Mathematics – Operator Algebras
Scientific paper
2011-07-12
Mathematics
Operator Algebras
32 pages
Scientific paper
10.1016/j.jfa.2011.11.009
An operator system $\cl S$ with unit $e$, can be viewed as an Archimedean order unit space $(\cl S,\cl S^+,e)$. Using this Archimedean order unit space, for a fixed $k\in \bb N$ we construct a super k-minimal operator system OMIN$_k(\cl S)$ and a super k-maximal operator system OMAX$_k(\cl S)$, which are the general versions of the minimal operator system OMIN$(\cl S)$ and the maximal operator system OMAX$(\cl S)$ introduced recently, such that for $k=1$ we obtain the equality, respectively. We develop some of the key properties of these super operator systems and make some progress on characterizing when an operator system $\cl S$ is completely boundedly isomorphic to either OMIN$_k(\cl S)$ or to OMAX$_k(\cl S)$. Then we apply these concepts to the study of k-partially entanglement breaking maps. We prove that for matrix algebras a linear map is completely positive from OMIN$_k(M_n)$ to OMAX$_k(M_m)$ for some fixed $k\le \min(n,m)$ if and only if it is a k-partially entanglement breaking map.
No associations
LandOfFree
The Super Operator System Structures and their applications in Quantum Entanglement Theory does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The Super Operator System Structures and their applications in Quantum Entanglement Theory, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Super Operator System Structures and their applications in Quantum Entanglement Theory will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-565990