Extended GHZ n-player games with classical probability of winning tending to 0

Details Extended GHZ n-player games with classical probability of winning tending to 0 Extended GHZ n-player games with classical probability of winning tending to 0

2004-08-13

arxiv.org/abs/quant-ph/0408090v4

Physics

Quantum Physics

4 pages, RevTeX4. Expanded text

Scientific paper

In 1990, Mermin presented a n player game that is won with certainty using n spin-1/2 particles in a GHZ state whilst no classical strategy (or local theory) can win with probability higher than ${1/2} + \frac{1}{2^{\lceil n/2 \rceil}}$ (which is larger than 1/2). This article first introduces a class of arithmetic games containing Mermin's and gives a quantum algorithm based on a generalized n party GHZ state that wins those games with certainty. It is then proved for a subclass of those games where each player is given a single bit of input that no classical strategy can win with a probability that is asymptotically larger than 1.6 times the inverse of the square root of n, thus giving a new and stronger Bell inequality.

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