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Heisenberg's uncertainty relation is commonly regarded as defining a level of unpredictability that is fundamentally incompatible with the deterministic laws embodied in classical field theories such as Einstein's general relativity. We…
Learning physical properties of a quantum system is essential for the developments of quantum technologies. However, Heisenberg's uncertainty principle constrains the potential knowledge one can simultaneously have about a system in quantum…
The discrete Frenet equation entails a local framing of a discrete, piecewise linear polygonal chain in terms of its bond and torsion angles. In particular, the tangent vector of a segment is akin the classical O(3) spin variable. Thus…
Heisenberg's uncertainty principle forms a fundamental element of quantum mechanics. Uncertainty relations in terms of entropies were initially proposed to deal with conceptual shortcomings in the original formulation of the uncertainty…
We extend the classical Heisenberg uncertainty principle to a fractional $L^p$ setting by investigating a novel class of uncertainty inequalities derived from the fractional Schr\"odinger equation. In this work, we establish the existence…
While there is a rigorously proven relationship about uncertainties intrinsic to any quantum system, often referred to as "Heisenberg's Uncertainty Principle," Heisenberg originally formulated his ideas in terms of a relationship between…
Heisenberg's uncertainty principle, which imposes intrinsic restrictions on our ability to predict the outcomes of incompatible quantum measurements to arbitrary precision, demonstrates one of the key differences between classical and…
For a simple set of observables we can express, in terms of transition probabilities alone, the Heisenberg Uncertainty Relations, so that they are proven to be not only necessary, but sufficient too, in order for the given observables to…
In the present paper, a discrete differential calculus is introduced and used to describe dynamical systems over arbitrary graphs. The discretization of space and time allows the derivation of Heisenberg-like uncertainty inequalities and of…
This note shows that Heisenberg's choice for a wave function in his original paper on the uncertainty principle is simply a renormalized characteristic function of a stable distribution with certain restrictions on the parameters. Relaxing…
In this paper we discuss some aspects of the Heisenberg uncertainty relation, mostly from the point of view of non self-adjoint operators. Some equivalence results, and some refinements of the inequality, are deduced, and some relevant…
In this paper we derive a Heisenberg-type uncertainty principle for the continuous Clifford wavelet transform. A brief review of Clifford algebra/analysis, wavelet transform on $\mathbb{R}$ and Clifford-Fourier transform and their…
Time-frequency concentration and resolution of the Cohen's class time-frequency distribution (CCTFD) has attracted much attention in time-frequency analysis. A variety of uncertainty principles of the CCTFD is therefore derived, including…
It is shown that the well-defined unbiased measurement or disturbance of a dynamical variable is not maintained for the precise measurement of the conjugate variable, independently of uncertainty relations. The conditionally valid…
We ask which is the best strategy to reveal uncertainty relations between comple- mentary observables of a continuous variable system for coarse-grained measurements. This leads to the derivation of new uncertainty relations for…
What does it take for real-deterministic c-valued (i.e., classical, commuting) variables to comply with the Heisenberg uncertainty principle? Here, we construct a class of real-deterministic c-valued variables out of the weak values…
In its original formulation, Heisenberg's uncertainty principle describes a trade-off relation between the error of a quantum measurement and the thereby induced disturbance on the measured object. However, this relation is not valid in…
The Heisenberg uncertainty principle and its extensions are all still inequalities form which hold the superior approximate estimations. Based on quantum covariant Poisson bracket theory, we propose quantum geomertainty relation to modify…
We revisit the uncertainty principle from the point of view suggested by A. Wigderson and Y. Wigderson. This approach is based on a primary uncertainty principle from which one can derive several inequalities expressing the impossibility of…
Quantum phase transitions are often embodied by the critical behavior of purely quantum quantities such as entanglement or quantum fluctuations. In critical regions, we underline a general scaling relation between the entanglement entropy…