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Quantum pseudo-telepathy is a phenomenon in quantum game theory resulting in anomalously high success rates in coordination games between separated players. These high success rates would require communication between the players in a purely classical (non-quantum) world; however, the game is set up such that during the game, communication is physically impossible. This means that for quantum pseudo-telepathy to occur, prior to the game the participants need to share a physical system in an entangled quantum state, and during the game have to execute measurements on this entangled state as part of their game strategy. Games in which the application of such a quantum strategy leads to pseudo-telepathy are also referred to as quantum non-locality games. In their 1999 paper,〔Gilles Brassard, Richard Cleve, Alain Tapp, "(The cost of exactly simulating quantum entanglement with classical communication )" (1999).〕 Gilles Brassard, Richard Cleve and Alain Tapp demonstrated that winning quantum strategies can exist in simple games for which in the absence of quantum entanglement a winning strategy can result only if the participants were allowed to communicate. The term quantum pseudo-telepathy was later introduced〔Gilles Brassard, Anne Broadbent, Alain Tapp, "(Multi-Party Pseudo-Telepathy )" (2003).〕 for this phenomenon. The prefix 'pseudo' is appropriate, as the quantum non-locality effects that are at the heart of the phenomenon do not allow any transfer of information, but rather eliminate the need to exchange information between the players for achieving a mutual win in the game. The phenomenon of quantum pseudo-telepathy is mostly used as a powerful and explicit thought experiment of the non-local characteristics of quantum mechanics. Yet, the effect is real and subject to experimental verification, as demonstrated by the experimental confirmation of the violation of the Bell inequalities. ==The Mermin-Peres magic square game== An example of quantum pseudo-telepathy can be observed in the following two-player coordination game in which, in each round, one participant fills one row and the other fills one column of a 3x3 table with plus and minus signs. The two players Alice and Bob are separated so that no communication between them is possible. In each round of the game, Alice is told which row is selected for her to fill in, and Bob is told which column is selected for him. Alice is not told which column Bob must fill in, and Bob is not told which row Alice must fill in. One may assume that the selection is done by chance or by a hostile party. Alice and Bob place their numbers according to the following rules. Alice must fill in her row such that there is an even number of minus signs in that row. Bob must fill in his column such that there is an odd number of minus signs in that column. If Alice and Bob place the same sign in the cell shared by their row and column, they win the round. If they place opposite signs, they lose the round. After the round is complete, the game board is cleared. They may play repeatedly, and they try to win as often as possible. In the classic (non-quantum) form of the game, Alice and Bob are permitted to agree on a game playbook in advance. The only rule is that they cannot communicate after they are separated. It is easy to see that any prior agreement between Alice and Bob on the use of specific tables filled with + and – signs is not going to enable them to win all the time. The reason is that a perfectly consistent table does not exist: it would be self-contradictory, with the sum of the minus signs in the table being even based on row sums, and being odd when using column sums. As a further illustration, if they use the partial table shown in the diagram (supplemented by a -1 for Alice and a +1 for Bob in the missing square) and the challenge rows and columns are selected at random, they will win 8/9 of the time. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Quantum pseudo-telepathy」の詳細全文を読む スポンサード リンク
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