Entropic uncertainties in quantum measurements

Official URL: https://risc01.sabanciuniv.edu/record=b2708484_(Table of contents)

We have studied entropic uncertainty relation for two types of quantum measurements in quantum information theory. One of them is the projective measurements that are constructed from the mutually unbiased bases and the other one is the symmetric informationally complete positive operator-valued measure. We present an optimal upper bound of entropic uncertainty relation for these two types of measurements. We have obtained a criterion for the extendibility of mutually unbiased bases in terms of Shannon entropy by means of the optimal upper bound of entropic uncertainty relation. We study time reversal operation for the latter type of measurement. We reveal that the notions of time reversal in quantum mechanics and in quantum operation formalism are not compatible with each other. We propose a harmonization of the notions, according to which symmetric informationally complete positive operator-valued measure is time reversal invariant. We also study on the algebraic relation between the two measurements; we provide an algebraic relation by which an analytical search of the existence of mutually unbiased bases could be studied in six-dimensional Hilbert space. Finally, a physical ground of the use of information energy in quantum information theory has been provided with recourse to Stokes parameters.