Geodesic
Bi-free entropy with respect to completely positive maps
Canadian journal of mathematics, Tome 76 (2024) no. 4, pp. 1163-1239

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DOI

In this paper, a notion of non-microstate bi-free entropy with respect to completely positive maps is constructed thereby extending the notions of non-microstate bi-free entropy and free entropy with respect to a completely positive map. By extending the operator-valued bi-free structures to allow for more analytical arguments, a notion of conjugate variables is constructed using both moment and cumulant expressions. The notions of free Fisher information and entropy are then extended to this setting and used to show minima of the Fisher information and maxima of the non-microstate bi-free entropy at bi-R-diagonal elements.
DOI : 10.4153/S0008414X23000366
Mots-clés : Bi-free probability, entropy, completely positive maps, bi-free cumulants, bi-R-diagonals 
Katsimpas, Georgios; Skoufranis, Paul. Bi-free entropy with respect to completely positive maps. Canadian journal of mathematics, Tome 76 (2024) no. 4, pp. 1163-1239. doi: 10.4153/S0008414X23000366
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     title = {Bi-free entropy with respect to completely positive maps},
     journal = {Canadian journal of mathematics},
     pages = {1163--1239},
     year = {2024},
     volume = {76},
     number = {4},
     doi = {10.4153/S0008414X23000366},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008414X23000366/}
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