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Playing quantum games by a scheme with pre- and post-selection

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Abstract

We propose a scheme to play quantum games by assuming that the two players interact with each other. Thus, by pre-selection, two players can choose their initial states, and some dilemma in classical game may be removed by post-selection, which is particularly useful for the cooperative games. We apply the proposal to both of BoS and Prisoners’ dilemma games in cooperative situations. The examples show that the proposal would guarantee a remarkably binding agreement between two parties. Any deviation during the game will be detected, and the game may be abnegated. By illuminating the examples, we find that the initial state in the cooperative game does not destroy process to get preferable payoffs by pre- and post-selections, which is not true in other schemes for implementing the quantum game. We point out that one player can use the scheme to detect his opponent’s choices if he is advantageous in information theory and technology.

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Acknowledgments

The authors are obliged to Professor Shengjun Wu’s fruitful discussion. This work is partially supported by the State Key Program for Basic Research of China SKPBR of China (2011CB922104, 2011CBA00205), NSFC (91021003, 91321310, 11274156), and PAPD.

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Author notes

  1. Guo-Fu Weng

    Present address: Department of Physics and Electronics, Tongren University, Tongren, 554300, Guizhou, People’s Republic of China

Authors and Affiliations

  1. National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing, 210093, People’s Republic of China

    Guo-Fu Weng & Yang Yu

  2. Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, Anhui, China

    Guo-Fu Weng & Yang Yu

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  1. Guo-Fu Weng
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Correspondence to Guo-Fu Weng.

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Weng, GF., Yu, Y. Playing quantum games by a scheme with pre- and post-selection. Quantum Inf Process 15, 147–165 (2016). https://doi.org/10.1007/s11128-015-1151-5

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  • DOI: https://doi.org/10.1007/s11128-015-1151-5

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