Rényi Entropy, Signed Probabilities, and the Qubit
Abstract
1. Introduction
2. Preliminaries
3. Rényi Entropy
4. Main Theorem
This says that we allow as potential quantum states only those states containing a minimum amount of uncertainty, as measured by the entropy of a corresponding probability distribution on phase space. Note that our Uncertainty Principle is a sequence of conditions, one for each k. This is because Rényi entropy itself is not a single functional but a sequence of functionals (indexed by k).Uncertainty Principle: A potential quantum state satisfies the Uncertainty Principle if for every k, there is a phase-space probability distribution that represents and satisfies .
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
- 1.
- Ifis a solution then so isfor any.
- 2.
- Ifis a solution thenis a solution, whereis obtained fromby permuting coordinates.
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Brandenburger, A.; La Mura, P.; Zoble, S. Rényi Entropy, Signed Probabilities, and the Qubit. Entropy 2022, 24, 1412. https://doi.org/10.3390/e24101412
Brandenburger A, La Mura P, Zoble S. Rényi Entropy, Signed Probabilities, and the Qubit. Entropy. 2022; 24(10):1412. https://doi.org/10.3390/e24101412
Chicago/Turabian StyleBrandenburger, Adam, Pierfrancesco La Mura, and Stuart Zoble. 2022. "Rényi Entropy, Signed Probabilities, and the Qubit" Entropy 24, no. 10: 1412. https://doi.org/10.3390/e24101412
APA StyleBrandenburger, A., La Mura, P., & Zoble, S. (2022). Rényi Entropy, Signed Probabilities, and the Qubit. Entropy, 24(10), 1412. https://doi.org/10.3390/e24101412