The quantum monty hall problem

  • Authors:

  • G. M. D'ariano;R. D. Gill;M. Keyl;R. F. Werner;B. Kümmerer;H. Maassen

  • Affiliations:

  • Quantum Optics and Information Group, Institute Nazionale de Fisica delta Materia, Unita di Pavia, Dipartimento di Fisica "A Volta", Pavia, Italy;Deptartment of Mathematics, University of Utrecht, Utrecht, Netherlands;Institut für Mathematische Physik, TU-Braunschweig, Braunschweig, Germany;Institut für Mathematische Physik, TU-Braunschweig, Braunschweig, Germany;Mathematisches Institut A, University of Stuttgart, Stuttgart, Germany;Subfaculteit Wiskunde, University of Nijmegen, Nijmegen, The Netherlands

  • Venue:
  • Quantum Information & Computation
  • Year:
  • 2002

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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.