Parallel repetition of expanded, and multiplayer, Quantum games: anchoring, optimal values, generalized error bounds, dependency-breaking as symmetry-breaking
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912535798611968 |
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| author | Rigas, Pete |
| author_facet | Rigas, Pete |
| contents | We demonstrate that parallel repetition of the multiplayer anchored optimal value, $ω\big( G_{\bot} \big)^{\otimes n}$, 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). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_09380 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Parallel repetition of expanded, and multiplayer, Quantum games: anchoring, optimal values, generalized error bounds, dependency-breaking as symmetry-breaking Rigas, Pete Quantum Physics Information Theory Probability 81P02, 81Q02 We demonstrate that parallel repetition of the multiplayer anchored optimal value, $ω\big( G_{\bot} \big)^{\otimes n}$, 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). |
| title | Parallel repetition of expanded, and multiplayer, Quantum games: anchoring, optimal values, generalized error bounds, dependency-breaking as symmetry-breaking |
| topic | Quantum Physics Information Theory Probability 81P02, 81Q02 |
| url | https://arxiv.org/abs/2508.09380 |