Parallel Repetition in the Two-Player Quantum Cloning Game
ORCID iD
Fenner 0000-0002-6028-9323
Document Type
Article
Subject Area(s)
Quantum Information Theory
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+√17)/16 > 9/16, so strong parallel repetition fails for the unrestricted game. A block Gram matrix argument gives the upper bound (11+√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.
Digital Object Identifier (DOI)
Publication Info
Published in 2026.
Rights
The article is under the CC By license
APA Citation
Naig, E. C., & Fenner, S. A. (2026). Parallel repetition in the two-player quantum cloning game. arXiv.Org. https://arxiv.org/abs/2608.00930
Python code to verify 2-copy lower bound