Abstract
It has been extensively shown in past literature that Bayesian game theory and quantum non-locality have strong ties between them. Pure entangled states have been used, in both common and conflict interest games, to gain advantageous payoffs, both at the individual and social level. In this paper, we construct a game for a mixed entangled state such that this state gives higher payoffs than classically possible, both at the individual level and the social level. Also, we use the I-3322 inequality so that states that aren’t useful advice for the Bell-CHSH1 inequality can also be used. Finally, the measurement setting we use is a restricted social welfare strategy (given this particular state).
Highlights
Quantum theory emerged when most physicists realized that physics at the atomic level could not be completely described by classical mechanics
It has been extensively shown in past literature that Bayesian game theory and quantum non-locality have strong ties between them
The above discussion raises the question: Can mixed entangled states be used as Quantum Social Welfare Advice (QSWA) for Bayesian games at all? We answer this question in the affirmative, by explicitly constructing a proofof-principle Bayesian game, where a mixed entangled state gives higher unfair payoffs and higher social payoffs than classical equilibria
Summary
Quantum theory emerged when most physicists realized that physics at the atomic level could not be completely described by classical mechanics. Though Heisenberg and Bohr, the further luminaries of the theory believed in the innate uncertainty in the behavior of atoms, Einstein never accepted it He fundamentally opposed the Copenhagen interpretation of Quantum Mechanics (QM). This led Bohr to publish a paper in the same journal, under the same name, 1Bell-Clauser-Horne-Shimony-Holt inequality, 1969. Quantum states that violate Bell’s inequality are all non-local states (entangled). We know that any two-qubit pure entangled state can be used as QSWA in some non-local game This result has interesting implications for quantum game theory in general, and quantum cryptographic protocols in particular. The utility of arbitrary (undistillable) bound entangled states in this context, remains an open problem that requires further study
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