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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Aczél, J.: Lectures on Functional Equations and Their Applications. Dover, New York (2006)
Dirac, P.A.M.: The physical interpretation of quantum mechanics. Proc. Royal Soc. A: Math. Phys. Eng. Sci. 180(980), 1–39 (1942)
Feynman, R.P.: Negative probability. In: Peat, F.D., Hiley, B. (eds.) Quantum Implications: Essays in Honour of David Bohm, pp. 235–248. Routledge & Kegan Paul Ltd., Abingdon-on-Thames, UK (1987)
Feynman, R., Leighton, R., Sands, M.: The Feynman Lectures on Physics. Addison Wesley, Boston, Massachusetts (2005)
Fishburn, P.C.: Utility Theory for Decision Making. Wiley, New York (1969)
Kreinovich, V., Ferson, S.: A new Cauchy-based black-box technique for uncertainty in risk analysis. Reliab. Eng. Syst. Saf. 85(1–3), 267–279 (2004)
Luce, R.D., Raiffa, R.: Games and Decisions: Introduction and Critical Survey. Dover, New York (1989)
Nguyen, H.T., Kosheleva, O., Kreinovich, V.: Decision making beyond Arrow’s ‘impossibility theorem’, with the analysis of effects of collusion and mutual attraction. Int. J. Intell. Syst. 24(1), 27–47 (2009)
Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge, U.K. (2000)
Rabinovich, S.G.: Measurement Errors and Uncertainty. Theory and Practice. Springer Verlag, Berlin (2005)
Raiffa, H.: Decision Analysis. Addison-Wesley, Reading, Massachusetts (1970)
Samorodnitsky, G., Taqqu, M.S.: Stable Non-Gaussian Random Proceses Stochastic Models with Infinite Variance. Chapman & Hall, New York (1994)
Sheskin, D.J.: Handbook of Parametric and Nonparametric Statistical Procedures. Chapman and Hall/CRC, Boca Raton, Florida (2011)
Acknowledgements
This work was supported in part:
\(\bullet \) by the National Science Foundation grants
\(\quad \bullet \) HRD-0734825 and HRD-1242122 (Cyber-ShARE Center of Excellence) and
\(\quad \bullet \) DUE-0926721, and
\(\bullet \) by the award “UTEP and Prudential Actuarial Science Academy and Pipeline Initiative” from Prudential Foundation.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this chapter
Cite this chapter
Pownuk, A., Kreinovich, V. (2018). (Hypothetical) Negative Probabilities Can Speed Up Uncertainty Propagation Algorithms. In: Hassanien, A., Elhoseny, M., Kacprzyk, J. (eds) Quantum Computing:An Environment for Intelligent Large Scale Real Application . Studies in Big Data, vol 33. Springer, Cham. https://doi.org/10.1007/978-3-319-63639-9_11
Download citation
DOI: https://doi.org/10.1007/978-3-319-63639-9_11
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-63638-2
Online ISBN: 978-3-319-63639-9
eBook Packages: EngineeringEngineering (R0)