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Random unistochastic matrices
K. Zyczkowski, W. Slomczynski, M. Kus +1
An ensemble of random unistochastic (orthostochastic) matrices is defined by taking squared moduli of elements of random unitary (orthogonal) matrices distributed according to the…
Manifolds of interconvertible pure states
Magdalena M. Sinolecka, Karol Zyczkowski, Marek Kus
Local orbits of a pure state of an N x N bi-partite quantum system are analyzed. We compute their dimensions which depends on the degeneracy of the vector of coefficients arising b…
Families of line-graphs and their quantization
Prot Pakonski, Gregor Tanner, Karol Zyczkowski
Any directed graph G with N vertices and J edges has an associated line-graph L(G) where the J edges form the vertices of L(G). We show that the non-zero eigenvalues of the adjacen…
CP^n, or, entanglement illustrated
I. Bengtsson, J. Braennlund, K. Zyczkowski
We show that many topological and geometrical properties of complex projective space can be understood just by looking at a suitably constructed picture. The idea is to view CP^n a…
Fractality of certain quantum states
Daniel Wojcik, Karol Zyczkowski
We prove the theorem announced in Phys. Rev. Lett. {\bf 85}:5022, 2001 concerning the existence and properties of fractal states for the Schrödinger equation in the infinite one-di…
Spectrum of the Frobenius-Perron operator for systems with stochastic perturbation
A. Ostruszka, K. Zyczkowski
We analyze the problem of evolution in a system with stochastic perturbation and point out that analytic properties of the noise present in the system might determine spectral prop…