When Quantum Nonlocality Does Not Play Dice
arXiv:2408.03665
The authors demonstrate that certain Bell inequalities can be maximally violated by quantum correlations yet certify no randomness for any fixed input pair, and they construct explicit examples using deterministic extensions of nonlocal games.
Abstract
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.
5+12 pages; 2+5 figures. v3: main text has been partly rewritten, in particular to make the connection to partly deterministic polytopes clearer. v4: abstract updated