Related papers: Semispectral measures as convolutions and their mo…
Quantum measurements are noncontextual, with outcomes independent of which other commuting observables are measured at the same time, when consistently analyzed using principles of Hilbert space quantum mechanics rather than classical…
The measurement of high-dimensional entangled states of orbital angular momentum prepared by spontaneous parametric down-conversion can be considered in two separate stages: a generation stage and a detection stage. Given a certain number…
Phase operators are constructed using a Klauder-Berezin coherent state quantization in finite Hilbert subspaces of the Hilbert space of Fourier series. The study of infinite dimensional limits of mean values of some observables phase leads…
We present explicit expressions for Fock-space projection operators that correspond to realistic final states in scattering experiments. Our operators automatically sum over unobserved quanta and account for non-emission into sub-regions of…
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…
We consider iterated function systems (finite or countable), together with linear and continuous operators on Hilbert spaces, which enable us to construct Markov-type operators. Under suitable conditions, these Markov-type operators have…
We give a characterization of commutative semispectral measures by means of Feller and Strong Feller Markov kernels. In particular: {itemize} we show that a semispectral measure $F$ is commutative if and only if there exist a self-adjoint…
We first give a condition for a normal operator on a Hilbert space to have no nonzero periodic points, then we give a characterization of normal operators with the whole space as periodic points. We proceed to study the structure of…
In early 90's Mandel and coworkers performed an experiment \cite{mandel} to examine the significance of quantum phase operators by measuring the phase between two optical fields. We show that this type of quantum mechanical phase…
Spectral measures arise in numerous applications such as quantum mechanics, signal processing, resonances, and fluid stability. Similarly, spectral decompositions (pure point, absolutely continuous and singular continuous) often…
We generalize the definition of convolution of vectors and tensors on the 2-sphere, and prove that it commutes with differential operators. Moreover, vectors and tensors that are normal/tangent to the spherical surface remain so after the…
In quantum mechanics, measurements are dynamical processes and thus they should be capable of inducing currents. The symmetries of the Hamiltonian and measurement operator provide an organizing principle for understanding the conditions for…
We study the mathematical structure of superoperators describing quantum measurements, including the \emph{entangling measurement}--the generalization of the standard quantum measurement that results in entanglement between the measurable…
We construct a set $M_d$ whose points parametrize families of Meixner polynomials in $d$ variables. There is a natural bispectral involution $b$ on $M_d$ which corresponds to a symmetry between the variables and the degree indices of the…
We study Schr\"odinger operators on $\R$ with measures as potentials. Choosing a suitable subset of measures we can work with a dynamical system consisting of measures. We then relate properties of this dynamical system with spectral…
We investigate spaces of operators which are invariant under translations or modulations by lattices in phase space. The natural connection to the Heisenberg module is considered, giving results on the characterisation of such operators as…
Quantum measurements can be described by operators that assign conditional probabilities to different outcomes while also describing unavoidable physical changes to the system. Here, we point out that operators describing information gain…
We develop a novel numerical bootstrap for unitary, crossing-symmetric conformal field theories, focusing on moment observables defined as weighted averages over conformal data. Providing a global and coarse-grained probe of the operator…
The transverse spatial attributes of an optical beam can be decomposed into the position, momentum and orbital angular momentum observables. The position and momentum of a beam is directly related to the quadrature amplitudes, whilst the…
We develop the method of similar operators to study the spectral properties of unbounded perturbed linear operators that can be represented by matrices of various kinds. The class of operators under consideration includes various…