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arXiv · 0808.1930

Geometry of density sates

Luis J. Boya·Kuldeep Dixit
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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.

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Luis J. Boya, Kuldeep Dixit. 2008-09-21. Geometry of density sates. https://doi.org/10.1103/physreva.78.042108

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