Related papers: Relation between fundamental estimation limit and …
The Heisenberg limit provides a fundamental bound on the achievable estimation precision with a limited number of $N$ resources used (e.g., atoms, photons, etc.). Using entangled quantum states makes it possible to scale the precision with…
Heisenberg's reciprocal relation between position measurement error and momentum disturbance is rigorously proven under the assumption that those error and disturbance are independent of the state of the measured object. A generalization of…
We introduce a new information-theoretic formulation of quantum measurement uncertainty relations, based on the notion of relative entropy between measurement probabilities. In the case of a finite-dimensional system and for any approximate…
This paper is devoted to the study of the classical limit of quantum mechanics. In more detail we will elaborate on a method introduced by Hepp in 1974 for studying the asymptotic behavior of quantum expectations in the limit as Plank's…
An analysis of quantum measurement is presented that relies on an information-theoretic description of quantum entanglement. In a consistent quantum information theory of entanglement, entropies (uncertainties) conditional on measurement…
It is considered constraints imposed by the quantum mechanics on the measurement of the density of the electromagnetic energy. First, the energy of the electromagnetic wave and the volume (time) are bound with the Heisenberg uncertainty…
The uncertainty relation, as one of the fundamental principles of quantum physics, captures the incompatibility of noncommuting observables in the preparation of quantum states. In this work, we derive two strong and universal uncertainty…
We construct uncertainty relation for arbitrary finite dimensional PT invariant non-Hermitian quantum systems within a special inner product framework. This construction is led by good observables which are a more general class of…
The Heisenberg uncertainty relation, which links the uncertainties of the position and momentum of a particle, has an important footprint on the quantum behavior of a physical system. Analogous to this principle, we propose that…
The Bell's inequality is a strong criterion to distinguish classical and quantum mechanical aspects of reality. Its violation is the net effect of the existence of non-locality in systems, an advantage for quantum mechanics (QM) over…
We study the formulation of the uncertainty principle in quantum mechanics in terms of entropic inequalities, extending results recently derived by Bialynicki-Birula [1] and Zozor et al. [2]. Those inequalities can be considered as…
In this essay, we argue that certain aspects of the measurement require revision in Quantum Gravity. Using entropic arguments, we propose that the number of measurement outcomes and the accuracy (or the range) of the measurement are limited…
Measurement of minuscule forces and displacements with ever greater precision encounters a limit imposed by a pillar of quantum mechanics: the Heisenberg uncertainty principle. A limit to the precision with which the position of an object…
In spite \smallskip of their popularity the \QTR{bf}{H}eisenberg's (``uncertainty'') \QTR{bf}{R}elations (HR) still generate controversies. The \QTR{bf}{T}raditional \QTR{bf}{I}nterpretation of HR (TIHR) dominate our days science, although…
For a pair of observables, they are called "incompatible", if and only if the commutator between them does not vanish, which represents one of the key features in quantum mechanics. The question is, how can we characterize the…
It is shown that all the known uncertainty relations are the secondary consequences of Robertson's relation. The basic idea is to use the Heisenberg picture so that the time development of quantum mechanical operators incorporate the…
Although Heisenberg's uncertainty principle is represented by a rigorously proven relation about intrinsic indeterminacy in quantum states, Heisenberg's error-disturbance relation (EDR) has been commonly believed as another aspect of the…
For the power-law quantum wave packet in configuration space, the variance of the position observable may be divergent. Accordingly, the information-entropic formulation of the uncertainty principle becomes more appropriate than the…
Given two or more non-commuting observables, it is generally not possible to simultaneously assign precise values to each. This quantum mechanical uncertainty principle is widely understood to be encapsulated by some form of uncertainty…
Unsolved controversies about uncertainty relations and quantum measurements still persists nowadays. They originate around the shortcomings regarding the conventional interpretation of uncertainty relations. Here we show that the respective…