Generalized uncertainty relations for multiple measurements

Entropic Uncertainty Relations for Successive Generalized Measurements

We derive entropic uncertainty relations for successive generalized measurements by using general descriptions of quantum measurement within two distinctive operational scenarios. In the first scenario, by merging two successive measurements into one we consider successive measurement scheme as a method to perform an overall composite measurement. In the second scenario, on the other hand, we c...

Entropic uncertainty relations for multiple measurements

We present the entropic uncertainty relations for multiple measurement settings which demonstrate the uncertainty principle of quantum mechanics. Those uncertainty relations are obtained for both cases with and without the presence of quantum memory, and can be proven by a unified method. Our results recover some well known entropic uncertainty relations for two observables, which show the unce...

Uncertainty Relations for Noise and Disturbance in Generalized Quantum Measurements

Heisenberg’s uncertainty relation for measurement noise and disturbance states that any position measurement with noise ǫ brings the momentum disturbance not less than h̄/2ǫ. This relation holds only for restricted class of measuring apparatuses. Here, Heisenberg’s uncertainty relation is generalized to a relation that holds for all the possible quantum measurements, from which conditions are ob...

Generalized Uncertainty Relations and Efficient Measurements in Quantum Systems

We consider two variants of a quantum-statistical generalization of the Cramér-Rao inequality that establishes an invariant lower bound on the mean square error of a generalized quantum measurement. The proposed complex variant of this inequality leads to a precise formulation of a generalized uncertainty principle for arbitrary states, in contrast to Helstrom’s variant [1] in which these relat...

Generalized Uncertainty Relations: