Related papers: Extreme Eigenvalues of Wishart Matrices: Applicati…
We present experimentally and numerically accessible quantities that can be used to differentiate among various families of random entangled states. To this end, we analyze the entanglement properties of bipartite reduced states of a…
The detection and estimation of quantum entanglement are the essential issues in the theory of quantum entanglement. We construct matrices based on the realignment of density matrices and the vectorization of the reduced density matrices,…
We study entanglement and other correlation properties of random states in high-dimensional bipartite systems. These correlations are quantified by parameters that are subject to the "concentration of measure" phenomenon, meaning that on a…
Consider a standard white Wishart matrix with parameters $n$ and $p$. Motivated by applications in high-dimensional statistics and signal processing, we perform asymptotic analysis on the maxima and minima of the eigenvalues of all the $m…
We present some new results on the joint distribution of an arbitrary subset of the ordered eigenvalues of complex Wishart, double Wishart, and Gaussian hermitian random matrices of finite dimensions, using a tensor pseudo-determinant…
We study experimentally accessible lower bounds on entanglement measures based on entropic uncertainty relations. Experimentally quantifying entanglement is highly desired for applications of quantum simulation experiments to fundamental…
The paper "An efficient sampling scheme for the eigenvalues of dual Wishart matrices", by I.~Santamar\'ia and V.~Elvira, [\emph{IEEE Signal Processing Letters}, vol.~28, pp.~2177--2181, 2021] \cite{SE21}, poses the question of efficient…
Random matrix theory has played an important role in various areas of pure mathematics, mathematical physics, and machine learning. From a practical perspective of data science, input data are usually normalized prior to processing. Thus,…
The probability that there are $k$ real eigenvalues for an $n$ dimensional real random matrix is known. Here we study this for the case of products of independent random matrices. Relating the problem of the probability that the product of…
We find the minimum and the maximum value for the local energy of an arbitrary finite bipartite system for any given amount of entanglement, also identifying families of states reaching these bounds and sharing formal analogies with thermal…
In this article, we present a novel approach to investigating entanglement in the context of quantum computing. Our methodology involves analyzing reduced density matrices at different stages of a quantum algorithm's execution and…
This paper is the second chapter of three of the author's undergraduate thesis. In this paper, we consider the random matrix ensemble given by $(d_b, d_w)$-regular graphs on $M$ black vertices and $N$ white vertices, where $d_b \in…
Uncertainty principle is an inherent nature of quantum system that undermines the precise measurement of incompatible observables and hence the applications of quantum theory. Entanglement, another unique feature of quantum physics, was…
Some tools and ideas are interchanged between random matrix theory and multivariate statistics. In the context of the random matrix theory, classes of spherical and generalised Wishart random matrix ensemble, containing as particular cases…
The spectral statistics and entanglement within the eigenstates of generic spin chain Hamiltonians are analysed. A class of random matrix ensembles is defined which include the most general nearest-neighbour qubit chain Hamiltonians. For…
We studied universality of Wishart ensembles whose covariance matrix has 2 distinct eigenvalues and the number of each of these eigenvalue goes to infinity in the asymptotic limit. In this case, the limiting eigenvalue distribution can be…
In a frequency selective slow-fading channel in a MIMO system, the channel matrix is of the form of a block matrix. This paper proposes a method to calculate the limit of the eigenvalue distribution of block matrices if the size of the…
A contemporary technological milestone is to build a quantum device performing a computational task beyond the capability of any classical computer, an achievement known as quantum adversarial advantage. In what ways can the entanglement…
The dynamics of a single qubit interacting by a sequence of pairwise collisions with an environment consisting of just two more qubits is analyzed. Each collision is modeled in terms of a random unitary operator with a uniform probability…
In recent years the Rosenzweig--Porter (RP) ensemble, obtained by adding a diagonal matrix with independent and identically distributed elements to a Gaussian random matrix, has been widely used as a minimal model for the emergence of…