Related papers: Estimating the spectrum of a density operator

In this work, we draw connections between the classical Shannon interpolation of bandlimited deterministic signals and the literature on estimating continuous-time random processes from their samples (known in various communities under…

This paper is devoted to analyzing the observer convergence rate for a class of linear control systems in a Hilbert space. To characterize the polynomial stability of the observer error system, we apply the spectral theory of linear…

Let $H$ be an infinite-dimensional separable Hilbert space and let $(X,d,\mu)$ be a metric measure space satisfying the doubling and upper Alhfors regularity conditions at small scale. We prove that every bounded continuous tight frame…

A new method to enclose the pseudospectrum via the numerical range of the inverse of a matrix or linear operator is presented. The method is applied to finite-dimensional discretizations of an operator on an infinite-dimensional Hilbert…

M.Levitin and E.Shargorodsky purposed in a recent article, [math.SP/0212087], the use of the so called ``second order relative spectrum'', to find eigenvalues of self-adjoint operators in gaps of the essential spectrum. Let $M$ be a…

Consider the question: what statistical ensemble corresponds to minimal prior knowledge about a quantum system ? For the case where the system is in fact known to be in a pure state there is an obvious answer, corresponding to the unique…

Let $T$ be a power-bounded linear operator on a Hilbert space $X$, and let $S$ be a bounded linear operator from another Hilbert space $Y$ to $X$. We investigate the non-exponential rate of decay of $\|T^nS\|$ as $n \to \infty$. First, when…

The Wigner function for one and two-mode quantum systems is explicitely expressed in terms of the marginal distribution for the generic linearly transformed quadratures. Then, also the density operator of those systems is written in terms…

This paper primarily investigates spectral properties of symmetric tensor products of Hilbert-space operators. For a unilateral weighted shift operator $S_w$, we present an algorithm to compute the point spectrum of its symmetric and…

We introduce a framework for subspace methods which approximate the spectra of self-adjoint, unbounded operators in a local region. Using the projection-valued measure, we derive integrated spectral inequalities that also apply to unbounded…

We introduce a new approach for estimating the invariant density of a multidimensional diffusion when dealing with high-frequency observations blurred by independent noises. We consider the intermediate regime, where observations occur at…

Using a reference molecular atlas to ensure self-consistency of wavelength calibration is widespread practice. Boesch \& Reiners (Astronomy \& Astrophysics 582 A43 (2015)) reported a line list from a discharge of molecular nitrogen from…

Gleason's theorem asserts the equivalence of von Neumann's density operator formalism of quantum mechanics and frame functions, which are functions on the pure states that sum to 1 on any orthonormal basis of Hilbert space of dimension at…

We derive an exact expression for the quantumness of a Hilbert space (defined in quant-ph/0302092), and show that in composite Hilbert spaces the signal states must contain at least some entangled states in order to achieve such a…

We study measures of quantum information when the space spanned by the set of accessible observables is not closed under products, i.e., we consider systems where an observer may be able to measure the expectation values of two operators,…

Given $n$ i.i.d. observations, we study the problem of estimating the spectrum of weighted Laplace operators of the form $\Delta_f=\Delta + \alpha \nabla \log f\cdot \nabla$, where $f$ is a positive probability density on a known compact…

The scope of this text is to study a process that induces another proof of the Spectral Embedding Theorem: that any densely defined symmetric operator can be extended by a multiplication operator through an embedding of the Hilbert space…

We study the eigenvalue profile of concentration operators (multiplication by an indicator function followed by projection) acting on reproducing kernel Hilbert spaces. The spectral profile of such operators provides a useful notion of…

In this note, we develop a framework to describe open quantum systems in the Heisenberg picture, i.e., via time evolving operator algebras. We point out the incompleteness of the previous proposals in this regard. We argue that a complete…

We study the operator that corresponds to the measurement of volume, in non-perturbative quantum gravity, and we compute its spectrum. The operator is constructed in the loop representation, via a regularization procedure; it is finite,…