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- W4295692728 abstract "Recent results showed it was possible to determine if a modest size 3XOR game has a perfect quantum strategy. We build on these and give an explicit polynomial time algorithm which constructs such a perfect strategy or refutes its existence. This new tool lets us numerically study the behavior of randomly generated 3XOR games with large numbers of questions. A key issue is: how common are pseudotelephathy games (games with perfect quantum strategies but no perfect classical strategies)? Our experiments strongly indicate that the probability of a randomly generated game being pseudotelpathic stays far from 1, indeed it is bounded below 0.15. We also find strong evidence that randomly generated 3XOR games undergo both a quantum and classical phase transition, transitioning from almost certainly perfect to almost certainly imperfect as the ratio of number of clauses ($m$) to number of questions ($n$) increases. The locations of these two phase transitions appear to coincide at $m/n approx 2.74$." @default.
- W4295692728 created "2022-09-14" @default.
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- W4295692728 date "2022-09-10" @default.
- W4295692728 modified "2023-10-18" @default.
- W4295692728 title "Satisfiability Phase Transtion for Random Quantum 3XOR Games" @default.
- W4295692728 doi "https://doi.org/10.48550/arxiv.2209.04655" @default.
- W4295692728 hasPublicationYear "2022" @default.
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