Measurement-Incompatibility Constraints for Maximal Randomness

• URL: http://arxiv.org/abs/2505.17585v2
• Date: Mon, 14 Jul 2025 03:09:52 GMT
• Title: Measurement-Incompatibility Constraints for Maximal Randomness
• Authors: Tianqi Zheng, Yi Li, Yu Xiang, Qiongyi He,
• Abstract summary: Certifying maximal quantum randomness without assumptions about system dimension remains a pivotal challenge for secure communication and foundational studies.<n>Here, we introduce a generalized framework to directly certify maximal randomness from observed probability distributions across systems with arbitrary user numbers.<n>Our results establish a versatile and experimentally accessible route to scalable randomness certification, with implications for quantum cryptography and the physics of nonlocal correlations.
• Score: 5.560127372386599
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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