Related papers: State Extended Uncertainty Relations
Constructive techniques to establish state-independent uncertainty relations for the sum of variances of arbitrary two observables are presented. We investigate the range of simultaneously attainable pairs of variances, which can be applied…
The well-known Robertson-Schr\"odinger uncertainty relations have state-dependent lower bounds which are trivial for certain states. We present a general approach to deriving tight state-independent uncertainty relations for qubit…
New uncertainty relations for n observables are established. The relations take the invariant form of inequalities between the characteristic coefficients of order r, r = 1,2,...,n, of the uncertainty matrix and the matrix of mean…
The celebrated Heisenberg Uncertainty Principle \Delta x \Delta p\ge \hbar/2 can allow measurement accuracies less than \Delta x or \Delta p. Classical analog of this is known as sub-Fourier sensitivity. We illustrate this phenomenon in a…
The disputed question of uncertainty relations (UR) on a circle is regarded as a particular element of a more general problem which refers to the quantum description of angular observables $L_z$ and $\phi$. The improvised $L_z-\phi$ UR are…
We investigate the additivity properties for both bipartite and multipartite systems by using entropic uncertainty relations (EUR) defined in terms of the joint Shannon entropy of probabilities of local measurement outcomes. In particular,…
The uncertainty relation is a distinguishing feature of quantum theory, characterizing the incompatibility of noncommuting observables in the preparation of quantum states. Recently, many uncertainty relations were proposed with improved…
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…
Uncertainty relations are usually formulated as trade-off relations between two or more observables. Here we show that the uncertainty of a single observable already has a nontrivial lower bound originating from the noncommutativity between…
The variance of an observable in a quantum state is usually used to describe Heisenberg uncertainty relation. For mixed states, the variance includes quantum uncertainty and classical uncertainty. By means of the skew information and the…
We derive an uncertainty relation for two unitary operators which obey a commutation relation of the form UV=exp[i phi] VU. Its most important application is to constrain how much a quantum state can be localised simultaneously in two…
Quantum uncertainty relations have deep-rooted significance on the formalism of quantum mechanics. Heisenberg's uncertainty relations attracted a renewed interest for its applications in quantum information science. Robertson derived a…
For a simple set of observables we can express, in terms of transition probabilities alone, the Heisenberg Uncertainty Relations, so that they are proven to be not only necessary, but sufficient too, in order for the given observables to…
We derive entropic uncertainty relations for successive generalized measurements by using general descriptions of quantum measurement within two {distinctive operational} scenarios. In the first scenario, by merging {two successive…
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.…
Heisenberg's uncertainty principle is usually taken to express a limitation of operational possibilities imposed by quantum mechanics. Here we demonstrate that the full content of this principle also includes its positive role as a…
Two special situations where the standard uncertainty product inequality appears to be useless are modified. One such case is noted to also trivialize the recently-introduced alternatives [Phys. Rev. Lett. 113, 260401 (2014); Sci. Rep. 6,…
This contribution to the present Workshop Proceedings outlines a general programme for identifying geometric structures--out of which to possibly recover quantum dynamics as well--associated to the manifold in Hilbert space of the quantum…
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…
The Heisenberg inequality \Delta X \Delta P \geq \hbar/2 can be replaced by an exact equality, for suitably chosen measures of position and momentum uncertainty, which is valid for all wavefunctions. The statistics of complementary…