TY - GEN
T1 - Parallel repetition for the GHZ game
T2 - 24th International Conference on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2021 and 25th International Conference on Randomization and Computation, RANDOM 2021
AU - Girish, Uma
AU - Holmgren, Justin
AU - Mittal, Kunal
AU - Raz, Ran
AU - Zhan, Wei
N1 - Publisher Copyright:
© Uma Girish, Justin Holmgren, Kunal Mittal, Ran Raz, and Wei Zhan; licensed under Creative Commons License CC-BY 4.0
PY - 2021/9/1
Y1 - 2021/9/1
N2 - We give a new proof of the fact that the parallel repetition of the (3-player) GHZ game reduces the value of the game to zero polynomially quickly. That is, we show that the value of the n-fold GHZ game is at most n−Ω(1). This was first established by Holmgren and Raz [18]. We present a new proof of this theorem that we believe to be simpler and more direct. Unlike most previous works on parallel repetition, our proof makes no use of information theory, and relies on the use of Fourier analysis. The GHZ game [15] has played a foundational role in the understanding of quantum information theory, due in part to the fact that quantum strategies can win the GHZ game with probability 1. It is possible that improved parallel repetition bounds may find applications in this setting. Recently, Dinur, Harsha, Venkat, and Yuen [7] highlighted the GHZ game as a simple three-player game, which is in some sense maximally far from the class of multi-player games whose behavior under parallel repetition is well understood. Dinur et al. conjectured that parallel repetition decreases the value of the GHZ game exponentially quickly, and speculated that progress on proving this would shed light on parallel repetition for general multi-player (multi-prover) games.
AB - We give a new proof of the fact that the parallel repetition of the (3-player) GHZ game reduces the value of the game to zero polynomially quickly. That is, we show that the value of the n-fold GHZ game is at most n−Ω(1). This was first established by Holmgren and Raz [18]. We present a new proof of this theorem that we believe to be simpler and more direct. Unlike most previous works on parallel repetition, our proof makes no use of information theory, and relies on the use of Fourier analysis. The GHZ game [15] has played a foundational role in the understanding of quantum information theory, due in part to the fact that quantum strategies can win the GHZ game with probability 1. It is possible that improved parallel repetition bounds may find applications in this setting. Recently, Dinur, Harsha, Venkat, and Yuen [7] highlighted the GHZ game as a simple three-player game, which is in some sense maximally far from the class of multi-player games whose behavior under parallel repetition is well understood. Dinur et al. conjectured that parallel repetition decreases the value of the GHZ game exponentially quickly, and speculated that progress on proving this would shed light on parallel repetition for general multi-player (multi-prover) games.
KW - GHZ
KW - Multi-player
KW - Parallel repetition
KW - Polynomial
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U2 - 10.4230/LIPIcs-APPROX/RANDOM.2021.62
DO - 10.4230/LIPIcs-APPROX/RANDOM.2021.62
M3 - Conference contribution
AN - SCOPUS:85115633965
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2021
A2 - Wootters, Mary
A2 - Sanita, Laura
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Y2 - 16 August 2021 through 18 August 2021
ER -