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We show that for any $\varepsilon>0$ there is an XOR game $G=G(\varepsilon)$ with $\Theta(\varepsilon^{-1/5})$ inputs for one player and $\Theta(\varepsilon^{-2/5})$ inputs for the other player such that $\Omega(\varepsilon^{-1/5})$ ebits are required for any strategy achieving bias that is at least a multiplicative factor $(1-\varepsilon)$ from optimal.
A convexity theorem for certain groups of transformations
Isidore Isaac Hirschman · 1952
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John F. Clauser, Michael A. Horne, Abner Shimony, and Richard A. Holt · 1969
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Quantum analogues of the bell inequalities. the case of two spatially separated domains
Boris S Tsirel’son · 1987
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