On Completion of the Cone of Completely Positive Linear Maps with Respect to the Energy-Constrained Diamond Norm
- Авторлар: Shirokov M.1,2
-
Мекемелер:
- Steklov Mathematical Institute of Russian Academy of Sciences
- Moscow Institute of Physics and Technology
- Шығарылым: Том 40, № 10 (2019)
- Беттер: 1549-1568
- Бөлім: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/205760
- DOI: https://doi.org/10.1134/S1995080219100238
- ID: 205760
Дәйексөз келтіру
Аннотация
For a given positive operator G we consider the cones of linear maps between Banach spaces of trace class operators characterized by the Stinespring-like representation with \(\sqrt G \)-bounded and \(\sqrt G \)-infinitesimal operators correspondingly. We prove the completeness of both cones w.r.t. the energy-constrained diamond norm induced by G (as an energy observable) and the coincidence of the second cone with the completion of the cone of completely positive linear maps w.r.t. this norm. We show that the sets of quantum channels and quantum operations are complete w.r.t. the energy-constrained diamond norm for any energy observable. Some properties of the maps belonging to the introduced cones are described. In particular, the corresponding generalization of the Kretschmann-Schlingemann-Werner theorem is obtained. We also give a nonconstructive description of the completion of the set of all Hermitian-preserving completely bounded linear maps w.r.t. the energy-constrained diamond norm.
Авторлар туралы
M. Shirokov
Steklov Mathematical Institute of Russian Academy of Sciences; Moscow Institute of Physics and Technology
Хат алмасуға жауапты Автор.
Email: msh@mi-ras.ru
Ресей, Moscow, 119991; Dolgoprudny, 141701