Related papers: Improved unitary uncertainty relations

The upper bound inequality for variance of weighted sum of correlated random variables is derived according to Cauchy-Schwarz's inequality, while the weights are non-negative with sum of 1. We also give a novel proof with positive…

Bounded uncertainty relations provide the minimum value of the uncertainty assuming some additional information on the state. We derive analytically an uncertainty relation bounded by a pair of constraints, those of purity and Gaussianity.…

We present uncertainty relations based on Wigner--Yanase--Dyson skew information with quantum memory. Uncertainty inequalities both in product and summation forms are derived. \mbox{It is} shown that the lower bounds contain two terms: one…

Uncertainty relations are one of the fundamental principles in physics. It began as a fundamental limitation in quantum mechanics, and today the word {\it uncertainty relation} is a generic term for various trade-off relations in nature. In…

We derive an entropic uncertainty relation for generalized positive-operator-valued measure (POVM) measurements via a direct-sum majorization relation using Schur concavity of entropic quantities in a finite-dimensional Hilbert space. Our…

For functions of independent random variables, various upper and lower variance bounds are revisited in diverse settings. These are then specialized to the Bernoulli, Gaussian, infinitely divisible cases and to Banach space valued random…

In recent letter [Phys.~Rev.~Lett {\bf 123}, 110602 (2019)], Y.~Hasegawa and T.~V.~Vu derived a thermodynamic uncertainty relation. But the bound of their relation is loose. In this comment, through minor changes, an improved bound is…

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 so-called preparation uncertainty can be understood in purely operational terms. Namely, it occurs when for some pair of observables, there is no preparation, for which they both exhibit deterministic statistics. However, the right-hand…

Entropic uncertainty relations $H(A)+H(B)\geqslant \gamma$ give a nonzero lower bound $\gamma$ to the sum of the Shannon entropies $H$ of the outcome probabilities of incompatible observables $A$ and $B$. They are better than the…

We propose a new scheme to express the uncertainty principle in form of inequality of the bipartite correlation functions for a given multipartite state, which provides an experimentally feasible and model-independent way to verify various…

In this paper we show how the superquadratic functions can be used as a tool for researching other types of convex functions like $\phi $-convexity, strong-convexity and uniform convexity. We show how to use inequalities satisfied by…

Uncertainty principle reveals the intrinsic differences between the classical and quantum worlds, which plays a significant role in quantum information theory. By using $\rho$-absolute variance, we introduce the uncertainty of quantum…

Recently, an entropic uncertainty relation for multiple measurements has been proposed by Liu et al. in [Phys. Rev. A 91, 042133 (2015)]. However, the lower bound of the relation is not always tight with respect to different measurements.…

This paper studies the Hardy-type inequalities on the discrete intervals. The first result is the variational formulas of the optimal constants. Using these formulas, one may obtain an approximating procedure and the known basic estimates…

We formulate some properties of a set of several mutually unbiased measurements. These properties are used for deriving entropic uncertainty relations. Applications of mutually unbiased measurements in entanglement detection are also…

Uncertainty relations for particle motion in curved spaces are discussed. The relations are shown to be topologically invariant. New coordinate system on a sphere appropriate to the problem is proposed. The case of a sphere is considered in…

Our knowledge of quantum mechanics can satisfactorily describe simple, microscopic systems, but is yet to explain the macroscopic everyday phenomena we observe. Here we aim to shed some light on the quantum-to-classical transition as seen…

We study fine-grained uncertainty relations for several quantum measurements in a finite-dimensional Hilbert space. The proposed approach is based on exact calculation or estimation of the spectral norms of corresponding positive matrices.…

As a very fundamental principle in quantum physics, uncertainty principle has been studied intensively via various uncertainty inequalities. Based on the information measure introduced by Brukner and Zeilinger in [Phys. Rev. Lett. 83, 3354…