Related papers: Tight Entropic Uncertainty Relations
We obtain uncertainty and certainty relations of state-independent form for the three Pauli observables with use of the R\'enyi entropies of order $\alpha\in(0;1]$. It is shown that these entropic bounds are tight in the sense that they are…
We formulate uncertainty relations for mutually unbiased bases and symmetric informationally complete measurements in terms of the R\'{e}nyi and Tsallis entropies. For arbitrary number of mutually unbiased bases in a finite-dimensional…
We derive two quantum uncertainty relations for position and momentum coarse-grained measurements. Building on previous results, we first improve the lower bound for uncertainty relations using the Renyi entropy, particularly in the case of…
Recently, Maccone and Pati have given two stronger uncertainty relations based on the sum of variances and one of them is nontrivial when the quantum state is not an eigenstate of the sum of the observables. We derive a family of weighted…
The entropic way of formulating Heisenberg's uncertainty principle not only plays a fundamental role in applications of quantum information theory but also is essential for manifesting genuine nonclassical features of quantum systems. In…
Quantifying quantum mechanical uncertainty is vital for the increasing number of experiments that reach the uncertainty limited regime. We present a method for computing tight variance uncertainty relations, i.e., the optimal…
Gaussian distribution of a quantum state with continuous spectrum is known to maximize the Shannon entropy at a fixed variance. Applying it to a pair of canonically conjugate quantum observables $\hat x$ and $\hat p$, quantum entropic…
In this work we use the extremization method of various information-theoretic measures (Fisher information, Shannon entropy, Tsallis entropy) for $d$-dimensional quantum systems, which complementary describe the spreading of the quantum…
We investigate entropic uncertainty relations for two or more binary measurements, for example spin-$\frac{1}{2}$ or polarisation measurements. We argue that the effective anti-commutators of these measurements, i.e. the anti-commutators…
A new lower boundary for the product of variances of two observables is obtained in the case, when these observables are entangled with the third one. This boundary can be higher than the Robertson--Schr\"odinger one. The special case of…
We consider the question of entropic uncertainty relations for prime power dimensions. In order to improve upon such uncertainty relations for higher dimensional quantum systems, we derive a tight lower bound amount of entropy for multiple…
The optimal state-independent lower bounds for the sum of variances or deviations of observables are of significance for the growing number of experiments that reach the uncertainty limited regime. We present a framework for computing the…
Entropic uncertainty relations demonstrate the intrinsic uncertainty of nature from an information-theory perspective. Recently, a quantum-memory-assisted entropic uncertainty relation for multiple measurements was proposed by Wu $et\ al.$…
This paper provides tight bounds on the R\'enyi entropy of a function of a discrete random variable with a finite number of possible values, where the considered function is not one-to-one. To that end, a tight lower bound on the R\'enyi…
Entropic uncertainty is a well-known concept to formulate uncertainty relations for continuous variable quantum systems with finitely many degrees of freedom. Typically, the bounds of such relations scale with the number of oscillator…
The entropic uncertainty relations are a very active field of scientific inquiry. Their applications include quantum cryptography and studies of quantum phenomena such as correlations and non-locality. In this work we find…
Commutator-based entropic uncertainty relations in multidimensional position and momentum spaces are derived, twofold generalizing previous entropic uncertainty relations for one-mode states. They provide optimal lower bounds and imply the…
We show within a very simple framework that different measures of fluctuations lead to uncertainty relations resulting in contradictory conclusions. More specifically we focus on Tsallis and Renyi entropic uncertainty relations and we get…
We propose an alternative measure of quantum uncertainty for pairs of arbitrary observables in the 2-dimensional case, in terms of collision entropies. We derive the optimal lower bound for this entropic uncertainty relation, which results…
From a recent geometric generalization of Thermodynamic Uncertainty Relations (TURs) we derive novel upper bounds on the nonlinear response of an observable of an arbitrary system undergoing a change of probabilistic state. Various…