Local randomness in Hardy's correlations: Implications from information causality principle

TL;DR

This paper investigates how the principle of information causality constrains local randomness in Hardy's nonlocal correlations, revealing stricter limitations than the no-signaling condition and highlighting quantum-specific restrictions.

Contribution

It provides a qualitative analysis of local randomness in Hardy's correlations under information causality, identifying new restrictions not derived from no-signaling principles.

Findings

Information causality imposes severe restrictions on local randomness.

Quantum mechanics imposes additional restrictions beyond information causality.

Maximally entangled states do not exhibit Hardy's non-local correlations.

Abstract

Study of nonlocal correlations in term of Hardy's argument has been quite popular in quantum mechanics. Recently Hardy's argument of non-locality has been studied in the context of generalized non-signaling theory as well as theory respecting information causality. Information causality condition significantly reduces the success probability for Hardy's argument when compared to the result based on non-signaling condition. Here motivated by the fact that maximally entangled state in quantum mechanics does not exhibit Hardy's non-local correlation, we do a qualitative study of the property of local randomness of measured observable on each side reproducing Hardy's non-locality correlation,in the context of information causality condition. On applying the necessary condition for respecting the principle of information causality, we find that there are severe restrictions on the local randomness of measured observable in contrast to results obtained from no-signaling condition.Still, there are some restrictions imposed by quantum mechanics that are not obtained from information causality condition.