Bi-Free Entropy with Respect to Completely Positive Maps
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arXiv
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| Format: | Preprint |
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2021
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| _version_ | 1866929596545368064 |
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| author | Katsimpas, Georgios Skoufranis, Paul |
| author_facet | Katsimpas, Georgios Skoufranis, Paul |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2106_13114 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Bi-Free Entropy with Respect to Completely Positive Maps Katsimpas, Georgios Skoufranis, Paul Operator Algebras 46L54, 46L53 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. |
| title | Bi-Free Entropy with Respect to Completely Positive Maps |
| topic | Operator Algebras 46L54, 46L53 |
| url | https://arxiv.org/abs/2106.13114 |