Measurement-Incompatibility Constraints for Maximal Randomness

TL;DR

This paper introduces a new framework for certifying maximal quantum randomness directly from observed data without relying on Bell inequalities, revealing a trade-off in measurement incompatibility among users that impacts device-independent protocols.

Contribution

It presents a generalized method to certify maximal randomness from observed distributions, independent of system dimension, and uncovers a novel incompatibility trade-off among users.

Findings

Achieves maximal randomness certification without Bell inequality violations.

Identifies a measurement incompatibility trade-off among users.

Provides a practical approach for scalable randomness certification.

Abstract

Certifying maximal quantum randomness without assumptions about system dimension remains a pivotal challenge for secure communication and foundational studies. Here, we introduce a generalized framework to directly certify maximal randomness from observed probability distributions across systems with arbitrary user numbers, without relying on the Bell-inequality violations. By analyzing probability distributions directly, we identify a class of quantum states and projective measurements that achieve maximal randomness in bipartite and tripartite scenarios, ensuring practical feasibility. Further analysis reveals a counterintuitive trade-off governing measurement incompatibility among users: sufficient incompatibility for one user permits arbitrarily small incompatibility for others, defying conventional symmetry assumptions in the Bell test. This asymmetry provides a pathway to optimize device-independent protocols by strategically distributing quantum resources. Our results establish a versatile and experimentally accessible route to scalable randomness certification, with implications for quantum cryptography and the physics of nonlocal correlations.