Parallel repetition of expanded, and multiplayer, Quantum games: anchoring, optimal values, generalized error bounds, dependency-breaking as symmetry-breaking

TL;DR

This paper proves that the probability of winning multiplayer anchored quantum games decreases exponentially with parallel repetition, using advanced probabilistic and information-theoretic techniques to analyze optimal values and error bounds.

Contribution

It introduces a novel analysis of parallel repetition decay for multiplayer anchored quantum games, extending previous work with new probabilistic and symmetry-breaking methods.

Findings

Exponential decay of game winning probability under parallel repetition.

Development of generalized error bounds for multiplayer quantum games.

Application of symmetry-breaking techniques to quantum game analysis.

Abstract

We demonstrate that parallel repetition of the multiplayer anchored optimal value, $\omega \big( G_{\bot} \big)^{\otimes n}$, decays exponentially. Central to our approach are several probabilistic computations, pertaining to: (1) the computation of expected values for quantifying how the winning probability of the game is likely to change under the anchoring transformation; (2) the computation of positive operator valued measurements, which can be placed into direct correspondence with several probabilistically defined quantities; (3) the computation of Relative, and Relative-min entropies; (4) and lastly, the computation of generalized error bounds, which have previously been analyzed by the author in several multiplayer game-theoretic settings (arXiv: 2505.06322, and arXiv: 2507.03035). This work builds upon observations originally provided by Bavarian, Vidick, and Yuen (arXiv: 1509.07466).