Related papers: Partial transposition of random states and non-cen…
The scaled standard Wigner matrix (symmetric with mean zero, variance one i.i.d. entries), and its limiting eigenvalue distribution, namely the semi-circular distribution, has attracted much attention. The $2k$th moment of the limit equals…
Power symmetric matrices defned and studied by R. Sinkhorn (1981) and their generalization by R.B. Bapat, S.K. Jain and K. Manjunatha Prasad (1999) have been utilized to give positive block matrices with trace one possessing positive…
We study the properties of the random quantum states induced from the uniformly random pure states on a bipartite quantum system by taking the partial trace over the larger subsystem. Most of the previous studies have adopted a viewpoint of…
We study the high-dimensional asymptotic regimes of correlated Wishart matrices $d^{-1}\mathcal{Y}\mathcal{Y}^T$, where $\mathcal{Y}$ is a $n\times d$ Gaussian random matrix with correlated and non-stationary entries. We prove that under…
When studying the perfect transfer of a quantum state from one site to another, it is typically assumed that one can receive the arriving state at a specific instant in time, with perfect accuracy. Here, we study how sensitive perfect state…
Random samples of quantum states are an important resource for various tasks in quantum information science, and samples in accordance with a problem-specific distribution can be indispensable ingredients. Some algorithms generate random…
We apply random matrix and free probability techniques to the study of linear maps of interest in quantum information theory. Random quantum channels have already been widely investigated with spectacular success. Here, we are interested in…
A Wishart matrix is said to be spiked when the underlying covariance matrix has a single eigenvalue $b$ different from unity. As $b$ increases through $b=2$, a gap forms from the largest eigenvalue to the rest of the spectrum, and with…
Continuous diffusion models have demonstrated remarkable performance in data generation across various domains, yet their efficiency remains constrained by two critical limitations: (1) the local adjacency structure of the forward Markov…
Random matrix theory has become a cornerstone in modern statistics and data science, providing fundamental tools for understanding high-dimensional covariance structures. Within this framework, the Wishart matrix plays a central role in…
We study the eigenvalue distribution of a random matrix, at a transition where a new connected component of the eigenvalue density support appears away from other connected components. Unlike previously studied critical points, which…
We solve the open question of the existence of four-qubit entangled symmetric states with positive partial transpositions (PPT states). We reach this goal with two different approaches. First, we propose a half-analytical-half-numerical…
Given a large, high-dimensional sample from a spiked population, the top sample covariance eigenvalue is known to exhibit a phase transition. We show that the largest eigenvalues have asymptotic distributions near the phase transition in…
Bipartite entangled quantum states with a positive partial transpose (PPT), i.e., PPT entangled states, are usually considered very weakly entangled. Since no pure entanglement can be distilled from them, they are also called bound…
We present two different descriptions of positive partially transposed (PPT) states. One is based on the theory of positive maps while the second description provides a characterization of PPT states in terms of Hilbert space vectors. Our…
We study extremality in various sets of states that have positive partial transposes. One of the tools we use for this purpose is the recently formulated criterion allowing to judge if a given state is extremal in the set of PPT states.…
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…
Statistical properties of coherent radiation propagating in a quasi - 1D random media is studied in the framework of random matrix theory. Distribution functions for the total transmission coefficient and the angular transmission…
We explore how the expectation values $\langle\psi |A| \psi\rangle$ of a largely arbitrary observable $A$ are distributed when normalized vectors $|\psi\rangle$ are randomly sampled from a high dimensional Hilbert space. Our analytical…
Let $X_N$ be a $N \times N$ real Wishart random matrix with aspect ratio $M/N$. The limit eigenvalue distribution of $X_N$ is the Marchenko-Pastur law with parameter $c = \lim_N M/N$. The limit moments $\{m_n\}_n$ are given by $m_n =…