Parallel Repetition in the Two-Player Quantum Cloning Game

• URL: http://arxiv.org/abs/2608.00930v1
• Date: Sun, 02 Aug 2026 02:08:35 GMT
• Title: Parallel Repetition in the Two-Player Quantum Cloning Game
• Abstract summary: Colisson Palais, Escol-Farrs, and Speelman bounded the value of $n$ copies between $(3/4)n$ and $cos2n(/8)$.<n>For every $n$, challenge-independent strategies have optimal value $(3/4)n$.
• Score: 0.2291770711277359
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study parallel repetition in the two-player quantum cloning game, a monogamy-of-entanglement game motivated by quantum position verification. Colisson Palais, Escolà-Farràs, and Speelman bounded the value of $n$ copies between $(3/4)^n$ and $\cos^{2n}(π/8)$. For two copies, we prove that neither bound is tight. An explicit challenge-dependent strategy achieves value $(5+\sqrt{17})/16>9/16$, so strong parallel repetition fails for the unrestricted game. A block Gram matrix argument gives the upper bound $(11+\sqrt{65})/32<\cos^4(π/8)$ and strictly improves the previous parallel-repetition upper bound for every $n$. For every $n$, challenge-independent strategies have optimal value $(3/4)^n$.

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