Stratificational and antipodean properties of boundary states for N x N density matrices

Details Stratificational and antipodean properties of boundary states for N x N density matrices Stratificational and antipodean properties of boundary states for N x N density matrices

2007-07-20

arxiv.org/abs/0707.3094v1

Physics

Quantum Physics

9 pages

Scientific paper

We investigate the space of N x N dimensional density matrices. We show that there exist strata such that boundary states \rho_{p} with p zero eigenvalues lie on or outside the spheres with radii r_{p}=\sqrt{p/N(N-p)}. Moreover, we show that if in a certain direction there is a boundary state with q=N-p equal eigenvalues, then in the opposite (antipodean) direction exists a boundary state with p=N-q equal eigenvalues.

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