Asymptotically Optimal Adversarial Strategies for the Probability Estimation Framework
arXiv:2306.06802 · doi:10.3390/e25091291
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 Bell scenarios.
arXiv comment54 pages
References in corpus (21)
- Experimental loophole-free violation of a Bell inequality using entangled electron spins separated by 1.3 km
- Significant-loophole-free test of Bell's theorem with entangled photons
- A strong loophole-free test of local realism
- Bell inequalities for arbitrarily high dimensional systems
- Non-local correlations as an information theoretic resource
- Event-Ready Bell Test Using Entangled Atoms Simultaneously Closing Detection and Locality Loopholes
- Monotonicity of a relative Rényi entropy
- Quantifying randomness in real networks
- Popescu-Rohrlich correlations as a unit of nonlocality
- Experimentally Generated Randomness Certified by the Impossibility of Superluminal Signals
- Interconversion of Nonlocal Correlations
- Device-independent Randomness Expansion with Entangled Photons
- Extremal correlations of the tripartite no-signaling polytope
- Experimental Realization of Device-Independent Quantum Randomness Expansion
- Experimental Low-Latency Device-Independent Quantum Randomness
- Quantifying Bell non-locality with the trace distance
- Quantum Correlations in the Minimal Scenario
- Certifying Quantum Randomness by Probability Estimation
- Quantum Randomness Generation by Probability Estimation with Classical Side Information
- Geometric Decompositions of Bell Polytopes with Practical Applications
- Tsirelson Polytopes and Randomness Generation