Related papers: Partial transposition of random states and non-cen…
We provide the probability distribution function of matrix elements each of which is the inner product of two vectors. The vectors we are considering here are independently distributed but not necessarily Gaussian variables. When the number…
We prove that the empirical density of states of quantum spin glasses on arbitrary graphs converges to a normal distribution as long as the maximal degree is negligible compared with the total number of edges. This extends the recent…
Many of the properties of the partial transposition are not clear so far. Here the number of the negative eigenvalues of K(T)(the partial transposition of K) is considered carefully when K is a two-partite state. There are strong evidences…
For a random quantum state on $H=C^d \otimes C^d$ obtained by partial tracing a random pure state on $H \otimes C^s$, we consider the whether it is typically separable or typically entangled. For this problem, we show the existence of a…
We consider the effect of a partial transpose on the limit $*$-distribution of a Haar distributed random unitary matrix. If we fix, $b$, the number of blocks, we show that the partial transpose can be decomposed into a sum of $b$ matrices…
We study the distribution of transmission eigenvalues of a quantum point contact with nearby impurities. In the semi-classical case (the chemical potential lies at the conductance plateau) we find that the transmission properties of this…
From both theoretical and experimental points of view symmetric states constitute an important class of multipartite states. Still, entanglement properties of these states, in particular those with positive partial transposition (PPT), lack…
We study the fluctuations, as $d,n\to \infty$, of the Wishart matrix $\mathcal{W}_{n,d}= \frac{1}{d} \mathcal{X}_{n,d} \mathcal{X}_{n,d}^{T} $ associated to a $n\times d$ random matrix $\mathcal{X}_{n,d}$ with non-Gaussian entries. We…
We study the decay of survival probability at quantum phase transitions (QPT). The semiclassical theory is found applicable in the vicinities of critical points with infinite degeneracy. The theory predicts a power law decay of the survival…
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 random pure states, invariant with respect to local unitary…
The Anderson transition in three dimensions in a randomly varying magnetic flux is investigated in detail by means of the transfer matrix method with high accuracy. Both, systems with and without an additional random scalar potential are…
Dynamical quantum phase transitions (DQPTs) occur at times when a quantum state exhibits a nonanalytic change in its return probability. This can be viewed as the probability of collapsing the evolved state to the initial state by quantum…
We revisit the moment method to obtain a slightly strengthened version of the usual semicircular law. Our version assumes only that the upper triangular entries of Hermitian random matrices are independent, have mean zero and variances…
Two quantum systems, each described as a random-matrix ensemble. are coupled to each other via a number of transition states. Each system is strongly coupled to a large number of channels. The average transmission probability is the product…
Dynamical quantum phase transitions (DQPTs) feature singular temporal behavior in transient quantum states during nonequilibrium real-time evolution. In this work we show that DQPTs in random Ising chains exhibit critical behavior with…
The Wishart distribution and its generalizations are among the most prominent probability distributions in multivariate statistical analysis, arising naturally in applied research and as a basis for theoretical models. In this paper, we…
Wishart ensemble is a useful and important random matrix model used in diverse fields. By realizing induced random mixed quantum states as Wishart ensemble with the fixed-trace one, using matrix integral technique we give a fast track to…
The noncentral Wishart distribution has become more mainstream in statistics as the prevalence of applications involving sample covariances with underlying multivariate Gaussian populations as dramatically increased since the advent of…
Numerical approximation of quantum states via convex combinations of states with positive partial transposes (bi-PPT state) in multipartite systems constitutes a fundamental challenge in quantum information science. We reformulate this…
We consider general Markov processes with absorption and provide criteria ensuring the exponential convergence in total variation of the distribution of the process conditioned not to be absorbed. The first one is based on two-sided…