Resolving game theoretical dilemmas with quantum states
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Date
2023
Authors
Iqbal, A.
Chappell, J.M.
Szabo, C.
Abbott, D.
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Quantum Information Processing, 2023; 23(1):5-1-5-25
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Azhar Iqbal, James M. Chappell, Claudia Szabo, Derek Abbott
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Abstract
We present a new framework for creating a quantum version of a classical game, based on Fine, s theorem. This theorem shows that for a given set of marginals, a system of Bell, s inequalities constitutes both necessary and sufficient conditions for the existence of the corresponding joint probability distribution. Using Fine, s theorem, we reexpress both the player payoffs and their strategies in terms of a set of marginals, thus paving the way for the consideration of sets of marginals, corresponding to entangled quantum states, for which no corresponding joint probability distribution may exist. By harnessing quantum states and employing Positive Operator-Valued Measures, POVMs, we then consider particular quantum states that can potentially resolve dilemmas inherent in classical games.
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© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.