Quantum version of the Monty Hall problem

Details Quantum version of the Monty Hall problem Quantum version of the Monty Hall problem

2001-09-07

arxiv.org/abs/quant-ph/0109035v3

Phys. Rev. A 65, 062318 (2002)

Physics

Quantum Physics

5 pages, RevTeX, no figures, v2: minor corrections to eq. 4,5,7 and 15, v3: published version, ackowledgements added

Scientific paper

10.1103/PhysRevA.65.062318

A version of the Monty Hall problem is presented where the players are permitted to select quantum strategies. If the initial state involves no entanglement the Nash equilibrium in the quantum game offers the players nothing more than can be obtained with a classical mixed strategy. However, if the initial state involves entanglement of the qubits of the two players, it is advantageous for one player to have access to a quantum strategy while the other does not. Where both players have access to quantum strategies there is no Nash equilibrium in pure strategies, however, there is a Nash equilibrium in quantum mixed strategies that gives the same average payoff as the classical game.

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