Covariant decomposable maps on C*-algebras and quantum dynamics

Krzysztof Szczygielski

doi:10.1016/j.laa.2025.12.002

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arXiv · 2504.01176

Covariant decomposable maps on C*-algebras and quantum dynamics

Krzysztof Szczygielski

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Abstract

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.

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BibTeX RIS

Krzysztof Szczygielski. 2025-04-01. Covariant decomposable maps on C*-algebras and quantum dynamics. https://doi.org/10.1016/j.laa.2025.12.002

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