Abstract
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 ) in any dimension ; the polytope isometry group is the symmetric group , and splits in chambers, the orbits of the states under the projective group . 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.
- Received 7 August 2008
DOI:https://doi.org/10.1103/PhysRevA.78.042108
©2008 American Physical Society