Cryptology ePrint Archive: Report 2017/1138

The Parallel Repetition of Non-Signaling Games: Counterexamples and Dichotomy

Justin Holmgren and Lisa Yang

Abstract: Non-signaling games are an important object of study in the theory of computation, for their role both in quantum information and in (classical) cryptography. In this work, we study the behavior of these games under parallel repetition.

We show that, unlike the situation both for classical games and for two-player non-signaling games, there are $k$-player non-signaling games (for $k \ge 3$) whose values do not tend to $0$ with sufficient parallel repetition. In fact, parallel repetition sometimes does not decrease their value whatsoever.

We show that in general:

1. Every game's non-signaling value under parallel repetition is either lower bounded by a positive constant or decreases exponentially with the number of repetitions.

2. Exponential decrease occurs if and only if the game's sub-non-signaling value (Lancien and Winter, CJTCS '16) is less than $1$.

Category / Keywords: foundations / parallel repetition, non-signaling strategies

Original Publication (with minor differences): STOC 2019

Date: received 24 Nov 2017, last revised 10 Feb 2019

Contact author: justin holmgren at gmail com

Available format(s): PDF | BibTeX Citation

Version: 20190210:225649 (All versions of this report)

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