Geometry of density sates

Abstract

We reconsider the geometry of pure and mixed states in a finite quantum system. The rangesof eigenvalues of the density matrices delimit a regular simplex (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.

7 pages, 6 figures

References in corpus (4)

• Bloch vectors for qudits
• Characterization of the Positivity of the Density Matrix in Terms of the Coherence Vector Representation
• Geometry of quantum systems: density states and entanglement
• Geometry of depolarizing channels

Cited by in corpus (9)

• Qutrit Magic State Distillation
• Geometry of the generalized Bloch sphere for qutrits
• The shape of higher-dimensional state space: Bloch-ball analog for a qutrit
• Parametrizations of density matrices
• Dynamics of Neural Networks with Continuous Attractors
• Coherent and incoherent contents of correlations
• Invariance of Bipartite Separability and PPT-Probabilities over Casimir Invariants of Reduced States
• Characterization of qutrit channels in terms of their covariance and symmetry properties
• Describing orbit space of global unitary actions for mixed qudit states