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UID:www.tcs.tifr.res.in/event/1164
DTSTAMP:20230914T125953Z
SUMMARY:Parallel Repetition for the GHZ Game: A Simpler Proof
DESCRIPTION:Speaker: Uma Girish (Princeton University)\n\nAbstract: \nWe gi
ve 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 parallel repetition of the GHZ g
ame is at most n^{-\\Omega(1)}. This was first established by Holmgren and
Raz [HR20]. 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 [GHZ89] 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 pos
sible that improved parallel repetition bounds may find applications in th
is setting. Recently\, Dinur\, Harsha\, Venkat\, and Yuen [DHVY17] highlig
hted the GHZ game as a simple three-player game\, which is in some sense m
aximally far from the class of multi-player games whose behavior under par
allel repetition is well understood. Dinur et al. conjectured that paralle
l repetition decreases the value of the GHZ game exponentially quickly\, a
nd speculated that progress on proving this would shed light on parallel r
epetition for general multi-player (multi-prover) games. This is based on
a joint work with Justin Holmgren\, Kunal Mittal\, Ran Raz and Wei Zhan.\n
YouTube link : https://www.youtube.com/watch?v=jxQ81fDMpOU\n
URL:https://www.tcs.tifr.res.in/web/events/1164
DTSTART;TZID=Asia/Kolkata:20210928T190000
DTEND;TZID=Asia/Kolkata:20210928T200000
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