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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.

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Metadaten
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):License LogoCreative Commons - CC BY - Namensnennung 4.0 International