Ruminations on Matrix Convexity and the Strong Subadditivity of Quantum Entropy
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866910541770915840 |
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| author | Aizenman, Michael Cipolloni, Giorgio |
| author_facet | Aizenman, Michael Cipolloni, Giorgio |
| contents | The familiar second derivative test for convexity, combined with resolvent calculus, is shown to yield a useful tool for the study of convex matrix-valued functions. We demonstrate the applicability of this approach on a number of theorems in this field. These include convexity principles which play an essential role in the Lieb-Ruskai proof of the strong subadditivity of quantum entropy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_10729 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Ruminations on Matrix Convexity and the Strong Subadditivity of Quantum Entropy Aizenman, Michael Cipolloni, Giorgio Quantum Physics Statistical Mechanics Information Theory Mathematical Physics 81Q05, 82B10, 26B25, 47H05 The familiar second derivative test for convexity, combined with resolvent calculus, is shown to yield a useful tool for the study of convex matrix-valued functions. We demonstrate the applicability of this approach on a number of theorems in this field. These include convexity principles which play an essential role in the Lieb-Ruskai proof of the strong subadditivity of quantum entropy. |
| title | Ruminations on Matrix Convexity and the Strong Subadditivity of Quantum Entropy |
| topic | Quantum Physics Statistical Mechanics Information Theory Mathematical Physics 81Q05, 82B10, 26B25, 47H05 |
| url | https://arxiv.org/abs/2210.10729 |