Accumulation of Device-Independent Quantum Randomness against Time-Ordered No-Signalling Adversaries

• URL: http://arxiv.org/abs/2506.17020v1
• Date: Fri, 20 Jun 2025 14:18:15 GMT
• Title: Accumulation of Device-Independent Quantum Randomness against Time-Ordered No-Signalling Adversaries
• Authors: Ravishankar Ramanathan, Yuan Liu, Yutian Wu,
• Abstract summary: A key ingredient is to identify how the entropy in the raw outputs of a Bell test accumulates over $n$ sequential runs.<n>We show that despite the findings for small $n$, the min-entropy does in fact accumulate linearly for large $n$.
• Score: 3.7482527016282963
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The question of security of practical device-independent protocols against no-signalling adversaries, the ultimate form of cryptographic security, has remained open. A key ingredient is to identify how the entropy in the raw outputs of a Bell test accumulates over $n$ sequential runs (termed time-ordered no-signalling) against a no-signalling adversary. Previous numerical and analytical investigations for small $n$ ($\leq 5$) had suggested that the min-entropy might not accumulate linearly in contrast to the case of quantum adversaries. Here we point out that despite the findings for small $n$, the min-entropy does in fact accumulate linearly for large $n$. We illustrate the difference in randomness accumulation against quantum and no-signalling adversaries with the paradigmatic example of the Chained Bell test for which we analytically derive the min-entropy. Finally, we illustrate the power of the no-signalling adversary by providing a class of attacks that allow an eavesdropper to perfectly guess the outputs of one player in general bipartite Pseudotelepathy games.

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