On positive maps in quantum information
Wladyslaw A. Majewski
TL;DR
This paper reviews positive maps in quantum information using Grothendieck's tensor product approach, discusses PPT states, and introduces a generalized concept of Choi matrices for quantum systems.
Contribution
It provides a Grothendieck-based characterization of positive maps and generalizes Choi matrices for quantum systems, advancing theoretical understanding.
Findings
Characterization of positive maps via Grothendieck approach
Belavkin-Ohya characterization of PPT states
Generalization of Choi matrices for quantum systems
Abstract
Using Grothendieck approach to the tensor product of locally convex spaces we review a characterization of positive maps as well as Belavkin-Ohya characterization of PPT states. Moreover, within this scheme, \textit{ a generalization of the idea of Choi matrices for genuine quantum systems will be presented}.
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