Related papers: Operators and POVMs generated by Parseval frames
This chapter uses categorical techniques to describe relations between various sets of operators on a Hilbert space, such as self-adjoint, positive, density, effect and projection operators. These relations, including various…
We study the spectral theory of operators, generated as direct sums of self-adjoint extensions of quasi-differential minimal operators on a multi-interval set (self-adjoint vector-operators), acting in a Hilbert space. Spectral theorems for…
The objective of this work is to develop a recursive, discrete time quantum filtering equation for a system that interacts with a probe, on which measurements are performed according to the Positive Operator Valued Measures (POVMs)…
It is well known that increasing functions do not preserve operator order in general; nor do decreasing functions reverse operator order. However, operator monotone increasing or operator monotone decreasing do. In this article, we employ a…
In this work, operator version of Popoviciu's inequality for positive selfadjoint operators in Hilbert spaces under positive linear maps for superquadratic functions is proved. Analogously, using the same technique operator version of…
Here we propose an implementation of all possible Positive Operator Value Measures (POVMs) of two-photon polarization states. POVMs are the most general class of quantum measurements. Our setup requires linear optics, Bell State…
There are self-adjoint operators which determine both spectral and semispectral measures. These measures have very different commutativity and covariance properties. This fact poses a serious question on the physical meaning of such a…
We construct the set of all general (i.e. not necessarily rank 1) symmetric informationally complete (SIC) positive operator valued measures (POVMs). In particular, we show that any orthonormal basis of a real vector space of dimension…
In this paper we generalize a strategy recently proposed by the author concerning intertwining operators. In particular we discuss the possibility of extending our previous results in such a way to construct (almost) isospectral…
In order to analyze joint measurability of given measurements, we introduce a Hermitian operator-valued measure, called $W$-measure, such that it has marginals of positive operator-valued measures (POVMs). We prove that ${W}$-measure is a…
For a quantum system with Hilbert space ${\cal H}$ of dimension $N$ and a set $S$ of $n$ Hermitian operators ${\cal O}_i$, a basic question is to understand the set $E_S \subset \mathbb{R}^n$ of points $\vec{e}$ where $e_i = {\rm tr}(\rho…
Let $H$ be a self-adjoint operator, bounded from below and let $O$ be a bounded self-adjoint operator with purely discrete spectrum. Suppose that (i) $E(H)=\inf \mathrm{spec}(H)$ is a simple eigenvalue, and (ii) $H$ strongly commutes with…
The Egoroff theorem for measurable $\bold X$-valued functions and operator-valued measures $\bold m: \Sigma \to L(\bold X, \bold Y)$, where $\Sigma$ is a $\sigma$-algebra of subsets of $T \neq \emptyset$ and $\bold X$, $\bold Y$ are both…
We compute explicit formulas for the curvature operators and Poincar\'e polynomials of all compact irreducible symmetric spaces. We can easily derive the Poincar\'e polynomials using quantum numbers, giving a formula that mirrors the known…
A quantum measurement, often referred to as positive operator-valued measurement (POVM), is a set of positive operators $P_j=P_j^\dag\geq 0$ summing to identity, $\sum_jP_j=\mathbb{1}$. This can be seen as a generalization of a probability…
Let E be an operator algebra on a Hilbert space with finite-dimensional generated C*-algebra. A classification is given of the locally finite algebras and the operator algebras obtained as limits of direct sums of matrix algebras over E…
In this paper we study the self-adjoint and co-isometry composition and weighted composition operator on $H_E(\zeta).$ We also discuss the conditions under which adjoint operator of a composition and weighted composition operator on…
A photodetector may be characterized by various figures of merit such as response time, bandwidth, dark count rate, efficiency, wavelength resolution, and photon-number resolution. On the other hand, quantum theory says that any measurement…
We study the positive-operator-valued measures on the projective real line covariant with respect to the projective group, assuming that the energy is a positive operator. This problem is similar to the more complicated problem of finding…
A Parseval frame is a spanning set for a Hilbert space which satisfies the Parseval identity: a vector can be expressed as a linear combination of the frame whose coefficients are inner products with the frame vectors. There is considerable…