This Quantum World/Game

< PREVIOUS A quantum game Here are the rules:Lev Vaidman, "Variations on the theme of the Greenberger-Horne-Zeilinger proof," Foundations of Physics 29, pp. 615-30, 1999. Two teams play against each other: Andy, Bob, and Charles (the "players") versus the "interrogators". Each player is asked either "What is the value of X?" or "What is the value of Y?" Only two answers are allowed: +1 or −1. Either each player is asked the X question, or one player is asked the X question and the two other players are asked the Y question. The players win if the product of their answers is −1 in case only X questions are asked, and if the product of their answers is +1 in case Y questions are asked. Otherwise they lose. The players are not allowed to communicate with each other once the questions are asked. Before that, they are permitted to work out a strategy. Is there a failsafe strategy? Can they make sure that they will win? Stop to ponder the question. Let us try pre-agreed answers, which we will call XA, XB, XC and YA, YB, YC. The winning combinations satisfy the following equations: Consider the first three equations. The product of their right-hand sides equals +1. The product of their left-hand sides equals XAXBXC, implying that XAXBXC = 1. (Remember that the possible values are ±1.) But if XAXBXC = 1, then the fourth equation XAXBXC = −1 obviously cannot be satisfied. The bottom line: There is no failsafe strategy with pre-agreed answers. NEXT >