Related papers: Position Uncertainty Measures on the Sphere
A study of the diffusion of a passive Brownian particle on the surface of a sphere and subject to the effects of an external potential, coupled linearly to the probability density of the particle's position, is presented through a numerical…
Heisenberg's uncertainty principle has been understood to set a limitation on measurements; however, the long-standing mathematical formulation established by Heisenberg, Kennard, and Robertson does not allow such an interpretation.…
Second quantization of a classical nonrelativistic one-particle system as a deformation quantization of the Schrodinger spinless field is considered. Under the assumption that the phase space of the Schrodinger field is $C^{\infty}$, both,…
We briefly present a new coordinate-invariant statistical test dedicated to the study of the orientations of transverse quantities of non-uniformly distributed sources on the celestial sphere. These quantities can be projected spin-axes or…
For theoretical approach of quantum measurements it is proposed a set of reconsidered conjectures. The proposed approach implies linear functional transformations for probability density and current but preserves the expressions for…
Heisenberg's uncertainty principle implies fundamental constraints on what properties of a quantum system can we simultaneously learn. However, it typically assumes that we probe these properties via measurements at a single point in time.…
Quantum mechanics predicts that measurements of incompatible observables carry a minimum uncertainty which is independent of technical deficiencies of the measurement apparatus or incomplete knowledge of the state of the system. Nothing yet…
We consider some possible phenomenological implications of the extended uncertainty principle, which is believed to hold for quantum mechanics in de Sitter spacetime. The relative size of the corrections to the standard results is however…
We describe rigorous quantum measurement theory in the Heisenberg picture by applying operator deformation techniques previously used in noncommutative quantum field theory. This enables the conventional observables (represented by…
Though the sharp Heisenberg Uncertainty Principle has been extensively studied in the entire Euclidean spaces, the counterpart on the half spaces or more general orthants has been missing in the literature. We investigate the sharp…
The evaluation of uncertainties in quantum measurements is problematic since the correct value of an observable between state preparation and measurement is experimentally inaccessible. In Ozawa's formulation of uncertainty relations for…
A simple model of quantum particle is proposed in which the particle in a {\it macroscopic} rest frame is represented by a {\it microscopic d}-dimensional oscillator, {\it s=(d-1)/2} being the spin of the particle. The state vectors 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 $\mathbb{P}$,…
The uncertainty relation, as one of the fundamental principles of quantum physics, captures the incompatibility of noncommuting observables in the preparation of quantum states. In this work, we derive two strong and universal uncertainty…
General characterizations of physical measurements are discussed within the framework of the classical information theory. The uncertainty relation for simultaneous measurements of two physical observables is defined in this framework for…
We show that for fermion states, measurements of any two finite outcome particle quantum numbers (e.g.\ spin) are not constrained by a minimum total uncertainty. We begin by defining uncertainties in terms of the outputs of a measurement…
The uncertainty relations for angle and angular momentum are revisited. We use the exponential of the angle instead of the angle itself and adopt dispersion as a natural measure of resolution. We find states that minimize the uncertainty…
We investigate, both analytically and numerically, the behavior of the electron gas on a sphere in the presence of point-like impurities. We find a criterion when the disorder can be regarded as small one and the main effect is the…
The di-fermion angular distribution observed in decays of inclusively produced vector particles is characterized by two frame-independent observables, reflecting the average spin-alignment of the produced particle and the magnitude of…
Heisenberg's uncertainty principle is formulated for a set of generalized measurements within the framework of majorization theory, resulting in a partial uncertainty order on probability vectors that is stronger than those based on…