We investigate completely positive maps for an open system interacting with its environment. The families of the initial states for which the reduced dynamics can be described by a completely positive map are identified within the framework of direct-sum decomposition of state space. They include not only separable states with vanishing or nonvanishing quantum discord but also entangled states. A general expression of the families as well as the Kraus operators for the completely positive maps are explicitly given. It significantly extends the previous results.We investigate completely positive maps for an open system interacting with its environment. The families of the initial states for which the reduced dynamics can be described by a completely positive map are identified within the framework of direct-sum decomposition of state space. They include not only separable states with vanishing or nonvanishing quantum discord but also entangled states. A general expression of the families as well as the Kraus operators for the completely positive maps are explicitly given. It significantly extends the previous results.

arXiv:1407.2051Physical Review AJul 7, 201419 citations

Completely positive mappings in quantum dynamics and measurement theory

Paul Busch, PEKKA J. LAHTI

Foundations of PhysicsDec 1, 199019 citations

Spectral and ergodic properties of completely positive maps and decoherence

Francesco Fidaleo, Federico Ottomano, Stefano Rossi

In an attempt to propose more general conditions for decoherence to occur, we study spectral and ergodic properties of unital, completely positive maps on not necessarily unital $C^*$ -algebras, with a particular focus on gapped maps for which the transient portion of the arising dynamical system can be separated from the persistent one. After some general results, we first devote our attention to the abelian case by investigating the unital $*$ -endomorphisms of, in general non-unital, $C^*$ -algebras, and their spectral structure. The finite-dimensional case is also investigated in detail, and examples are provided of unital completely positive maps for which the persistent part of the associated dynamical system is equipped with the new product making it a $C^*$ -algebra, and the map under consideration restricts to a unital $*$ -automorphism for this new $C^*$ -structure, thus generating a conservative dynamics on that persistent partIn an attempt to propose more general conditions for decoherence to occur, we study spectral and ergodic properties of unital, completely positive maps on not necessarily unital $C^*$-algebras, with a particular focus on gapped maps for which the transient portion of the arising dynamical system can be separated from the persistent one. After some general results, we first devote our attention to the abelian case by investigating the unital $*$-endomorphisms of, in general non-unital, $C^*$-algebras, and their spectral structure. The finite-dimensional case is also investigated in detail, and examples are provided of unital completely positive maps for which the persistent part of the associated dynamical system is equipped with the new product making it a $C^*$-algebra, and the map under consideration restricts to a unital $*$-automorphism for this new $C^*$-structure, thus generating a conservative dynamics on that persistent part

Jan 1, 20226 citations

Quantum dynamical semigroups and non-decomposable positive maps

Fabio Benatti, Roberto Floreanini B, Marco Piani

arXiv:quant-ph/0401146Physics Letters AMay 8, 200422 citations

In an attempt to propose more general conditions for decoherence to occur, we study spectral and ergodic properties of unital, completely positive maps on not necessarily unital

C^*

-algebras, with a particular focus on gapped maps for which the transient portion of the arising dynamical system can be separated from the persistent one. After some general results, we first devote our attention to the abelian case by investigating the unital

*

-endomorphisms of, in general non-unital,

C^*

-algebras, and their spectral structure. The finite-dimensional case is also investigated in detail, and examples are provided of unital completely positive maps for which the persistent part of the associated dynamical system is equipped with the new product making it a

C^*

-algebra, and the map under consideration restricts to a unital

*

-automorphism for this new

C^*

-structure, thus generating a conservative dynamics on that persistent part