相关论文: Position Uncertainty Measures on the Sphere
Uncertainty lower bounds for parameter estimations associated with a unitary family of mixed-state density matrices are obtained by embedding the space of density matrices in the Hilbert space of square-root density matrices. In the…
A pair of uncertainty relations relevant for quantum states of multislit interferometry is derived, based on the mutually commuting "modular" position and momentum operators and their complementary counterparts, originally introduced by…
We consider successive measurements of position and momentum of a single particle. Let P be the conditional probability to measure the momentum k with precision dk, given a previously successful position measurement q with precision dq.…
Uncertainty quantification is a critical aspect of machine learning models, providing important insights into the reliability of predictions and aiding the decision-making process in real-world applications. This paper proposes a novel way…
Exploiting the geometric nature of statistical divergences, we devise a way to define associated induced uncertainty measures for discrete and finite probability distributions. We also report new uncertainty measures and discuss their…
A new quantum-stochastic differential calculus is derived for representing continuous quantum measurement of the position operator. Closed nonlinear quantum-stochastic differential equation is given for the quantum state of the observed…
We analyze the decoherence of a particle's spatial superposition moving along a stationary worldline through the Minkowski vacuum. The particle is modeled via an internal degree of freedom that couples to a scalar field, and an external…
The notions of error and disturbance appearing in quantum uncertainty relations are often quantified by the discrepancy of a physical quantity from its ideal value. However, these real and ideal values are not the outcomes of simultaneous…
We propose a projection-based class of uniformity tests on the hypersphere using statistics that integrate, along all possible directions, the weighted quadratic discrepancy between the empirical cumulative distribution function of the…
A universal formulation of uncertainty relations for quantum measurements is presented with additional focus on the representability of quantum observables by classical observables over a given state. Owing to the simplicity and operational…
Unsolved controversies about uncertainty relations and quantum measurements still persists nowadays. They originate around the shortcomings regarding the conventional interpretation of uncertainty relations. Here we show that the respective…
Order parameters based on spherical harmonics and Fourier coefficients already play a significant role in condensed matter research in the context of systems of spherical or point particles. Here, we extend these types of order parameter to…
We present some forms of uncertainty principle which involve in a new way localization operators, the concept of $\varepsilon$-concentration and the standard deviation of $L^2$ functions. We show how our results improve the classical…
The uncertainty principle generally prohibits determination of certain pairs of quantum mechanical observables with arbitrary precision and forms the basis of indeterminacy in quantum mechanics. It was Heisenberg who used the famous…
The investigations presented in this study are directed at relativistic modifications of the uncertainty relation derived from the curvature of the background spacetime. These findings generalize previous work which is recovered in the…
For deuteron photo- and electrodisintegration the selection of complete sets of polarization observables is discussed in detail by applying a recently developed new criterion for the check of completeness of a chosen set of observables. The…
The uncertainty relation of three quantities in quantum mechanics is estimated in terms of commutators. The Pauli matrices are used to find a contribution of third-order commutators. The resulting inequality refines the Heisenberg…
The unknown state of matter at ultra-high density, large proton/neutron number asymmetry, and low temperature is a major long-standing problem in modern physics. Neutron stars provide the only known setting in the Universe where matter in…
Supersonic beams of polar molecules are deflected using inhomogeneous electric fields. The quantum-state selectivity of the deflection is used to spatially separate molecules according to their quantum state. A detailed analysis of the…
The problem of characterising the accuracy of, and disturbance caused by a joint measurement of position and momentum is investigated. In a previous paper the problem was discussed in the context of the unbiased measurements considered by…