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Abstract: A quantum logic gate of particular interest to both electrical engineers andgame theorists is the quantum multiplexer. This shared interest is due to thefacts that an arbitrary quantum logic gate may be expressed, up to arbitraryaccuracy, via a circuit consisting entirely of variations of the quantummultiplexer, and that certain one player games, the history dependent Parrondogames, can be quantized as games via a particular variation of the quantummultiplexer. However, to date all such quantizations have lacked a certainfundamental game theoretic property.The main result in this dissertation is the development of quantizations ofhistory dependent quantum Parrondo games that satisfy this fundamental gametheoretic property. Our approach also yields fresh insight as to what should beconsidered as the proper quantum analogue of a classical Markov process andgives the first game theoretic measures of multiplexer behavior.

Autor: Faisal Shah Khan

Fuente: https://arxiv.org/

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