2006/05/08 by Jon Magne Leinaas, Jan Myrheim, Eirik Ovrum · 1 citation
Computer Science · Physics and Astronomy · #Quantum Electrodynamics and Casimir Effect #Quantum Information and Cryptography #Quantum Mechanics and Applications #quant-ph
paper · pdf · doi:10.1103/physreva.74.012313
31 pages, 6 figures
arxiv created 2006/05/08 · openalex publication_date 2006/07/19 · arxiv updated 2013/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study geometrical aspects of entanglement, with the Hilbert--Schmidt norm defining the metric on the set of density matrices. We focus first on the simplest case of two two-level systems and show that a ``relativistic'' formulation leads to a complete analysis of the question of separability. Our approach is based on Schmidt decomposition of density matrices for a composite system and nonunitary transformations to a standard form. The positivity of the density matrices is crucial for the method to work. A similar approach works to some extent in higher dimensions, but is a less powerful tool. We further present a numerical method for examining separability and illustrate the method by a numerical study of bound entanglement in a composite system of two three-level systems.