Cryptographic Quantum Bound on Nonlocality

TL;DR

This paper investigates the limitations of information causality in quantum nonlocality, showing that partially entangled states introduce randomness that prevents reaching quantum bounds, and extends nonlocality inequalities to incorporate cryptographic principles.

Contribution

It demonstrates that information causality alone cannot fully define quantum boundaries and extends nonlocality inequalities to account for randomness in partially entangled states.

Findings

Partially entangled states produce randomness limiting information transfer.

Information causality is insufficient to fully characterize quantum nonlocality.

Extended inequalities incorporate cryptographic principles affecting nonlocal correlations.

Abstract

Information causality states that the information obtainable by a receiver cannot be greater than the communication bits from a sender, even if they utilize no-signaling resources. This physical principle successfully explains some boundaries between quantum and post-quantum nonlocal correlations, where the obtainable information reaches the maximum limit. We show that no-signaling resources of pure partially entangled states produce randomness (or noise) in the communication bits, and achievement of the maximum limit is impossible, i.e., the information causality principle is insufficient for the full identification of the quantum boundaries already for bipartite settings. The nonlocality inequalities such as so-called the Tsirelson inequality are extended to show how such randomness affects the strength of nonlocal correlations. As a result, a relation followed by most of quantum correlations in the simplest Bell scenario is revealed. The extended inequalities reflect the cryptographic principle such that a completely scrambled message cannot carry information.