In this article we provide a review of geometrical methods employed in the analysis of
quantum phase transitions and non-equilibrium dissipative phase transitions. After a …

The purpose of this review is to present some of the latest developments using random
techniques, and in particular, random matrix techniques in quantum information theory. Our …

Quantum information theory is a branch of science at the frontier of physics, mathematics,
and information science, and offers a variety of solutions that are impossible using classical …

Several well-established geometric and topological methods underscore the mathematical
treatment of the subject, emphasizing a coherent perspective at a rather sophisticated level …

We study various methods to generate ensembles of random density matrices of a fixed size
N, obtained by partial trace of pure states on composite systems. Structured ensembles of …

The eigenvalues of a parameter-dependent Hamiltonian matrix form a band structure in
parameter space. In such N-band systems, the quantum geometric tensor (QGT), consisting …

We compute the volume of the (N 2− 1)-dimensional set Script MN of density matrices of size
N with respect to the Bures measure and show that it is equal to that of an (N 2− 1) …

Statistical properties of ensembles of random density matrices are investigated. We compute
traces and von Neumann entropies averaged over ensembles of random density matrices …

Bloch-vector spaces for N-level systems are investigated from the spherical-coordinate point
of view in order to understand their geometrical aspects. We present a characterization of …

Various problems concerning the geometry of the space of Hermitian operators on a Hilbert
space are addressed. In particular, we study the canonical Poisson and Riemann–Jordan …