Parallel repetition of expanded, and multiplayer, Quantum games: anchoring, optimal values, generalized error bounds, dependency-breaking as symmetry-breaking

2025/08/12 by Rigas, Pete · 1 citation
#81P02 #81Q02 #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Information Theory (cs.IT) #Probability (math.PR) #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.2508.09380

Abstract

We demonstrate that parallel repetition of the multiplayer anchored optimal value, ω( G_\bot )^{⊗ n}, decays exponentially. Central to our approach are several probabilistic computations, pertaining to: (1) the computation of expected values for quantifying how the winning probability of the game is likely to change under the anchoring transformation; (2) the computation of positive operator valued measurements, which can be placed into direct correspondence with several probabilistically defined quantities; (3) the computation of Relative, and Relative-min entropies; (4) and lastly, the computation of generalized error bounds, which have previously been analyzed by the author in several multiplayer game-theoretic settings (arXiv: 2505.06322, and arXiv: 2507.03035). This work builds upon observations originally provided by Bavarian, Vidick, and Yuen (arXiv: 1509.07466).

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