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- Publisher
- Springer International Publishing
- Copyright
- © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
- ISBN
- 978-3-030-76103-5
- Pages
- 27 –37
- DOI
- 10.1007/978-3-030-76104-2_3
- Publisher site
- See Chapter on Publisher Site
Abstract
[Because we can treat quantum states as probability distributions, we can apply the concepts and methods of probability theory to them, including Shannon’s theory of information. The structures that I will discuss in the following sections came to my attention thanks to Shannon theory. In particular, the question of recurring interest is, “Out of all the extremal states of quantum state space—i.e., the ‘pure’ states ρ=ψ⟩⟨ψ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho = {\left| \psi \big \rangle \!\big \langle \psi \right| }$$\end{document}—which minimize the Shannon entropy of their probabilistic representation?” I will focus on the cases of dimensions 2, 3 and 8, where the so-called sporadic SICs occur. In these cases, the information-theoretic question of minimizing Shannon entropyShannon entropy leads to intricate geometrical structures.]
Published: Jun 1, 2021