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Uncertainty relations are old, yet potentially rewarding to explore. By introducing a quantity called the uncertainty matrix, we provide a link between purity and observable incompatibility, and derive several stronger uncertainty relations in both forward and reverse directions for arbitrary quantum states, i.e., mixed as well as pure, and arbitrary incompatible quantum observables, none of which suffer from the problem of triviality. Besides the tightness, the interpretations of terms in these uncertainty relations may be of independent inter- est. We provide the possible generalization of stronger uncertainty relations to sum of variances of more than two observables. We also demonstrate applications of techniques used here to, firstly, obtain a simple reverse quantum speed limit for quantum states undergoing Markovian dynamical evolution, and secondly, to provide a lower bound for fidelity between two quantum states.
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 Heisenberg. Here w
In this work we study various notions of uncertainty for angular momentum in the spin-s representation of SU(2). We characterize the uncertainty regions given by all vectors, whose components are specified by the variances of the three angular moment
The notions of error and disturbance appearing in quantum uncertainty relations are often quantified by the discrepancy of a physical quantity from its ideal value. However, these real and ideal values are not the outcomes of simultaneous measurement
The information-theoretic formulation of quantum measurement uncertainty relations (MURs), based on the notion of relative entropy between measurement probabilities, is extended to the set of all the spin components for a generic spin s. For an appro
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 relations are e