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A201488 Decimal expansion of maximal success probability of the CHSH game. 5
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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
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
LINKS
J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, Proposed Experiment to Test Local Hidden-Variable Theories, Phys. Rev. Lett. 23 (1969), pp. 880-884.
Claude Crépeau, Louis Salvail, Jean-Raymond Simard, and Alain Tapp, Classical and quantum strategies for two-prover bit commitments, Ninth Workshop on Quantum Information Processing (2006).
Erica Klarreich, The Proof in the Quantum Pudding, Quanta Magazine, 21 Aug 2013.
Stephen J. Summers and Reinhard Werner, The vacuum violates Bell's inequalities, Physics Letters A 110:5 (1985), pp. 257-259.
Wikipedia, CHSH inequality
FORMULA
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
EXAMPLE
0.853553390593273762200422181052424519642417968844237...
MATHEMATICA
RealDigits[Cos[Pi/8]^2, 10, 120][[1]] (* Harvey P. Dale, Jan 21 2012 *)
PROG
(PARI) cos(Pi/8)^2 \\ Charles R Greathouse IV, Dec 02 2011
CROSSREFS
Sequence in context: A140133 A086723 A011406 * A200141 A011466 A154509
KEYWORD
nonn,cons,nice
AUTHOR
STATUS
approved

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Last modified June 25 01:31 EDT 2024. Contains 373691 sequences. (Running on oeis4.)