cp's OEIS Frontend

A201488 Decimal expansion of maximal success probability of the CHSH game.

%I A201488 #53 May 20 2025 00:15:07
%S A201488 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,
%T A201488 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,
%U A201488 3,1,1,9,6,1,5,5,2,6,7,5,9,7,1,2,5,9,6
%N A201488 Decimal expansion of maximal success probability of the CHSH game.
%C A201488 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.
%C A201488 The optimality of this probability follows from Tsirelson's inequality and is implicit in the CHSH paper.
%C A201488 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
%C A201488 Weight factor in Laguerre-Gauss quadrature, corresponding to the smallest root of the Laguerre polynomial of degree 2. - _A.H.M. Smeets_, May 15 2025
%H A201488 J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, <a href="https://www.researchgate.net/publication/228109500_Proposed_Experiment_to_Test_Local_Hidden-Variable_Theories">Proposed Experiment to Test Local Hidden-Variable Theories</a>, Phys. Rev. Lett. 23 (1969), pp. 880-884.
%H A201488 Claude Crépeau, Louis Salvail, Jean-Raymond Simard, and Alain Tapp, <a href="http://crypto.cs.mcgill.ca/~crepeau/PDF/CSST06.pdf">Classical and quantum strategies for two-prover bit commitments</a>, Ninth Workshop on Quantum Information Processing (2006).
%H A201488 Erica Klarreich, <a href="https://www.quantamagazine.org/quantum-computing-test-offers-boost-to-quantum-cryptography-20130821/">The Proof in the Quantum Pudding</a>, Quanta Magazine, 21 Aug 2013.
%H A201488 Stephen J. Summers and Reinhard Werner, <a href="https://doi.org/10.1016/0375-9601(85)90093-3">The vacuum violates Bell's inequalities</a>, Physics Letters A 110:5 (1985), pp. 257-259.
%H A201488 Wikipedia, <a href="https://en.wikipedia.org/wiki/CHSH_inequality">CHSH inequality</a>
%H A201488 Wikipedia, <a href="http://en.wikipedia.org/wiki/Quantum_pseudo-telepathy">Quantum pseudo-telepathy</a>
%H A201488 Wikipedia, <a href="https://en.wikipedia.org/wiki/Tsirelson&#39;s_bound">Tsirelson's bound</a>
%H A201488 <a href="/index/Al#algebraic_02">Index entries for algebraic numbers, degree 2</a>.
%F A201488 Equals cos^2(Pi/8) = (1 + 1/sqrt(2))/2.
%F A201488 Equals (theta_3(0, q^2)/theta_3(0, q))^2 where q = 1/e^Pi. - _Michael Somos_, Dec 02 2022
%e A201488 0.853553390593273762200422181052424519642417968844237...
%t A201488 RealDigits[Cos[Pi/8]^2,10,120][[1]] (* _Harvey P. Dale_, Jan 21 2012 *)
%o A201488 (PARI) cos(Pi/8)^2 \\ _Charles R Greathouse IV_, Dec 02 2011
%Y A201488 Cf. A020765, A019863.
%K A201488 nonn,cons,nice
%O A201488 0,1
%A A201488 _Charles R Greathouse IV_, Dec 02 2011