2008/08/31 by Luis J. Boya, Kuldeep Dixit · 16 citations
Computer Science · Mathematics · Physics and Astronomy · #Combinatorics #Eigenvalues and eigenvectors #Geometry #Group (periodic table) #Interpretation (philosophy) #Mathematics #Measure (data warehouse) #Noncommutative and Quantum Gravity Theories #Physics #Polytope #Pure mathematics #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum mechanics #quant-ph
paper · pdf · doi:10.1103/physreva.78.042108
published in Physical Review A 78(4) (American Physical Society) · 7 pages, 6 figures
arxiv created 2008/09/21 · openalex publication_date 2008/10/17 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We reconsider the geometry of pure and mixed states in a finite quantum system. The ranges of eigenvalues of the density matrices delimit a regular symplex (hypertetrahedron TN) in any dimension N; the polytope isometry group is the symmetric group SN+1, and splits TN in chambers, the orbits of the states under the projective group PU(N+1). The type of states correlates with the vertices, edges, faces, etc., of the polytope, with the vertices making up a base of orthogonal pure states. The entropy function as a measure of the purity of these states is also easily calculable; we draw and consider some isentropic surfaces. The Casimir invariants acquire then also a more transparent interpretation.