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A201488
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Decimal expansion of maximal success probability of the CHSH game.
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5
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8, 5, 3, 5, 5, 3, 3, 9, 0, 5, 9, 3, 2, 7, 3, 7, 6, 2, 2, 0, 0, 4, 2, 2, 1, 8, 1, 0, 5, 2, 4, 2, 4, 5, 1, 9, 6, 4, 2, 4, 1, 7, 9, 6, 8, 8, 4, 4, 2, 3, 7, 0, 1, 8, 2, 9, 4, 1, 6, 9, 9, 3, 4, 4, 9, 7, 6, 8, 3, 1, 1, 9, 6, 1, 5, 5, 2, 6, 7, 5, 9, 7, 1, 2, 5, 9, 6
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OFFSET
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0,1
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COMMENTS
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A referee chooses two random bits and gives one to each of two players who share an entangled quantum state but are not permitted to communicate. The players each choose a bit to send to the referee. If both of the bits from the referee are 1, then the players win if their chosen bits are different; otherwise they win if their chosen bits are the same. The best classical win probability is 3/4, but this can be improved in a quantum setting.
The optimality of this probability follows from Tsirelson's inequality and is implicit in the CHSH paper.
Ratio of leg length to base length in an isosceles triangle with the property that the areas of the two smaller excircles sum up to the area of the third excircle. - Martin Janecke, Aug 05 2012
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LINKS
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FORMULA
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Equals cos^2(Pi/8) = (1 + 1/sqrt(2))/2.
Equals (theta_3(0, q^2)/theta_3(0, q))^2 where q = 1/e^Pi. - Michael Somos, Dec 02 2022
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EXAMPLE
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0.853553390593273762200422181052424519642417968844237...
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MATHEMATICA
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RealDigits[Cos[Pi/8]^2, 10, 120][[1]] (* Harvey P. Dale, Jan 21 2012 *)
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PROG
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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