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When Quantum Nonlocality Does Not Play Dice
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Bell nonlocality is widely viewed as a signature of intrinsic randomness, effectively playing the role of a 'dice' at the heart of many device-independent cryptographic protocols. We show that this connection has a fundamental limitation: there exist Bell inequalities that are maximally violated by quantum correlations yet certify no randomness for any fixed input pair. We develop a systematic construction based on symmetric deterministic extensions of nonlocal games, and use it to obtain explicit examples of such inequalities. We also construct maximally nonlocal quantum correlations that, for every input pair, admit a convex decomposition into strategies with predetermined outputs for those inputs. Our results reveal a strong form of determinism compatible with quantum nonlocality and delineate the limits of device-independent randomness certification.
Forward citations
Cited by 3 Pith papers
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Accumulation of Device-Independent Quantum Randomness against Time-Ordered No-Signalling Adversaries
Linear min-entropy accumulation is claimed for time-ordered no-signalling adversaries in Bell tests with monogamous non-local games, while most bipartite pseudo-telepathy games are claimed not to certify randomness ag...
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No Bound Randomness in Quantum Nonlocality
Any nonlocal quantum behavior certifies some device-independent randomness when all input pairs are used for generation; the input-averaged guessing probability is a faithful, monotonic nonlocality measure.
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Measurement-Incompatibility Constraints for Maximal Randomness
A construction certifies maximal randomness in bipartite and tripartite scenarios directly from probability distributions, with an incompatibility trade-off that lets all but one user use nearly compatible measurements.
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