Related papers: Universality in Uncertainty Relations for a Quantu…
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…
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.…
Using tangent bundle geometry we construct an equivalent reformulation of classical field theory on flat spacetimes which simultaneously encodes the perspectives of multiple observers. Its generalization to curved spacetimes realizes a new…
Quantum states can be subjected to classical measurements, whose incompatibility, or uncertainty, can be quantified by a comparison of certain entropies. There is a long history of such entropy inequalities between position and momentum.…
We consider particles prepared by the von Neumann-L\"uders projection. For those particles the standard deviation of the momentum is discussed. We show that infinite standard deviations are not exceptions but rather typical. A necessary and…
Universally valid uncertainty relations are proven in a model independent formulation for inherent and unavoidable extra noises in arbitrary joint measurements on single systems, from which Heisenber's original uncertainty relation is…
Quantum mechanics predicts that measurements of incompatible observables carry a minimum uncertainty which is independent of technical deficiencies of the measurement apparatus or incomplete knowledge of the state of the system. Nothing yet…
Two generalizations of Kempf's quadratic canonical commutation relation in one dimension are considered. The first one is the most general quadratic commutation relation. The corresponding nonzero minimal uncertainties in position and…
Quantum uncertainty relations are formulated in terms of relative entropy between distributions of measurement outcomes and suitable reference distributions with maximum entropy. This type of entropic uncertainty relation can be applied…
The uncertainty principle restricts potential information one gains about physical properties of the measured particle. However, if the particle is prepared in entanglement with a quantum memory, the corresponding entropic uncertainty…
We proved that the uncertainty relation fits in with many-particle system and the equality of the relation corresponds to the thermodynamic equilibrium state, the inequality of the relation corresponds to the thermodynamic non-equilibrium…
An important task faced by all approaches of quantum gravity is to incorporate superpositions and quantify quantum uncertainties of spacetime causal relations. We address this task in 2D. By identifying a global $Z_2$ symmetry of 1+1D…
We give a bound to the precision in the estimation of a parameter in terms of the expectation value of an observable. It is an extension of the Cramer-Rao inequality and of the Heisenberg uncertainty relation, where the estimation precision…
Entropic uncertainty relations for the position and momentum within the generalized uncertainty principle are examined. Studies of this principle are motivated by the existence of a minimal observable length. Then the position and momentum…
A geometric approach to formulate the uncertainty principle between quantum observables acting on an $N$-dimensional Hilbert space is proposed. We consider the fidelity between a density operator associated with a quantum system and a…
Various theories that aim at unifying gravity with quantum mechanics suggest modifications of the Heisenberg algebra for position and momentum. From the perspective of quantum mechanics, such modifications lead to new uncertainty relations…
Uncertainty relations are old, yet potentially rewarding to explore. By introducing a quantity called the uncertainty matrix, we provide a link between purity and observable incompatibility, and derive several stronger uncertainty relations…
The condition for the unitarity of a quantum field is investigated in semiclassical gravity from the Wheeler-DeWitt equation. It is found that the quantum field preserves unitarity asymptotically in the Lorentzian universe, but does not…
A numerical illustration of a universally valid Heisenberg uncertainty relation, which was proposed recently, is presented by using the experimental data on spin-measurements by J. Erhart, et al.[ Nature Phys. {\bf 8}, 185 (2012)]. This…
We provide a decision-theoretic framework for dealing with uncertainty in quantum mechanics. This uncertainty is two-fold: on the one hand there may be uncertainty about the state the quantum system is in, and on the other hand, as is…