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Correspondence between quantization schemes for two-player nonzero-sum games and CNOT complexity

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Abstract

The well-known quantization schemes for two-player nonzero-sum games are Eisert–Wilkens–Lewenstein scheme and Marinatto–Weber scheme. In this work, we establish the connection between the two schemes from the perspective of quantum circuits. Further, we provide the correspondence between any game quantization schemes and the CNOT complexity, where CNOT complexity is up to the local unitary operations. While CNOT complexity is known to be useful in the analysis of universal quantum circuit, in this work, we find its applicability in quantum game theory.

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Acknowledgements

The authors gratefully acknowledge the anonymous reviewers for their critical suggestions, in particular pointing the references [14, 15] which certainly add value to our main results.

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Authors and Affiliations

  1. Department of Physics, School of Advanced Sciences, VIT University, Vellore, 632014, India

    V. Vijayakrishnan & S. Balakrishnan

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  1. V. Vijayakrishnan
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  2. S. Balakrishnan
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Correspondence to S. Balakrishnan.

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Vijayakrishnan, V., Balakrishnan, S. Correspondence between quantization schemes for two-player nonzero-sum games and CNOT complexity. Quantum Inf Process 17, 102 (2018). https://doi.org/10.1007/s11128-018-1870-5

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  • DOI: https://doi.org/10.1007/s11128-018-1870-5

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