Related papers: POVM Quantization
Useful relations describing arbitrary parameters of given quantum systems can be derived from simple physical constraints imposed on the vectors in the corresponding Hilbert space. This is well known and it usually proceeds by partitioning…
The original purpose of measurements is to provide us with information about a previously unknown physical property of the system observed. In the Hilbert space formalism of quantum mechanics, this physical meaning of measurement…
The expectation value <O> of an arbitrary operator O can be obtained via a universal measuring apparatus that is independent of O, by changing only the data-processing of the outcomes. Such a ``universal detector'' performs a joint…
In this second paper on loop quantization of Gowdy model, we introduce the kinematical Hilbert space on which appropriate holonomies and fluxes are well represented. The quantization of the volume operator and the Gauss constraint is…
Recent works have proposed the use of the formalism of Positive Operator Valued Measures to describe time measurements in quantum mechanics. This work aims to expand on the work done by other authors, by generalizing the previously proposed…
We review a few useful concepts about polarization measurements in the quantum domain. Using a perfectly general formalism, we show how to build the quantum counterpart of some classical quantities like Stokes parameters and Mueller…
We address the problem of constructing positive operator-valued measures (POVMs) in finite dimension $n$ consisting of $n^2$ operators of rank one which have an inner product close to uniform. This is motivated by the related question of…
Generalized quantum measurements play a crucial role in quantum mechanics, and symmetric informationally complete positive operator-valued measurements (SIC POVMs) provide a powerful and flexible framework for extracting information from…
In this work, we consider the task of faithfully simulating a quantum measurement, acting on a joint bipartite quantum state, in a distributed manner. In the distributed setup, the constituent sub-systems of the joint quantum state are…
Let $\mathbb{P}$ be the complete metric space consisting of positive invertible operators on an infinite-dimensional Hilbert space with the Thompson metric. We introduce the notion of operator means of probability measures on $\mathbb{P}$,…
Superposition is an essential feature of quantum mechanics. From the Schrodinger's cat to quantum algorithms such as Deutsch-Jorsza algorithm, quantum superposition plays an important role. It is one fundamental and crucial question how to…
In this report, we present a framework for implementing an arbitrary $n$-outcome generalized quantum measurement (POVM) on an $m$-qubit register as a sequence of two-outcome measurements requiring only single ancillary qubit. Our procedure…
We study measurements of the unitary generalization of Pauli operators. First, an analytical (constructive) solution to the eigenproblem of these operators is presented. Next, in the case of two subsystems, the Schmidt form of the…
We give a complete characterization for pure quantum measurements, i.e., for POVMs which are extremals in the convex set of all POVMs. Such measurements are free from classical noise. The characterization is valid both in discrete and…
The space of positive operator-valued measures on the Borel sets of a compact (or even locally compact) Hausdorff space with values in the algebra of linear operators acting on a d-dimensional Hilbert space is studied from the perspectives…
The formulation of Geometric Quantization contains several axioms and assumptions. We show that for real polarizations we can generalize the standard geometric quantization procedure by introducing an arbitrary connection on the…
We study extreme points of the set of finite-outcome positive-operator-valued measures (POVMs) on finite-dimensional Hilbert spaces and particularly the possible ranks of the effects of an extreme POVM. We give results discussing ways of…
Starting from the famous Pauli problem on the possibility to associate quantum states with probabilities, the formulation of quantum mechanics in which quantum states are described by fair probability distributions (tomograms, i.e.…
A coarse-grained quantum operator technique is used along with the formalism of Bohmian mechanics endowed with stochastic character at the quantum level in order to address some central issues in the quantum theory of measurement. A…
We propose an exercise in which one attempts to deduce the formalism of quantum mechanics solely from phenomenological observations. The only assumed inputs are the multi-time probability distributions estimated from the results of…