Related papers: Heisenberg Uncertainty Relations as Statistical In…
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…
Uncertainty relations are a distinctive characteristic of quantum theory that impose intrinsic limitations on the precision with which physical properties can be simultaneously determined. The modern work on uncertainty relations employs…
The canonical commutation relation is a cornerstone of quantum theory and underlies the Heisenberg uncertainty principle. Although uncertainty relations have been extensively tested, direct verifications of the underlying commutation…
We introduce the probability distributions describing quantum observables in conventional quantum mechanics and clarify their relations to the tomographic probability distributions describing quantum states. We derive the evolution equation…
We introduce a quantum version for the statistical complexity measure, in the context of quantum information theory, and use it as a signalling function of quantum order-disorder transitions. We discuss the possibility for such transitions…
What does it take for real-deterministic c-valued (i.e., classical, commuting) variables to comply with the Heisenberg uncertainty principle? Here, we construct a class of real-deterministic c-valued variables out of the weak values…
Heisenberg's uncertainty principle has recently led to general measurement uncertainty relations for quantum systems: incompatible observables can be measured jointly or in sequence only with some unavoidable approximation, which can be…
This work completes the program started in \cite{bb1,bb2,bb3} to derive the Heisenberg uncertainty relation for relativistic particles. Sharp uncertainty relations for massive relativistic particles with spin 0 and spin 1 are derived. The…
Uncertainty relations (URs) like the Heisenberg-Robertson or the time-energy UR are often considered to be hallmarks of quantum theory. Here, a simple derivation of these URs is presented based on a single classical inequality from…
In the course of the last decades entropic uncertainty relations have attracted much attention not only due to their fundamental role as manifestation of non-classicality of quantum mechanics, but also as major tools for applications of…
The density operator of a quantum state can be represented as a complex joint probability of any two observables whose eigenstates have non-zero mutual overlap. Transformations to a new basis set are then expressed in terms of complex…
An approach is presented treating decision theory as a probabilistic theory based on quantum techniques. Accurate definitions are given and thorough analysis is accomplished for the quantum probabilities describing the choice between…
Both classical and respectively quantum observables can be modeled as somewhat similar examples of random variables. In such a model the associated measurements preserve the values spectrum of an observable but change the corresponding…
In standard formulations of the uncertainty principle, two fundamental features are typically cast as impossibility statements: two noncommuting observables cannot in general both be sharply defined (for the same state), nor can they be…
We define predictive states and predictive complexity for quantum systems composed of distinct subsystems. This complexity is a generalization of entanglement entropy. It is inspired by the statistical or forecasting complexity of…
Transition probabilities are an important and useful tool in quantum mechanics. However, in their present form, they are limited in scope and only apply to pure quantum states. In this article we extend their applicability to mixed states…
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…
Inferential models have recently gained in popularity for valid uncertainty quantification. In this paper, we investigate inferential models by exploring relationships between inferential models, fiducial inference, and confidence curves.…
We present critical arguments against individual interpretation of Bohr's complementarity and Heisenberg's uncertainty principles. Statistical interpretation of these principles is discussed in the contextual framework. We support the…
The proof of the Heisenberg uncertainty relation is modified to produce two improvements: (a) the resulting inequality is stronger because it includes the covariance between the two observables, and (b) the proof lifts certain restrictions…