Parallel Repetition in the Two-Player Quantum Cloning Game

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 $\cos^{2n}(\pi/8)$. 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 $(11+\sqrt{65})/32<\cos^4(\pi/8)$ and strictly improves the previous parallel-repetition upper bound for every $n$. For every $n$, challenge-independent strategies have optimal value $(3/4)^n$.

arXiv:2608.00930 [quant-ph]

(or arXiv:2608.00930v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2608.00930 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

verify_counterexample.py

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