(Hypothetical) Negative Probabilities Can Speed Up Uncertainty Propagation Algorithms

Authors

Andrzej Pownuk, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

2-2017

Comments

Technical Report: UTEP-CS-17-08a

To appear in Aboul Ella Hassanien, Mohamed Elhoseny, Ahmed Farouk, and Janusz Kacprzyk (eds.), Quantum Computing: an Environment for Intelligent Large Scale Real Application, Springer Verlag

Abstract

One of the main features of quantum physics is that, as basic objects describing uncertainty, instead of (non-negative) probabilities and probability density functions, we have complex-valued probability amplitudes and wave functions. In particular, in quantum computing, negative amplitudes are actively used. In the current quantum theories, the actual probabilities are always non-negative. However, there have been some speculations about the possibility of actually negative probabilities. In this paper, we show that such hypothetical negative probabilities can lead to a drastic speed up of uncertainty propagation algorithms.