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Uncertainty relations are usually formulated as trade-off relations between two or more observables. Here we show that the uncertainty of a single observable already has a nontrivial lower bound originating from the noncommutativity between…
Recently, Zheng constructs a quantum-control-assisted multipartite variance-based uncertainty relation, which successfully extends the conditional uncertainty relation to the multipartite case [Annalen der physik, 533, 2100014 (2021)]. We…
Within a self-consistent framework of q-deformed Heisenberg algebra and its equivalent framework of q-deformed boson commutation relations, which relate to the under-cutting phenomenon of Heisenberg's minimal uncertainty relation, special…
For a symmetric Hamiltonian system, lower bounds for the number of relative equilibria surrounding stable and formally unstable relative equilibria on nearby energy levels are given.
The usual Heisenberg uncertainty relation for position and momentum may be replaced by an exact equality, for suitably chosen measures of position and momentum uncertainty. This "exact" uncertainty relation is valid for_all_ pure states,…
Spacetime variations of physical constants can be associated with the existence of Higgs-like scalar field(s) that couple non-universally to the baryonic matter. Recent results of astronomical spectral measurements of the fractional changes…
Heisenberg's uncertainty principle states that the position and momentum of a particle cannot be sharply determined simultaneously. Standard-deviation and entropic formulations capture the spread of the probability distribution but say…
By invoking quantum estimation theory we formulate bounds of errors in quantum measurement for arbitrary quantum states and observables in a finite-dimensional Hilbert space. We prove that the measurement errors of two observables satisfy…
Recently, [10,11], the Heisenberg Uncertainty relation and the No-Cloning property in Quantum Mechanics and Quantum Computation, respectively, have been extended to versions of Quantum Mechanics and Quantum Computation which are…
We calculate the uncertainties in the position and momentum of a particle in the 1D potential V(x)=F|x|, F>0, when the position and momentum operators obey the deformed commutation relation [x,p]=i\hbar(1+\beta p^2), \beta>0. As in the…
We address the question, does a system A being entangled with another system B, put any constraints on the Heisenberg uncertainty relation (or the Schrodinger-Robertson inequality)? We find that the equality of the uncertainty relation…
One of the formulations of Heisenberg uncertainty principle, concerning so-called measurement uncertainty, states that the measurement of one observable modifies the statistics of the other. Here, we derive such a measurement uncertainty…
We suggest to use the photon homodyne detection experimental data for checking the Heisenberg and Schr\"{o}dinger-Robertson uncertainty relations, by means of measuring optical tomograms of the photon quantum states.
In this work we determine a lower bound to the mean value of the quantum potential for an arbitrary state. Furthermore, we derive a generalized uncertainty relation that is stronger than the Robertson-Schr\"odinger inequality and hence also…
A non-moving electron hydrogen model is proposed, resolving a long standing contradiction (94 years) in the hydrogen atom. This, however, forces to not use the "in an orbit point particle kinetic energy" as the phenomenon responsible for…
Combining the quantum scale invariance with the absence of new degrees of freedom above the electroweak scale leads to stability of the latter against perturbative quantum corrections. Nevertheless, the hierarchy between the weak and the…
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…
A general theory of preparational uncertainty relations for a quantum particle in one spatial dimension is developed. We derive conditions which determine whether a given smooth function of the particle's variances and its covariance is…
We study the consequences of the generalized Heisenberg uncertainty relation which admits a minimal uncertainty in length such as the case in a theory of quantum gravity. In particular, the theory of quantum harmonic oscillators arising…
One of the formulations of Heisenberg uncertainty principle, concerning so-called measurement uncertainty, states that the measurement of one observable modifies the statistics of the other. Here, we derive such a measurement uncertainty…