Related papers: Covariant decomposable maps on C*-algebras and quantum dynamics

Covariant decomposable maps on C*-algebras and quantum dynamics

URL: http://arxiv.org/abs/2504.01176v1
Date: Tue, 01 Apr 2025 20:32:52 GMT
Title: Covariant decomposable maps on C*-algebras and quantum dynamics
Authors: Krzysztof Szczygielski,
Abstract summary: We provide a certain characterization of the operator sum representation of maps on $mathbbM_n (mathbbC)$.<n>A connection to quantum dynamics is established by specifying sufficient and necessary conditions for covariance of D-divisible quantum evolution families.
Score: 0.0
License: http://creativecommons.org/licenses/by/4.0/
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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