A LOWER BOUND ON THE VALUE OF ENTANGLED BINARY GAMES

作者：Beigi Salman^*

来源：Quantum Information & Computation, 2010, 10(11-12): 911-924.

• Non-local games
• Non-local correlations
• SDP relaxation

A two-player one-round binary game consists of two cooperative players who each replies by one bit to a message that he receives privately; they win the game if both questions and answers satisfy some predetermined property. A game is called entangled if the players are allowed to share a priori entanglement. It is well-known that the maximum winning probability (value) of entangled XOR-games (binary games in which the predetermined property depends only on the XOR of the two output bits) can be computed by a semidefinite program. In this paper we extend this result in the following sense; if a binary game is uniform, meaning that in an optimal strategy the marginal distributions of the output of each player are uniform, then its entangled value can be efficiently computed by a semidefinite program. We also introduce a lower bound on the entangled value of a general two-player one-round game; this bound depends on the size of the output set of each player and can be computed by a semidefinite program. In particular, we show that if the game is binary, omega(q) is its entangled value, and omega(sdp) is the optimum value of the corresponding semidefinite program, then 0.68 omega(sdp) < omega(q) <= omega(sdp).

• 出版日期2010-11