \emph {macroscopic realism per se } and \emph {noninvasive measurability}. We derive these inequalities under a different set of assumptions, namely the assumptions of \emph{predictability} and \emph{no signaling in time}. As a novel implication of this derivation, we show that LGI can be used to certify randomness in a device independent way.