2008/09/11 by Andreas Osterloh, A. Osterloh · 1 citation
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #quant-ph
paper · pdf · doi:10.1007/s00340-009-3859-3
published as Appl. Phys. B 98, 609 (2010). The final publication is available at www.springerlink.com. · 9 pages, 10 figures, revtex4
arxiv created 2008/09/11 · openalex publication_date 2010/01/06 · arxiv updated 2010/03/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/29
The role of SU(2) invariants for the classification of multiparty entanglement is discussed and exemplified for the Kempe invariant I5 of pure three-qubit states. It is found to being an independent invariant only in presence of both W-type entanglement and threetangle. In this case, constant I5 admits for a wide range of both threetangle and concurrences. Furthermore, the present analysis indicates that an SL3 orbit of states with equal tangles but continuously varying I5 must exist. This means that I5 provides no information on the entanglement in the system in addition to that contained in the tangles (concurrences and threetangle) themselves. Together with the numerical evidence that I5 is an entanglement monotone this implies that SU(2) invariance or the monotone property are too weak requirements for the characterization and quantification of entanglement for systems of three qubits, and that SL(2,C) invariance is required. This conclusion can be extended to general multipartite systems (including higher local dimension) because the entanglement classes of three-qubit systems appear as subclasses.