Rényi entropy, signed probabilities, and the qubit
- The states of the qubit, the basic unit of quantum information, are 2×2 positive semi-definite Hermitian matrices with trace 1. We contribute to the program to axiomatize quantum mechanics by characterizing these states in terms of an entropic uncertainty principle formulated on an eight-point phase space. We do this by employing Rényi entropy (a generalization of Shannon entropy) suitably defined for the signed phase-space probability distributions that arise in representing quantum states.
| Document Type: | Article |
|---|---|
| Language: | English |
| Author: | Adam BrandenburgerORCiD, Pierfrancesco La MuraORCiD, Stuart Zoble |
| Chairs and Professorships: | Chair of Economics and Information Systems |
| DOI: | https://doi.org/10.3390/e24101412 |
| Parent Title (English): | Entropy : an international and interdisciplinary journal of entropy and information studies |
| ISSN: | 1099-4300 |
| Volume: | 24 |
| Issue: | 10 |
| Year of Completion: | 2022 |
| Article Number: | 1412 |
| Tag: | Quibit; Rényi entropy; Signed probability; Uncertainty principle |
| Note: | This article belongs to the special issue "Rényi entropy : sixty years later" (2022) |
| Content Focus: | Academic Audience |
| Peer Reviewed: | Yes |
| Rankings: | SJR Ranking / Q2 |
| Licence (German): |  Creative Commons - CC BY - Namensnennung 4.0 International |