(Hypothetical) Negative Probabilities Can Speed Up Uncertainty Propagation Algorithms
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 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.
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