Related papers: A Universal Formulation of Uncertainty Relation fo…
We discuss some applications of various versions of uncertainty relations for both discrete and continuous variables in the context of quantum information theory. The Heisenberg uncertainty relation enables demonstration of the EPR paradox.…
The Heisenberg uncertainty principle is one of the fundamental pillars of quantum mechanics and quantum field theory. It is normally introduced by postulating the commutation relations $[\hat{x}^i, \hat{p}^j] = i\hbar \delta^{ij}$. However,…
We study the commutation relations, uncertainty relations and spectra of position and momentum operators within the framework of quantum group % symmetric Heisenberg algebras and their (Bargmann-) Fock representations. As an effect of the…
We prove a new sum uncertainty relation in quantum theory which states that the uncertainty in the sum of two or more observables is always less than or equal to the sum of the uncertainties in corresponding observables. This shows that the…
The concept of quantum coherence, including various ways to quantify the degree of coherence with respect to the prescribed basis, is currently the subject of active research. The complementarity of quantum coherence in different bases was…
In quantum mechanics, the variance-based Heisenberg-type uncertainty relations are a series of mathematical inequalities posing the fundamental limits on the achievable accuracy of the state preparations. In contrast, we construct and…
We report a universal improvement to the standard Robertson--Schr\"odinger uncertainty relation. Our result shows that the Robertson--Schr\"odinger lower bound can be supplemented by a new noncommutativity-induced term. This term represents…
For angular observables pairs (angular momentum-angle and number-phase) the adequate reference element of normality is not the Robertson-Schr\"{o}dinger uncertainty relation but a Schwarz formula regarding the quantum fluctuations. Beyond…
A common knowledge suggests that trajectories of particles in quantum mechanics always have quantum uncertainties. These quantum uncertainties set by the Heisenberg uncertainty principle limit precision of measurements of fields and forces,…
Indirect measurement can be used to read out the outcome of a quantum system without resorting to a straightforward approach, and it is the foundation of the measurement uncertainty relations that explain the incompatibility of conjugate…
In quantum theory, it is known for a pair of noncommutative observables that there is no state on which they take simultaneously definite values, and that there is no joint measurement of them. They are called preparation uncertainty and…
It is generally believed that classical regime emerges as a limiting case of quantum theory. Exploring such quantum-classical correspondences in a more transparent manner is central to the deeper understanding of foundational aspects and…
While the slogan "no measurement without disturbance" has established itself under the name Heisenberg effect in the consciousness of the scientifically interested public, a precise statement of this fundamental feature of the quantum world…
Heisenberg's reciprocal relation between position measurement error and momentum disturbance is rigorously proven under the assumption that those error and disturbance are independent of the state of the measured object. A generalization of…
The standard uncertainty relations (UR) in quantum mechanics are typically used for unbounded operators (like the canonical pair). This implies the need for the control of the domain problems. On the other hand, the use of (possibly…
We derive two quantum uncertainty relations for position and momentum coarse-grained measurements. Building on previous results, we first improve the lower bound for uncertainty relations using the Renyi entropy, particularly in the case of…
It is proved that the width of a function and the width of the distribution of its values cannot be made arbitrarily small simultaneously. In the case of ergodic stochastic processes, an ensuing uncertainty relationship is demonstrated for…
The Ehrenfest theorem and the Robertson uncertainty relation are well-known basic equations in quantum mechanics. However, there exist problematic cases, where the Ehrenfest theorem and the Robertson uncertainty relation are not correct.…
In the history of quantum mechanics, various types of uncertainty relationships have been introduced to accommodate different operational meanings of Heisenberg uncertainty principle. We derive an optimized entropic uncertainty relation…
In two articles, the authors claim that the Heisenberg uncertainty principle limits the precision of simultaneous measurements of the position and velocity of a particle and refer to experimental evidence that supports their claim. It is…