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): | ![]() |