On the largest Bell violation attainable by aquantum state

摘要

We study the projective tensor norm as a measure of the largest Bell violation of a quantum state. Inorder to do this, weconsider a truncated version of a well-known SDP relaxation for the quantum value of a two-prover one-round game, one which has extra restrictions on the dimension of the SDP solutions. Our main result provides a quite accurate upper bound for the distance between the classical value of a Bell inequality and the corresponding value of the relaxation. Along the way, wegive a simple proof that the best complementation constant of ?_2~n in ?_1(?_∞)is of order (In n)~(1/2)lnn. Asa direct consequence, weshow that we cannot remove a logarithmic factor when we are computing the largest Bell violation attainable by the maximally entangled state.