Related papers: Improved unitary uncertainty relations
The uncertainty principle is one of the fundamental features of quantum mechanics and plays an essential role in quantum information theory. We study uncertainty relations based on variance for arbitrary finite $N$ quantum observables. We…
We highlight overlap as one of the simplest inequalities in linear space that yields a number of useful results. One obtains the Cauchy-Schwarz inequality as a special case. More importantly, a variant of it is seen to work desirably in…
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…
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…
Measurement uncertainty relations are quantitative bounds on the errors in an approximate joint measurement of two observables. They can be seen as a generalization of the error/disturbance tradeoff first discussed heuristically by…
Recently,D.Mondal et.al[Phys. Rev. A. 95, 052117(2017)]creatively introduce a new interesting concept of reverse uncertainty relation which indicates that one cannot only prepare quantum states with joint small uncertainty, but also with…
Historically, the element of uncertainty in quantum mechanics has been expressed through mathematical identities called uncertainty relations, a great many of which continue to be discovered. These relations use diverse measures to quantify…
We study the Schr\"odinger-Robertson uncertainty relations in an algebraic framework. Moreover, we show that some specific commutation relations imply new equalities, which are regarded as equality versions of well-known inequalities such…
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 present the uncertainty relations in terms of the symmetrized \r{ho}-absolute variance, which generalizes the uncertainty relations for arbitrary operator (not necessarily Hermitian) to quantum channels. By recalling the quantity…
We present an equivalence theorem to unify the two classes of uncertainty relations, i.e., the variance-based ones and the entropic forms, which shows that the entropy of an operator in a quantum system can be built from the variances of a…
We present unified approach to different recent entanglement criteria. Although they were developed in different ways, we show that they are all applications of a more general principle given by the Cauchy-Schwarz inequality. We explain…
We improve the entropic uncertainty relations for position and momentum coarse-grained measurements. We derive the continuous, coarse-grained counterparts of the discrete uncertainty relations based on the concept of majorization. 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…
Following to the Weil method we generalize the Heisenberg-Robertson uncertainty relation for arbitrary two operators. Consideration is made in spherical coordinates, where the distant variable is restricted from one side, . By this reason…
This chapter provides a principled introduction to uncertainty relations underlying sparse signal recovery. We start with the seminal work by Donoho and Stark, 1989, which defines uncertainty relations as upper bounds on the operator norm…
Majorization uncertainty relations are derived for arbitrary quantum operations acting on a finite-dimensional space. The basic idea is to consider submatrices of block matrices comprised of the corresponding Kraus operators. This is an…
The uncertainty relation is one of the key ingredients of quantum theory. Despite the great efforts devoted to this subject, most of the variance-based uncertainty relations are state-dependent and suffering from the triviality problem of…
Uncertainty is a fundamental and important concept in quantum mechanics. In this work, using the technique in matrix theory, we propose an uncertainty relation of four observables and show that the uncertainty constant is tight. It is…
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…