Positive operator valued measures and the quantum Monty Hall problem

A quantum version of the Monty Hall problem, based upon the Positive Operator Valued Measures (POVM) formalism, is proposed. It is shown that basic normalization and symmetry arguments lead univocally to the associated POVM elements, and that the classical probabilities associated with the Monty Hall scenario are recovered for a natural choice of the measurement operators.Facultad de Ciencias Exacta

Quantum version of the Monty Hall problem

©2002 The American Physical SocietyA 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 that obtained with a classical mixed strategy. However, if the initial state involves entanglement of the qutrits 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.A. P. Flitney and D. Abbot

The quantum Monty Hall problem

Treballs Finals de Grau de Física, Facultat de Física, Universitat de Barcelona, Curs: 2019, Tutor: Miquel Montero TorralboWe consider a variation of the Monty Hall problem and we present a quantum version of it in which the quiz show master does not know where the prize is and can accidentally reveal it. We prove that if the quiz show master is allowed to play quantum and the player is not the game becomes a fair game in contrast with the classical version of the gam

Positive operator valued measures and the quantum Monty Hall problem

A quantum version of the Monty Hall problem, based upon the Positive Operator Valued Measures (POVM) formalism, is proposed. It is shown that basic normalization and symmetry arguments lead univocally to the associated POVM elements, and that the classical probabilities associated with the Monty Hall scenario are recovered for a natural choice of the measurement operators.Facultad de Ciencias Exacta

Noisy quantum Monty Hall game

The influence of spontaneous emission channel and generalized Pauli channel on quantum Monty Hall Game is analysed. The scheme of Flittney and Abbott is reformulated using the formalism of density matrices. Optimal classical strategies for given quantum strategies are found. The whole presented scheme illustrates how quantum noise may change the odds of a zero-sum game.Comment: 10 pages, 3 figure