Involutive Markov categories and the quantum de Finetti theorem
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Acceso en línea: | |
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| _version_ | 1866908791716446208 |
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| author | Fritz, Tobias Lorenzin, Antonio |
| author_facet | Fritz, Tobias Lorenzin, Antonio |
| contents | Markov categories have recently emerged as a powerful high-level framework for probability theory and theoretical statistics. Here we study a quantum version of this concept, called involutive Markov categories. These are equivalent to Parzygnat's quantum Markov categories, but we argue that they offer a simpler and more practical approach. Our main examples of involutive Markov categories have pre-C*-algebras, including infinite-dimensional ones, as objects, together with completely positive unital maps as morphisms in the picture of interest. In this context, we prove a quantum de Finetti theorem for both the minimal and the maximal C*-tensor norms, and we develop a categorical description of such quantum de Finetti theorems which amounts to a universal property of state spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_09666 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Involutive Markov categories and the quantum de Finetti theorem Fritz, Tobias Lorenzin, Antonio Category Theory Operator Algebras Quantum Physics Markov categories have recently emerged as a powerful high-level framework for probability theory and theoretical statistics. Here we study a quantum version of this concept, called involutive Markov categories. These are equivalent to Parzygnat's quantum Markov categories, but we argue that they offer a simpler and more practical approach. Our main examples of involutive Markov categories have pre-C*-algebras, including infinite-dimensional ones, as objects, together with completely positive unital maps as morphisms in the picture of interest. In this context, we prove a quantum de Finetti theorem for both the minimal and the maximal C*-tensor norms, and we develop a categorical description of such quantum de Finetti theorems which amounts to a universal property of state spaces. |
| title | Involutive Markov categories and the quantum de Finetti theorem |
| topic | Category Theory Operator Algebras Quantum Physics |
| url | https://arxiv.org/abs/2312.09666 |