On bipartite operators defined by sets of completely different permutations. (English) Zbl 1445.81007
The authors introduce a class of bipartite operators acting on \(H\otimes H\) (\(H\) being an \(n\)-dimensional Hilbert space) defined by a set of \(n\) Completely Different Permutations (CDPs).
It is shown that any set of CDPs gives rise to a certain direct sum decomposition of the total Hilbert space which enables one simple construction of the corresponding bipartite operator.
In particular, if set of CDPs defines an abelian group, then the corresponding bipartite operator displays an additional property – the partially transposed operator again corresponds to (in general different) set of CDPs.
The technique may be used to construct new classes of the so-called PPT (positive under partial transposition) states which are of great importance for quantum information.
Reviewer: Jiangtao Yuan (Henan)
MSC:
| 81P40 | Quantum coherence, entanglement, quantum correlations |
| 81P16 | Quantum state spaces, operational and probabilistic concepts |
| 20B30 | Symmetric groups |
| 15B48 | Positive matrices and their generalizations; cones of matrices |
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