Related papers: Position and momentum cannot both be lazy: Quantum…
Position measurements are examined under the assumption that object position x_t and probe position X_t just after the measurement are expressed by a linear combination of positions x_0 and X_0 just before the measurement. The Heisenberg…
We derive new Heisenberg-type uncertainty relations for both joint measurability and the error-disturbance tradeoff for arbitrary observables of finite-dimensional systems. The relations are formulated in terms of a directly operational…
Planck-scale quantum spacetime undergoes probabilistic local curvature fluctuations whose distributions cannot explicitly depend on position otherwise vacuum's small-scale quantum structure would fail to be statistically homogeneous. Since…
Based on the assumption that the probability density of finding a free particle is independent of position, we infer the form of the eigenfunction for the free particle, $\bra{x} p > = \exp(ipx/\hbar)/\sqrt{2\pi\hbar}$. The canonical…
Quantum mechanics postulates the existence of states determined by a particle position at a single time. This very concept, in conjunction with superposition, induces much of the quantum-mechanical structure. In particular, it implies the…
Systems switching between different dynamical phases is an ubiquitous phenomenon. The general understanding of such a process is limited. To this end, we present a general expression that captures fluctuations of a system exhibiting a…
Studying the relations between entanglement and coherence is essential in many quantum information applications. For this, we consider the concurrence, intrinsic concurrence and first-order coherence, and evaluate the proposed trade-off…
The more information a measurement provides about a quantum system's position statistics, the less information a subsequent measurement can provide about the system's momentum statistics. This information trade-off is embodied in the…
Quantum coherence is the outcome of the superposition principle. Recently, it has been theorized as a quantum resource, and is the premise of quantum correlations in multipartite systems. It is therefore interesting to study the coherence…
Optimal simultaneous control of position and momentum can be achieved by maximizing the probabilities of finding their experimentally observed values within two well-defined intervals. The assumption that particles move along straight lines…
The spread of the wave-function, or quantum uncertainty, is a key notion in quantum mechanics. At leading order, it is characterized by the quadratic moments of the position and momentum operators. These evolve and fluctuate independently…
Uncertainty relations provide fundamental limits on what can be said about the properties of quantum systems. For a quantum particle, the commutation relation of position and momentum observables entails Heisenberg's uncertainty relation. A…
In the Entropic Dynamics (ED) approach to quantum theory the particles have well-defined positions but since they follow non differentiable Brownian trajectories they cannot be assigned an instantaneous momentum. Nevertheless, four…
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 consider the uncertainty relation between position and momentum of a particle on $ S^1 $ (a circle). Since $ S^1 $ is compact, the uncertainty of position must be bounded. Consideration on the uncertainty of position demands delicate…
The idea to base the uncertainty relation for photons on the electromagnetic energy distribution in space enabled us to derive a sharp inequality that expresses the uncertainty relation [Phys. Rev. Lett. {\bf 108}, 140401 (2012)]. An…
In Bayesian statistics, a continuity property of the posterior distribution with respect to the observable variable is crucial as it expresses well-posedness, i.e., stability with respect to errors in the measurement of data. Essentially,…
We re-derive the Schr\"{o}dinger-Robertson uncertainty principle for the position and momentum of a quantum particle. Our derivation does not directly employ commutation relations, but works by reduction to an eigenvalue problem related to…
We consider the quantum and classical Liouville dynamics of a non-integrable model of two coupled spins. Initially localised quantum states spread exponentially to the system dimension when the classical dynamics are chaotic. The long-time…
The conditions for observation of the particle coordinates, required by logic of the Special Relativity and filtering the quantum field effects, are described. A general relation between the corresponding density of probability and the wave…