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arXiv · 1306.5372

Remarks on free mutual information and orbital free entropy

Masaki Izumi·Yoshimichi Ueda
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Abstract

The present notes provide a proof of $i^*(\mathbb{C}P+\mathbb{C}(I-P)\,;\mathbb{C}Q+\mathbb{C}(I-Q)) = -\chi_\mathrm{orb}(P,Q)$ for any pair of projections $P,Q$ with $\tau(P)=\tau(Q)=1/2$. The proof includes new extra observations, such as a subordination result in terms of Loewner equations. A study of the general case is also given.

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Masaki Izumi, Yoshimichi Ueda. 2013-06-23. Remarks on free mutual information and orbital free entropy. https://doi.org/10.1215/00277630-3335530

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