2013/04/30 by Gilad Gour, Nolan R. Wallach · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1103/physrevlett.111.060502
published as Phys. Rev. Lett. 111, 060502 (2013) · 5+10 pages, published version
openalex publication_date 2013/08/08 · arxiv created 2013/08/15 · arxiv updated 2013/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We provide a systematic classification of multiparticle entanglement in terms of equivalence classes of states under stochastic local operations and classical communication (SLOCC). We show that such an SLOCC equivalency class of states is characterized by ratios of homogenous polynomials that are invariant under local action of the special linear group. We then construct the complete set of all such SL-invariant polynomials (SLIPs). Our construction is based on Schur-Weyl duality and applies to any number of qudits in all (finite) dimensions. In addition, we provide an elegant formula for the dimension of the homogenous SLIPs space of a fixed degree as a function of the number of qudits. The expressions for the SLIPs involve in general many terms, but for the case of qubits we also provide much simpler expressions.