Related papers: The Uncertainty Principle in Harmonic Analysis -- …
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…
This paper summarises a numerical investigation of phase mixing in time-independent Hamiltonian systems that admit a coexistence of regular and chaotic phase space regions, allowing also for low amplitude perturbations idealised as periodic…
Representing and quantifying uncertainty in physical parameterisations is a central challenge in weather and climate modelling, and approaches are often developed separately for different timescales. Here, we introduce a unified framework…
We study the variance in the measurement of observables during scattering events, as computed using amplitudes. The classical regime, characterised by negligible uncertainty, emerges as a consequence of an infinite set of relationships…
Several recent works encourage the use of a Bayesian framework when assessing performance and fairness metrics of a classification algorithm in a supervised setting. We propose the Uncertainty Matters (UM) framework that generalizes a…
Number-phase uncertainty relations are formulated in terms of unified entropies which form a family of two-parametric extensions of the Shannon entropy. For two generalized measurements, unified-entropy uncertainty relations are given in…
This paper originates from a naive attempt to establish various non-commutative Fourier theoretic inequalities for an inclusion of simple C*-algebras equipped with a conditional expectation of index-finite type. In this setting, we discuss…
In this paper, we review recent results on stability and instability in logarithmic Sobolev inequalities, with a particular emphasis on strong norms. We consider several versions of these inequalities on the Euclidean space, for the…
We approach uncertainty principles of Cowling-Price-Heis-\\enberg-type as a variational principle on modulation spaces. In our discussion we are naturally led to compact localization operators with symbols in modulation spaces. The optimal…
We consider the problem of rationalizing choice data by a preference satisfying an arbitrary collection of invariance axioms. Examples of such axioms include quasilinearity, homotheticity, independence-type axioms for mixture spaces,…
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…
Understanding the uncertainty of a neural network's (NN) predictions is essential for many purposes. The Bayesian framework provides a principled approach to this, however applying it to NNs is challenging due to large numbers of parameters…
We explore the modification of the entropic formulation of uncertainty principle in quantum mechanics which measures the incompatibility of measurements in terms of Shannon entropy. The deformation in question is the type so called…
We develop an information theoretic interpretation of the number-phase complementarity in atomic systems, where phase is treated as a continuous positive operator valued measure (POVM). The relevant uncertainty principle is obtained as an…
Uncertainty principle is one of the cornerstones of quantum theory. In the literature, there are two types of uncertainty relations, the operator form concerning the variances of physical observables and the entropy form related to entropic…
The quantum multiparameter estimation is very different from the classical multiparameter estimation due to Heisenberg's uncertainty principle in quantum mechanics. When the optimal measurements for different parameters are incompatible,…
By use of window functions, time-frequency analysis tools like Short Time Fourier Transform overcome a shortcoming of the Fourier Transform and enable us to study the time- frequency characteristics of signals which exhibit transient os-…
In this paper, we study the problem of control of discrete-time linear time varying systems over uncertain channels. The uncertainty in the channels is modeled as a stochastic random variable. We use exponential mean square stability of the…
Metric regularity is among the central concepts of nonlinear and variational analysis, constrained optimization, and their numerous applications. However, metric regularity can be elusive for some important ill-posed classes of problems…
A theory is developed to describe the nonlocal effect of spacetime quantization on position measurements transverse to macroscopic separations. Spacetime quantum states close to a classical null trajectory are approximated by plane…