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 -Farrà s, and Speelman bounded the value of $n$ copies between $(3/4{)}^n$ and ${\cos }^{2n}(\ddot{I}€/8)$. 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 $(11+\sqrt{65})/32<{\cos }^4(\ddot{I}€/8)$ and strictly improves the previous parallel-repetition upper bound for every $n$. For every $n$, challenge-independent strategies have optimal value $(3/4{)}^n$.

11 pages