Related papers: Compact smallest eigenvalue expressions in Wishart…
We discuss an application of the random matrix theory in the context of estimating the bipartite entanglement of a quantum system. We discuss how the Wishart ensemble (the earliest studied random matrix ensemble) appears in this quantum…
We consider rectangular random matrices of size $p\times n$ belonging to the real Wishart-Laguerre ensemble also known as the chiral Gaussian orthogonal ensemble. This ensemble appears in many applications like QCD, mesoscopic physics, and…
The statistical behaviour of the smallest eigenvalue has important implications for systems which can be modeled using a Wishart-Laguerre ensemble, the regular one or the fixed trace one. For example, the density of the smallest eigenvalue…
In this paper we study entanglement of the reduced density matrix of a bipartite quantum system in a random pure state. It transpires that this involves the computation of the smallest eigenvalue distribution of the fixed trace Laguerre…
We analyze the properties of entangled random pure states of a quantum system partitioned into two smaller subsystems of dimensions $N$ and $M$. Framing the problem in terms of random matrices with a fixed-trace constraint, we establish,…
We compute analytically the density $\varrho_{N,M}(\lambda)$ of Schmidt eigenvalues, distributed according to a fixed-trace Wishart-Laguerre measure, and the average R\'enyi entropy $\langle\mathcal{S}_q\rangle$ for reduced density matrices…
Consider the model of bipartite entanglement for a random pure state emerging in quantum information and quantum chaos, corresponding to the fixed trace Laguerre unitary ensemble (LUE) in Random Matrix Theory. We focus on correlation…
The statistics of the smallest eigenvalue of Wishart-Laguerre ensemble is important from several perspectives. The smallest eigenvalue density is typically expressible in terms of determinants or Pfaffians. These results are of utmost…
We analytically calculate the average value of i-th largest Schmidt coefficient for random pure quantum states. Schmidt coefficients, i.e., eigenvalues of the reduced density matrix, are expressed in the limit of large Hilbert space size…
For the correlated Gaussian Wishart ensemble we compute the distribution of the smallest eigenvalue and a related gap probability.We obtain exact results for the complex (\beta=2) and for the real case (\beta=1). For a particular set of…
We investigate the asymptotic behavior of the empirical eigenvalues distribution of the partial transpose of a random quantum state. The limiting distribution was previously investigated via Wishart random matrices indirectly (by…
Wishart random matrix theory is of major importance for the analysis of correlated time series. The distribution of the smallest eigenvalue for Wishart correlation matrices is particularly interesting in many applications. In the complex…
A recent conjecture regarding the average of the minimum eigenvalue of the reduced density matrix of a random complex state is proved. In fact, the full distribution of the minimum eigenvalue is derived exactly for both the cases of a…
We investigate the random eigenvalues coming from the beta-Laguerre ensemble with parameter p, which is a generalization of the real, complex and quaternion Wishart matrices of parameter (n,p). In the case that the sample size n is much…
We study the probability distribution function (PDF) of the smallest eigenvalue of Laguerre-Wishart matrices $W = X^\dagger X$ where $X$ is a random $M \times N$ ($M \geq N$) matrix, with complex Gaussian independent entries. We compute…
A strategy to evaluate the distribution of the largest Schmidt eigenvalue for entangled random pure states of bipartite systems is proposed. We point out that the multiple integral defining the sought quantity for a bipartition of sizes N,…
We use the idea of a Wigner surmise to compute approximate distributions of the first eigenvalue in chiral Random Matrix Theory, for both real and complex eigenvalues. Testing against known results for zero and maximal non-Hermiticity in…
We consider the large deviations of the smallest eigenvalue of the Wishart-Laguerre Ensemble. Using the Coulomb gas picture we obtain rate functions for the large fluctuations to the left and the right of the hard edge. Our findings are…
Rectangular real $N \times (N + \nu)$ matrices $W$ with a Gaussian distribution appear very frequently in data analysis, condensed matter physics and quantum field theory. A central question concerns the correlations encoded in the spectral…
We study the universality of spectral statistics of large random matrices. We consider $N\times N$ symmetric, hermitian or quaternion self-dual random matrices with independent, identically distributed entries (Wigner matrices) where the…