Related papers: Strong Majorization Entropic Uncertainty Relations
We define the entropic bounds, i.e minimal uncertainty for pairs of unitary testers in distinguishing between unitary transformations not unlike the well known entropic bounds for observables. We show that in the case of specific sets of…
Uncertainty relations provide constraints on how well the outcomes of incompatible measurements can be predicted, and, as well as being fundamental to our understanding of quantum theory, they have practical applications such as for…
Uncertainty relations give upper bounds on the accuracy by which the outcomes of two incompatible measurements can be predicted. While established uncertainty relations apply to cases where the predictions are based on purely classical data…
Entropic uncertainty relations for the position and momentum within the generalized uncertainty principle are examined. Studies of this principle are motivated by the existence of a minimal observable length. Then the position and momentum…
Given two orthornormal bases A and B, the basic form of the entropic uncertainty principle is stated in terms of the sum of the Shannon entropies of the probabilities of measuring A and B onto a given quantum state. State independent lower…
Entropic uncertainty relations demonstrate the intrinsic uncertainty of nature from an information-theory perspective. Recently, a quantum-memory-assisted entropic uncertainty relation for multiple measurements was proposed by Wu $et\ al.$…
Extending a recent result by Frank and Lieb, we show an entropic uncertainty principle for mixed states in a Hilbert space relatively to pairs of positive operator valued measures that are independent in some sense. This yields…
Number-phase uncertainty relations are formulated in terms of unified entropies which form a family of two-parametric extensions of the Shannon entropy. For two generalized measurements, unified-entropy uncertainty relations are given in…
We derive and experimentally investigate a strong uncertainty relation valid for any $n$ unitary operators, which implies the standard uncertainty relation as a special case, and which can be written in terms of geometric phases. It is…
We revisit generalized entropic formulations of the uncertainty principle for an arbitrary pair of quantum observables in two-dimensional Hilbert space. R\'enyi entropy is used as uncertainty measure associated with the distribution…
We investigate the fine-grained uncertainty relations for qubit system by measurements corresponding respectively to two and three spin operators. Then we derive the general bound for a combination of two probabilities of projective…
We derive the lower bound of uncertainty relations of two unitary operators for a class of states based on the geometric-arithmetic inequality and Cauchy-Schwarz inequality. Furthermore, we propose a set of uncertainty relations for three…
Uncertainty lower bounds for parameter estimations associated with a unitary family of mixed-state density matrices are obtained by embedding the space of density matrices in the Hilbert space of square-root density matrices. In the…
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…
We present the entropic uncertainty relations for multiple measurement settings in quantum mechanics. Those uncertainty relations are obtained for both cases with and without the presence of quantum memory. They take concise forms which can…
We utilize quantum superposition principle to establish the improvable upper and lower bounds on the stronger uncertainty relation, i.e., the "weighted-like" sum of the variances of observables. Our bounds include some free parameters which…
In Hall's reformulation of the uncertainty principle, the entropic uncertainty relation occupies a core position and provides the first nontrivial bound for the information exclusion principle. Based upon recent developments on the…
We construct inequalities between R\'{e}nyi entropy and the indexes of coincidence of probability distributions, based on which we obtain improved state-dependent entropic uncertainty relations for general symmetric informationally complete…
This is a review of the problem of Mutually Unbiased Bases in finite dimensional Hilbert spaces, real and complex. Also a geometric measure of "mubness" is introduced, and applied to some recent calculations in six dimensions (partly done…
In the first part of this thesis, we present a general technique for establishing local and uniform continuity bounds for Schur concave functions. Our technique uses a particular relationship between majorization and the trace distance…