2008/04/30 by Andreas Osterloh, D. Ž. Ðoković, Dragomir Z. Djokovic +1 · 9 citations
Computer Science · Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #quant-ph
paper · pdf · doi:10.1063/1.3075830
published as J. Math. Phys. 50, 033509 (2009). · 29 pages, 3 eps figures, aipproc. Minor modifications and corrections. Length change only due to style change
arxiv created 2009/02/17 · openalex publication_date 2009/03/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
It is a recent observation that entanglement classification for qubits is closely related to local SL(2,\CC)-invariants including the invariance under qubit permutations, which has been termed SL^* invariance. In order to single out the SL^* invariants, we analyze the SL(2,\CC)-invariants of four resp. five qubits and decompose them into irreducible modules for the symmetric group S4 resp. S5 of qubit permutations. A classifying set of measures of genuine multipartite entanglement is given by the ideal of the algebra of SL^*-invariants vanishing on arbitrary product states. We find that low degree homogeneous components of this ideal can be constructed in full by using the approach introduced in [Phys. Rev. A 72, 012337 (2005)]. Our analysis highlights an intimate connection between this latter procedure and the standard methods to create invariants, such as the Ω-process. As the degrees of invariants increase, the alternative method proves to be particularly efficient.