The sum of entropic uncertainties for the measurement of two non-commuting observables is not always reduced by the amount of entanglement (quantum memory) between two parties, and in certain cases may be impacted by quantum correlations beyond entan
glement (discord). An optimal lower bound of entropic uncertainty in the presence of any correlations may be determined by fine-graining. Here we express the uncertainty relation in a new form where the maximum possible reduction of uncertainty is shown to be given by the extractable classical information. We show that the lower bound of uncertainty matches with that using fine-graining for several examples of two-qubit pure and mixed entangled states, and also separable states with non-vanishing discord. Using our uncertainty relation we further show that even in the absence of any quantum correlations between the two parties, the sum of uncertainties may be reduced with the help of classical correlations.
We show that the uncertainty relation as expressed in the Robertson-Schrodinger generalized form can be used to detect the mixedness of three-level quantum systems in terms of measureable expectation values of suitably chosen observables when prior k
nowledge about the basis of the given state is known. In particular, we demonstrate the existence of observables for which the generalized uncertainty relation is satisfied as an equality for pure states and a strict inequality for mixed states corresponding to single as well as bipartite sytems of qutrits. Examples of such observables are found for which the magnitude of uncertainty is proportional to the linear entropy of the system, thereby providing a method for measuring mixedness.
