Asymptotically Optimal Adversarial Strategies for the Probability Estimation Framework

• URL: http://arxiv.org/abs/2306.06802v1
• Date: Sun, 11 Jun 2023 22:58:01 GMT
• Title: Asymptotically Optimal Adversarial Strategies for the Probability Estimation Framework
• Authors: Soumyadip Patra and Peter Bierhorst
• Abstract summary: We present a self-contained proof of the optimality of the PEF method for certifying randomness in quantum non-locality experiments. We apply these results to the (2,2,2) Bell scenario, obtaining an analytic characterisation of the optimal adversarial attacks bound by no-signalling principles. We also study extensions of the analysis to quantum-limited adversaries in the (2,2,2) Bell scenario and no-signalling adversaries in higher $(n,m,k)$ Bell scenarios.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The Probability Estimation Framework involves direct estimation of the probability of occurrences of outcomes conditioned on measurement settings and side information. It is a powerful tool for certifying randomness in quantum non-locality experiments. In this paper, we present a self-contained proof of the asymptotic optimality of the method. Our approach refines earlier results to allow a better characterisation of optimal adversarial attacks on the protocol. We apply these results to the (2,2,2) Bell scenario, obtaining an analytic characterisation of the optimal adversarial attacks bound by no-signalling principles, while also demonstrating the asymptotic robustness of the PEF method to deviations from expected experimental behaviour. We also study extensions of the analysis to quantum-limited adversaries in the (2,2,2) Bell scenario and no-signalling adversaries in higher $(n,m,k)$ Bell scenarios.

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