Related papers: Generalized Uncertainty Relation Between an Observ…
Using a recent construction of observables characterizing the time of occurence of an effect in quantum theory, we present a rigorous derivation of the standard time-energy uncertainty relation. In addition, we prove an uncertainty relation…
We here consider a generalization of the Klein-Gordon scalar wave equation which involves a single arbitrary function. The quantization may be viewed as allowing $\hbar$ to be a function of the momentum or wave vector rather than a…
Following to the Weil method we generalize the Heisenberg-Robertson uncertainty relation for arbitrary two operators. Consideration is made in spherical coordinates, where the distant variable is restricted from one side, . By this reason…
Uncertainty principle is one of the cornerstones of quantum theory. In the literature, there are two types of uncertainty relations, the operator form concerning the variances of physical observables and the entropy form related to entropic…
We analyze the Schwarz inequality and its generalizations, as well as inequalities resulting from the Jensen inequality. They are used in quantum theory to derive the Heisenberg-Robertson (HR) and Schroedinger-Robertson (SR) uncertainty…
It is generally argued that the combined effect of Heisenberg principle and general relativity leads to a minimum time uncertainty. Most of the analyses supporting this conclusion are based on a perturbative approach to quantization. We…
Relative fluctuations of observables in discrete stochastic systems are bounded at all times by the mean dynamical activity in the system, quantified by the mean number of jumps. This constitutes a kinetic uncertainty relation that is…
We use quantum estimation theory to derive a thermodynamic uncertainty relation in Markovian open quantum systems, which bounds the fluctuation of continuous measurements. The derived quantum thermodynamic uncertainty relation holds for…
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…
The thermodynamic uncertainty relation expresses a universal trade-off between precision and entropy production, which applies in its original formulation to current observables in steady-state systems. We generalize this relation to…
Conventional quantum uncertainty relations (URs) contain dispersions of two observables. Generalized URs are known which contain three or more dispersions. They are derived here starting with suitable generalized Cauchy inequalities. It is…
A generalized framework is developed which uses a set description instead of wavefunction to emphasize the role of the observer. Such a framework is found to be very effective in the study of the measurement problem and time's arrow.…
The Heisenberg-Robertson uncertainty relation quantitatively expresses the impossibility of jointly sharp preparation of incompatible observables. However it does not capture the concept of incompatible observables because it can be trivial…
Time averaging of weak values using the quantum transition path time probability distribution enables us to establish a general uncertainty principle for the weak values of two not necessarily Hermitian operators. This new principle is a…
In the conventional formulation, it is broadly accepted that simultaneous measurability and commutativity of observables are equivalent. However, several objections have been claimed that there are cases in which even nowhere commuting…
A generalized Cauchy-Schwarz inequality is derived and applied to uncertainty relation in quantum mechanics. We see a modification in the uncertainty relation and minimum uncertainty wave packet.
General characterization of physical measurements is discussed within the framework of a classical information theory. Uncertainty relation for simultaneous measurements of two physical observables is defined in this framework for…
As a foundation of modern physics, uncertainty relations describe an ultimate limit for the measurement uncertainty of incompatible observables. Traditionally, uncertain relations are formulated by mathematical bounds for a specific state.…
A survey on the generalizations of Heisenberg uncertainty relation and a general scheme for their entangled extensions to several states and observables is presented. The scheme is illustrated on the examples of one and two states and…
Uncertainty relations express limits on the extent to which the outcomes of distinct measurements on a single state can be made jointly predictable. The existence of nontrivial uncertainty relations in quantum theory is generally considered…