Related papers: Purity and Covariance Matrix
Spontaneous emission can create coherences in a multilevel atom having close lying levels, subject to the condition that the atomic dipole matrix elements are non-orthogonal. This condition is rarely met in atomic systems. We report the…
Natural frequencies and normal modes are basic properties of a structure which play important roles in analyses of its vibrational characteristics. As their computation reduces to solving eigenvalue problems, it is a natural arena for…
We obtain a sharp convergence rate for banded covariance matrix estimates of stationary processes. A precise order of magnitude is derived for spectral radius of sample covariance matrices. We also consider a thresholded covariance matrix…
The covariance matrices of power-spectrum (P(k)) measurements from galaxy surveys are difficult to compute theoretically. The current best practice is to estimate covariance matrices by computing a sample covariance of a large number of…
We address the problem of two interacting atoms of different species inside a cavity and find the explicit solutions of the corresponding eigenvalues and eigenfunctions using a new invariant. This model encompasses various commonly used…
In this paper we consider feedback control algorithms for the rapid purification of a bipartite state consisting of two qubits, when the observer has access to only one of the qubits. We show 1) that the algorithm that maximizes the average…
We propose a data-driven way to reduce the noise of covariance matrices of nonstationary systems. In the case of stationary systems, asymptotic approaches were proved to converge to the optimal solutions. Such methods produce eigenvalues…
The possible compatibility of density matrices for single-party subsystems is described by linear constraints on their respective spectra. Whenever some of those quantum marginal constraints are saturated, the total quantum state has a…
The principle of local covariance which was recently introduced admits a generally covariant formulation of quantum field theory. It allows a discussion of structural properties of quantum field theory as well as the perturbative…
We study purity decay -- a measure of bipartite entanglement -- in a chain of $n$ qubits under the action of various geometries of nearest-neighbor random two-site unitary gates. We use a Markov chain description of average purity…
The need to retain the relative phases in quantum mechanics implies an addition law parametrized by a phase of two density operators required for the purification of a density matrix. This is shown with quantum tomography and the Wigner…
Coherence and correlation are key features of the quantum system. Quantifying these quantities are astounding task in the framework of resource theory of quantum information processing. In this article, we identify an affinity-based metric…
We develop a method for estimating well-conditioned and sparse covariance and inverse covariance matrices from a sample of vectors drawn from a sub-gaussian distribution in high dimensional setting. The proposed estimators are obtained by…
General covariance is a crucial notion in the study of field theories in curved spacetime. A field theory defined with respect to a semi-Riemannian metric is generally covariant if two metrics which are related by a diffeomorphism produce…
Phase is a basic ingredient for quantum states since quantum mechanics uses complex numbers to describe quantum states. In this letter, we introduce a rigorous framework to quantify the phase of quantum states. To do so, we regard phase as…
We studied the interaction of a two-level atom with a frequency modulated cavity mode in an ideal optical cavity. The system, described by a Jaynes-Cumming Hamiltonian, gave rise to a set of stiff nonlinear first order equations solved…
We offer a method to estimate a covariance matrix in the special case that \textit{both} the covariance matrix and the precision matrix are sparse --- a constraint we call double sparsity. The estimation method is maximum likelihood,…
Covariance matrices are important tools for obtaining reliable parameter constraints. Advancements in cosmological surveys lead to larger data vectors and, consequently, increasingly complex covariance matrices, whose number of elements…
We study time dependence of various measures of entanglement (covariance entanglement coefficient, purity entanglement coefficient, normalized distance coefficient, entropic coefficients) between resonantly coupled modes of the…
We show that the covariance matrix of a quantum state can be reconstructed from position measurements using the simple notion of polar duality, familiar from convex geometry. In particular, all multidimensional Gaussian states (pure or…