Related papers: Minimum uncertainty measurements of angle and angu…
Introductory courses on quantum mechanics usually include lectures on uncertainty relations, typically the inequality derived by Robertson and, perhaps, other statements. For the benefit of the lecturers, we present a unified approach --…
We investigate the classical problem of motion of a mathematical pendulum with an oscillating pivot. This simple mechanical setting is frequently used as the prime example of a system exhibiting the parametric resonance phenomenon, which…
The apparent random outcome of a quantum measurement is conjectured to be fundamentally determined by the microscopic state of the macroscopic measurement apparatus. The apparatus state thus plays the role of a hidden variable which, in…
Weighting methods are widely used to adjust for covariates in observational studies, sample surveys, and regression settings. In this paper, we study a class of recently proposed weighting methods which find the weights of minimum…
Uncertainty principle is one of the most essential features in quantum mechanics and plays profound roles in quantum information processing. We establish tighter summation form uncertainty relations based on metric-adjusted skew information…
Uncertainty relations describe the lower bound of product of standard deviations of observables. By revealing a connection between standard deviations of quantum observables and numerical radius of operators, we establish a universal…
We analyze various uncertainty measures for spatial diffusion processes. In this manifestly non-quantum setting, we focus on the existence issue of complementary pairs whose joint dispersion measure has strictly positive lower bound.
We describe a six-parameter family of the minimum-uncertainty squeezed states for the harmonic oscillator in nonrelativistic quantum mechanics. They are derived by the action of corresponding maximal kinematical invariance group on the…
The general expression of the angular distance between two point sources as measured by an arbitrary observer is given. The modelling presented here is rigorous, covariant and valid in any space-time. The sources of light may be located at…
We study a possible improvement of uncertainty relations. The Heisenberg uncertainty relation employs commutator of a pair of conjugate observables to set the limit of quantum measurement of the observables. The Schroedinger uncertainty…
Uncertainty relations are fundamental in quantum mechanics. Here I propose state-independent variance-based uncertainty relations for two or more arbitrary observables in finite dimensional spaces. The uncertainty relations provide…
Many methods now exist to prepare free electrons into orbital angular momentum states, and the predicted applications of these electron states as probes of materials and scattering processes are numerous. The development of electron orbital…
We propose a scheme to distinguish the orbital angular momentum state of the Laguerre-Gaussian (LG) beam based on the electromagnetically induced transparency modulated by a microwave field in atomic ensembles. We show that the transverse…
There are various measures of predictive uncertainty in the literature, but their relationships to each other remain unclear. This paper uses a decomposition of statistical pointwise risk into components, associated with different sources…
In this paper, we investigate the applicability of the astrometric method to the determination of the lens parameters for gravitational microlensing events toward both the LMC and the Galactic bulge. For this analysis, we investigate the…
We describe a connection between minimal uncertainty states and holomorphy-type conditions on the images of the respective wavelet transform. The most familiar example is the Fock-Segal-Bargmann transform generated by the Gaussian, however,…
We discuss the uncertainty relation for the azimuthal angle $\phi$ and the $z$-component of the angular momentum $L_z$. To this end we derive the uncertainty relation for an arbitrary pair of observables and discuss the conditions for its…
Using multi-photon entangled input states, we estimate the phase uncertainty in a noiseless Mach-Zehnder interferometer (MZI) using photon-counting detection. We assume a flat prior uncertainty and use Bayesian inference to construct a…
The quantification of the "measurement uncertainty" aspect of Heisenberg's Uncertainty Principle---that is, the study of trade-offs between accuracy and disturbance, or between accuracies in an approximate joint measurement on two…
Quantum mechanics relates probability of an observable event to the absolute square of the corresponding probability amplitude. It may, therefore, seem that the information about the amplitudes' phases must be irretrievably lost in the…