Related papers: Extreme Eigenvalues of Wishart Matrices: Applicati…
The entanglement spectrum, i.e., the full distribution of Schmidt eigenvalues of the reduced density matrix, contains more information than the conventional entanglement entropy and has been studied recently in several many-particle…
We consider the reduced density matrix $\rho_{A}^{(m)}$ of a bipartite system $AB$ of dimensionality $mn$ in a Gaussian ensemble of random, complex pure states of the composite system. For a given dimensionality $m$ of the subsystem $A$,…
We study the dynamics of the entanglement spectrum, that is the time evolution of the eigenvalues of the reduced density matrices after a bipartition of a one-dimensional spin chain. Starting from the ground state of an initial Hamiltonian,…
We studied the universality of Wishart ensembles whose covariance matrix has 2 distinct eigenvalues. We studied the asymptotic limit when the number of both eigenvalues goes to infinity and obtained universality results. In this case, the…
The random matrix ensembles are applied to the quantum statistical systems. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The linear operators describing the…
Quantum entanglement plays a crucial role in quantum information, quantum teleportation and quantum computation. The information about the entanglement content between subsystems of the composite system is encoded in the Schmidt…
The Schmidt coefficients capture all entanglement properties of a pure bipartite state and therefore determine its usefulness for quantum information processing. While the quantification of the corresponding properties in mixed states is…
The correlated Wishart model provides the standard benchmark when analyzing time series of any kind. Unfortunately, the real case, which is the most relevant one in applications, poses serious challenges for analytical calculations. Often…
We discuss the problem of characterizing upper bounds on entanglement in a bipartite quantum system when only the reduced density matrices (marginals) are known. In particular, starting from the known two-qubit case, we propose a family of…
These lecture notes provide a comprehensive, self-contained introduction to the analysis of Wishart matrix moments. This study may act as an introduction to some particular aspects of random matrix theory, or as a self-contained exposition…
Quantum networks are natural scenarios for the communication of information among distributed parties, and the arena of promising schemes for distributed quantum computation. Measurement-based quantum computing is a prominent example of how…
The newfound importance of ``entanglement as a resource'' in quantum computation and quantum communication compels us to quantify it in as many distinct ways as possible. Here we explore a new measure of entanglement for mixed quantum…
We characterize the multipartite entanglement of a system of n qubits in terms of the distribution function of the bipartite purity over all balanced bipartitions. We search for those (maximally multipartite entangled) states whose purity…
Let $\mathbf{W}$ be a correlated complex non-central Wishart matrix defined through $\mathbf{W}=\mathbf{X}^H\mathbf{X}$, where $\mathbf{X}$ is $n\times m \, (n\geq m)$ complex Gaussian with non-zero mean $\boldsymbol{\Upsilon}$ and…
The probability of large deviations of the smallest Schmidt eigenvalue for random pure states of bipartite systems, denoted as $A$ and $B$, is computed analytically using a Coulomb gas method. It is shown that this probability, for large…
This paper deals with the asymptotic distribution of Wishart matrix and its application to the estimation of the population matrix parameter when the population eigenvalues are block-wise infinitely dispersed. We show that the appropriately…
We study the quantum entanglement caused by unitary operators that have classical limits that can range from the near integrable to the completely chaotic. Entanglement in the eigenstates and time-evolving arbitrary states is studied…
Previous results indicate that while chaos can lead to substantial entropy production, thereby maximizing dynamical entanglement, this still falls short of maximality. Random Matrix Theory (RMT) modeling of composite quantum systems,…
The spectra of empirical correlation matrices, constructed from multivariate data, are widely used in many areas of sciences, engineering and social sciences as a tool to understand the information contained in typically large datasets. In…
Data sets collected at different times and different observing points can possess correlations at different times $and$ at different positions. The doubly correlated Wishart model takes both into account. We calculate the eigenvalue density…