The Connes-Kirchberg Problem and infinite-dimensional phenomena in quantum information theory
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911294238490624 |
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| author | Musat, Magdalena |
| author_facet | Musat, Magdalena |
| contents | We give an overview of results tying together a circle of problems connected to the Connes Embedding Problem, Kirchberg's reformulations thereof, Tsirelson's conjecture and its relation to quantum information theory, and a class of quantum channels, called factorizable, introduced by Anantharaman-Delaroche. While parts of the article are more expository, there are new results, including obstructions for channels to being $k$-noisy (admitting a factorization through a full matrix algebra). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_00432 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Connes-Kirchberg Problem and infinite-dimensional phenomena in quantum information theory Musat, Magdalena Operator Algebras 46L10, 81P45, 47L90 We give an overview of results tying together a circle of problems connected to the Connes Embedding Problem, Kirchberg's reformulations thereof, Tsirelson's conjecture and its relation to quantum information theory, and a class of quantum channels, called factorizable, introduced by Anantharaman-Delaroche. While parts of the article are more expository, there are new results, including obstructions for channels to being $k$-noisy (admitting a factorization through a full matrix algebra). |
| title | The Connes-Kirchberg Problem and infinite-dimensional phenomena in quantum information theory |
| topic | Operator Algebras 46L10, 81P45, 47L90 |
| url | https://arxiv.org/abs/2512.00432 |