Strong Parallel Repetition for a Monogamy-of-Entanglement Game

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 $(3/4)^n$ .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 $(3/4)^n$.

quant-pharXiv:2608.00930Aug 4, 20260 citations

Parallel Repetition of entangled games on the uniform distribution

André Chailloux, Giannicola, Scarpa

Présentation

Oct 25, 20130 citations

Strong Parallel Repetition Theorem for Free Projection Games

Boaz Barak, Anup Rao, Ran Raz +2 more

Lecture notes in computer scienceJan 1, 200927 citations

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