Positive operator valued measures and the quantum Monty Hall problem

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.

The quantum monty hall problem

The well-known classical Monty Hall problem, also known under various other names [1], is set in the context of a television game show. It can be seen as a two person game, in which a player P tries to win a prize, but a show master (or Quiz master) Q tries to make it difficult for her [2]. Like other games of this sort [3, 4] it can be “quantized”, i.e., its key elements can be formulated in a...

The Monty Hall Problem

A range of solutions to the Monty Hall problem is developed, with the aim of connecting popular (informal) solutions and the formal mathematical solutions of introductory text-books. Under Riemann’s slogan of replacing calculations with ideas, we discover bridges between popular solutions and rigorous (formal) mathematical solutions by using various combinations of symmetry, symmetrization, ind...

The Monty Hall Problem, Reconsidered

Positive Operator-Valued Measures in Quantum Decision Theory

Semantics and Memory Semantic Composition Inspired by Quantum Measurement. . . . . . . . . . . . . . 41 William Blacoe Expansion-by-Analogy: A Vector Symbolic Approach to Semantic Search . . . 54 Trevor Cohen, Dominic Widdows, and Thomas Rindflesch Subadditivity of Episodic Memory States: A Complementarity Approach . . . . 67 Jacob Denolf A Vector Field Approach to Lexical Semantics. . . . . . ...