Random Bures mixed states and the distribution of their purity (2009)
Osipov, Vladimir Al., Sommers, Hans-Juergen, Zyczkowski, Karol
Ensembles of random density matrices determined by various probability measures are analysed. A simple and efficient algorithm to generate at random density matrices distributed according to the...
Schur function averages for the real Ginibre ensemble (2009)
Sommers, Hans-Juergen, Khoruzhenko, Boris A
We derive an explicit simple formula for expectations of all Schur functions in the real Ginibre ensemble. It is a positive integer for all entries of the partition even and zero otherwise. The...
Subnormalized states and trace-nonincreasing maps (2007)
Cappellini, Valerio, Sommers, Hans-Juergen, Zyczkowski, Karol
We investigate the set of completely positive, trace-nonincreasing linear maps acting on the set M_N of mixed quantum states of size N. Extremal point of this set of maps are characterized and its...
Distribution of G-concurrence of random pure states (2006)
Cappellini, Valerio, Sommers, Hans-Juergen, Zyczkowski, Karol
Average entanglement of random pure states of an N x N composite system is analyzed. We compute the average value of the determinant D of the reduced state, which forms an entanglement monotone....
Statistical properties of random density matrices (2004)
Sommers, Hans-Juergen, Zyczkowski, Karol
Statistical properties of ensembles of random density matrices are investigated. We compute traces and von Neumann entropies averaged over ensembles of random density matrices distributed according...
Bures volume of the set of mixed quantum states (2003)
Sommers, Hans-Juergen, Zyczkowski, Karol
We compute the volume of the N^2-1 dimensional set M_N of density matrices of size N with respect to the Bures measure and show that it is equal to that of a N^2-1 dimensional hyper-halfsphere of...
Hilbert--Schmidt volume of the set of mixed quantum states (2003)
Zyczkowski, Karol, Sommers, Hans-Juergen
We compute the volume of the convex N^2-1 dimensional set M_N of density matrices of size N with respect to the Hilbert-Schmidt measure. The hyper--area of the boundary of this set is also found and...
Sommers, Hans-Juergen, Savin, Dmitry V., Sokolov, Valentin V.
The probability distribution of the proper delay times during scattering on a chaotic system is derived in the framework of the random matrix approach and the supersymmetry method. The result...
Induced measures in the space of mixed quantum states (2000)
Zyczkowski, Karol, Sommers, Hans-Juergen
We analyze several product measures in the space of mixed quantum states. In particular we study measures induced by the operation of partial tracing. The natural, rotationally invariant measure on...
Savin, Dmitry V., Fyodorov, Yan V., Sommers, Hans-Juergen
We write explicitly a transformation of the scattering phases reducing the problem of quantum chaotic scattering for systems with M statistically equivalent channels at nonideal coupling to that for...
Truncations of random unitary matrices (1999)
Zyczkowski, Karol, Sommers, Hans-Juergen
We analyze properties of non-hermitian matrices of size M constructed as square submatrices of unitary (orthogonal) random matrices of size N>M, distributed according to the Haar measure. In this way...
Haake, Fritz, Sommers, Hans-Juergen, Weber, Joachim
We consider the spectral form factor of random unitary matrices as well as of Floquet matrices of kicked tops. For a typical matrix the time dependence of the form factor looks erratic; only after a...
Almost-Hermitian Random Matrices: Eigenvalue Density in the Complex Plane (1996)
Fyodorov, Yan V., Khoruzhenko, Boris A., Sommers, Hans-Juergen
We consider an ensemble of large non-Hermitian random matrices of the form $\hat{H}+i\hat{A}_s$, where $\hat{H}$ and $\hat{A}_s$ are Hermitian statistically independent random $N\times N$ matrices....