Related papers: Tight entropic uncertainty relations for systems w…
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…
We conjecture new uncertainty relations which restrict correlations between results of measurements performed by two separated parties on a shared quantum state. The first uncertainty relation bounds the sum of two mutual informations when…
We show that a proper expression of the uncertainty relation for a pair of canonically-conjugate continuous variables relies on entropy power, a standard notion in Shannon information theory for real-valued signals. The resulting…
Entropic uncertainty relations are powerful tools, especially in quantum cryptography. They typically bound the amount of uncertainty a third-party adversary may hold on a measurement outcome as a result of the measurement overlap. However,…
Uncertainty relations give upper bounds on the accuracy by which the outcomes of two incompatible measurements can be predicted. While established uncertainty relations apply to cases where the predictions are based on purely classical data…
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…
The aim of this focus letter is to present a comprehensive classification of the main entropic forms introduced in the last fifty years in the framework of statistical physics and information theory. Most of them can be grouped into three…
There is a renewed interest in the uncertainty principle, reformulated from the information theoretic point of view, called the entropic uncertainty relations. They have been studied for various integrable systems as a function of their…
Incompatible observables can be approximated by compatible observables in joint measurement or measured sequentially, with constrained accuracy as implied by Heisenberg's original formulation of the uncertainty principle. Recently, Busch,…
Statistical mechanics for states with complex eigenvalues, which are described by Gel'fand triplet and represent unstable states like resonances, are discussed on the basis of principle of equal ${\it a priori}$ probability. A new entropy…
Entropic uncertainty relations in a finite dimensional Hilbert space are investigated. Making use of the majorization technique we derive explicit lower bounds for the sum of R\'enyi entropies describing probability distributions associated…
There is no single universally accepted definition of "Complexity". There are several perspectives on complexity and what constitutes complex behaviour or complex systems, as opposed to regular, predictable behaviour and simple systems. In…
How violently do two quantum operators disagree? Different fields of physics feature different measures of incompatibility: (i) In quantum information theory, entropic uncertainty relations constrain measurement outcomes. (ii) In condensed…
Given a narrow signal over the real line, there is a limit to the localisation of its Fourier transform. In spaces of prime dimensions, Tao derived a sharp state-independent uncertainty relation which holds for the support sizes of a pure…
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…
Uncertainty relation is one of the fundamental building blocks of quantum theory. Nevertheless, the traditional uncertainty relations do not fully capture the concept of incompatible observables. Here we present a stronger…
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…
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…
We formulate uncertainty relations for arbitrary $N$ observables. Two uncertainty inequalities are presented in terms of the sum of variances and standard deviations, respectively. The lower bounds of the corresponding sum uncertainty…
The new estimates of the conditional Shannon entropy are introduced in the framework of the model describing a discrete response variable depending on a vector of d factors having a density w.r.t. the Lebesgue measure in R^d. Namely, the…