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arXiv:quant-ph/0211191 · International Journal of Theoretical Physics

An Invitation to Quantum Game Theory

Edward W. Piotrowski, Jan Sładkowski

Published May 1, 2003• 195 citations
arXivHTMLPDF
DOI
10.1023/a:1025443111388

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Brief announcement

Heger Arfaoui, Pierre Fraigniaud

When playing the boolean game (δ,f), two players, upon reception of respective inputs x and y, must respectively output a and b satisfying δ(a, b)=f(x, y), in absence of any communication. It is known that, for δ(a, b)=a ⊕ b, the ability for the players to use entangled quantum bits (qbits) helps. In this paper, we show that, for δ different from the exclusive-or operator, quantum correlations do not help. This result is an invitation to revisit the theory of distributed checking, a.k.a. distributed verification, currently sticked to the usage of decision functions δ based on the AND-operator, hence potentially preventing us from using the potential benefit of quantum effects.

ACM Symposium on Principles of Distributed Computing (PODC)•Jul 16, 2012•0 citations
We illustrate how quantum information theory and free (i.e. noncommutative) semialgebraic geometry often study similar objects from different perspectives. We give examples in the context of positivity and separability, quantum magic squares, quantum correlations in non-local games, and positivity in tensor networks, and we show the benefits of combining the two perspectives. This paper is an invitation to consider the intersection of the two fields, and should be accessible for researchers from either field.
Bisimulation is a fundamental concept in the classical concurrency theory for comparing the behaviour of nondeterministic processes. It admits elegant characterisations from various perspectives such as fixed point theory, modal logics, game theory, coalgebras etc. In this paper, we review some key ideas used in the formulations and characterisations of reasonable notions of bisimulations for both probabilistic and quantum processes. To some extent the transition from probabilistic to quantum concurrency theory is smooth and natural. However, new ideas need also to be introduced. We have not yet reached the stage of formally verifying quantum communication protocols and quantum algorithms using bisimulations implemented by automatic tools. We discuss some recent efforts in this direction.
When playing the boolean game (δ,f), two players, upon reception of respective inputs x and y, must respectively output a and b satisfying δ(a, b)=f(x, y), in absence of any communication. It is known that, for δ(a, b)=a ⊕ b, the ability for the players to use entangled quantum bits (qbits) helps. In this paper, we show that, for δ different from the exclusive-or operator, quantum correlations do not help. This result is an invitation to revisit the theory of distributed checking, a.k.a. distributed verification, currently sticked to the usage of decision functions δ based on the AND-operator, hence potentially preventing us from using the potential benefit of quantum effects.