Covariant decomposable maps on C*-algebras and quantum dynamics
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912750473576448 |
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| author | Szczygielski, Krzysztof |
| author_facet | Szczygielski, Krzysztof |
| contents | We characterize covariant positive decomposable maps between unital C*-algebras in terms of a dilation theorem, which generalizes a seminal result by H. Scutaru from Rep. Math. Phys. 16 (1):79-87, 1979. As a case study, we provide a certain characterization of the operator sum representation of maps on $\mathbb{M}_{n}(\mathbb{C})$, covariant with respect to the maximal commutative subgroup of $\mathrm{U}(n)$. A connection to quantum dynamics is established by specifying sufficient and necessary conditions for covariance of D-divisible (decomposably divisible) quantum evolution families, recently introduced in J. Phys. A: Math. Theor. 56 (2023) 485202. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_01176 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Covariant decomposable maps on C*-algebras and quantum dynamics Szczygielski, Krzysztof Operator Algebras Mathematical Physics Functional Analysis Quantum Physics We characterize covariant positive decomposable maps between unital C*-algebras in terms of a dilation theorem, which generalizes a seminal result by H. Scutaru from Rep. Math. Phys. 16 (1):79-87, 1979. As a case study, we provide a certain characterization of the operator sum representation of maps on $\mathbb{M}_{n}(\mathbb{C})$, covariant with respect to the maximal commutative subgroup of $\mathrm{U}(n)$. A connection to quantum dynamics is established by specifying sufficient and necessary conditions for covariance of D-divisible (decomposably divisible) quantum evolution families, recently introduced in J. Phys. A: Math. Theor. 56 (2023) 485202. |
| title | Covariant decomposable maps on C*-algebras and quantum dynamics |
| topic | Operator Algebras Mathematical Physics Functional Analysis Quantum Physics |
| url | https://arxiv.org/abs/2504.01176 |