Equivalence between Bell inequalities and quantum Minority game

Details Equivalence between Bell inequalities and quantum Minority game Equivalence between Bell inequalities and quantum Minority game

2008-03-05

arxiv.org/abs/0803.0579v2

Phys. Lett. A 373 (2009) 521-524

Physics

Quantum Physics

v1 4 pages ReTeX, 2 figures (1 EPS); v2 11 pages LateX, 2 figures, changes to format, minor changes to wording (including titl

Scientific paper

10.1016/j.physleta.2008.12.003

We show that, for a continuous set of entangled four-partite states, the task of maximizing the payoff in the symmetric-strategy four-player quantum Minority game is equivalent to maximizing the violation of a four-particle Bell inequality with each observer choosing the same set of two dichotomic observables. We conclude the existence of direct correspondences between (i) the payoff rule and Bell inequalities, and (ii) the strategy and the choice of measured observables in evaluating these Bell inequalities. We also show that such a correspondence between Bell polynomials (in a single plane) and four-player, symmetric, binary-choice quantum games is unique to the four-player quantum Minority game and its "anti-Minority" version. This indicates that the four-player Minority game not only plays a special role among quantum games but also in studies of Bell-type quantum nonlocality.

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