Related papers: Tighter sum uncertainty relations via variance and…
We analyze the uncertainty relation for the sum of variances, which is called in some papers, the stronger uncertainty relation for all incompatible observables. We show that this uncertainty relation for the sum of variances of the…
We analyze the weak and critical points of various uncertainty relations that follow from the inequalities for the norms of vectors in the Hilbert space of states of a quantum system. There are studied uncertainty relations for sums of…
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 prove a new sum uncertainty relation in quantum theory which states that the uncertainty in the sum of two or more observables is always less than or equal to the sum of the uncertainties in corresponding observables. This shows that the…
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…
We show how preparation uncertainty relations that are formulated as sums of variances may be tightened by using the quantum Fisher information to quantify quantum fluctuations. We apply this to derive stronger angular momentum uncertainty…
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 shall give a new Schr\"odinger type uncertainty relation for a quantity representing a quantum uncertainty, introduced by S.Luo in \cite{Luo1}. Our result improves the Heisenberg uncertainty relation shown in \cite{Luo1} for a mixed…
Uncertainty relations are pivotal in delineating the limits of simultaneous measurements for observables. In this paper, we derive four novel uncertainty and reverse uncertainty relations for the sum of variances of two incompatible…
Uncertainty relation is a fundamental issue in quantum mechanics and quantum information theory. By using modified generalized variance (MGV), and modified generalized Wigner-Yanase-Dyson skew information (MGWYD), we identify the total and…
We present a versatile inequality of uncertainty relations which are useful when one approximates an observable and/or estimates a physical parameter based on the measurement of another observable. It is shown that the optimal choice for…
We study quantum information inequalities and show that the basic inequality between the quantum variance and the metric adjusted skew information generates all the multi-operator matrix inequalities or Robertson type determinant…
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…
We give a trace inequality related to the uncertainty relation based on the monotone or anti-monotone pair skew information which is one of generalizations of result given by Ko and Yoo. It includes our result for generalized…
We utilize quantum superposition principle to establish the improvable upper and lower bounds on the stronger uncertainty relation, i.e., the "weighted-like" sum of the variances of observables. Our bounds include some free parameters which…
A Bell-type inequality is proposed in terms of Wigner-Yanase skew information, which is quadratic and involves only one local spin observable at each site. This inequality presents a hierarchic classification of all states of multipartite…
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…
Learning physical properties of a quantum system is essential for the developments of quantum technologies. However, Heisenberg's uncertainty principle constrains the potential knowledge one can simultaneously have about a system in quantum…
A generalized Cauchy-Schwarz inequality is derived and applied to uncertainty relation in quantum mechanics. We see a modification in the uncertainty relation and minimum uncertainty wave packet.
Uncertainty relations describe the lower bound of product of standard deviations of observables. By revealing a connection between standard deviations of quantum observables and numerical radius of operators, we establish a universal…