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The Quantum Monty Hall Problem

G. M. D'Ariano·R. D. Gill·M. Keyl·B. Kuemmerer·H. Maassen·R. F. Werner
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Abstract

We consider a quantum version of a well-known statistical decision problem, whose solution is, at first sight, counter-intuitive to many. In the quantum version a continuum of possible choices (rather than a finite set) has to be considered. It can be phrased as a two person game between a player P and a quiz master Q. Then P always has a strategy at least as good as in the classical case, while Q's best strategy results in a game having the same value as the classical game. We investigate the consequences of Q storing his information in classical or quantum ways. It turns out that Q's optimal strategy is to use a completely entangled quantum notepad, on which to encode his prior information.

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G. M. D'Ariano, R. D. Gill, M. Keyl, B. Kuemmerer, H. Maassen, R. F. Werner. 2002-02-21. The Quantum Monty Hall Problem. https://arxiv.org/abs/quant-ph/0202120

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