Covariant decomposable maps on C*-algebras and quantum dynamics

2025/04/01 by Szczygielski, Krzysztof
#FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Operator Algebras (math.OA) #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.2504.01176

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 \mathbbM_n(ℂ), covariant with respect to the maximal commutative subgroup of 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.

Related

• Decomposable dynamics on matrix algebras
• Decomposable semigroups on C*-algebras and D-divisible dynamical maps
• Extensions and Dilations for C^*-dynamical Systems
• A resolution of quantum dynamical semigroups
• Spectral and ergodic properties of completely positive maps and decoherence