2002/02/28 by Todd Tilma, Mark Byrd, Mark S. Byrd +2 · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Algebraic structures and combinatorial models #Bipartite graph #Element (criminal law) #Euler angles #Euler's formula #Parametrization (atmospheric modeling) #Quantum #Quantum Information and Cryptography #Quantum entanglement #Qubit #math-ph #math.MP
paper · pdf · doi:10.1088/0305-4470/35/48/315
published as J. Phys. A: Math. Gen. 35 (2002) 10445-10465 · 23 pages, no figures; changed title and abstract and rewrote certain areas in line with referee comments. To be published in J. Phys. A: Math. and Gen
arxiv created 2002/11/06 · openalex publication_date 2002/11/19 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
In this paper we give an explicit parametrization for all two-qubit density matrices. This is important for calculations involving entanglement and many other types of quantum information processing. To accomplish this we present a generalized Euler angle parametrization for SU (4) and all possible two-qubit density matrices. The important group-theoretical properties of such a description are then manifest. We thus obtain the correct Haar (Hurwitz) measure and volume element for SU (4) which follows from this parametrization. In addition, we study the role of this parametrization in the Peres–Horodecki criteria for separability and its corresponding usefulness in calculating entangled two-qubit states as represented through the parametrization.