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Triangle room paradox of negative probabilities of events

Vorobyev, Oleg Yu. (2016): Triangle room paradox of negative probabilities of events. Published in: Proceedings of the XV FAMEMS-2016 Conference and the Workshop on Hilbert's sixth problem, Krasnoyarsk, Russia (30 September 2016): pp. 94-97.

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Abstract

Here an improved generalization of Feynman’s paradox of negative probabilities [1, 2] for observing three events is considered. This version of the paradox is directly related to the theory of quantum computing. Imagine a triangular room with three windows, where there are three chairs, on each of which a person can seat [4]. In any of the windows, an observer can see only the corresponding pair of chairs. It is known that if the observer looks at a window (to make a pairwise observation), the picture will be in the probabilistic sense the same for all windows: only one chair from the observed pair is occupied with a probability of 1/2, and there are never busy or free both chairs at once. Paradoxically, existing theories based on Kolmogorov’s probability theory do not answer the question that naturally arises after such pairs of observations of three events: «What is really happening in a triangular room, how many people are there and with what is the probability distribution they are sitting on three chairs?».

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