Related papers: Extremum-entropy-based Heisenberg-like uncertainty…
Heisenberg's uncertainty principle forms a fundamental element of quantum mechanics. Uncertainty relations in terms of entropies were initially proposed to deal with conceptual shortcomings in the original formulation of the uncertainty…
In this paper, we study entropic uncertainty relations on a finite-dimensional Hilbert space and provide several tighter bounds for multi-measurements, with some of them also valid for R\'{e}nyi and Tsallis entropies besides the Shannon…
The entropic uncertainty relations are a very active field of scientific inquiry. Their applications include quantum cryptography and studies of quantum phenomena such as correlations and non-locality. In this work we find…
The paper examines relationships between the Shannon entropy and the $\ell_{\alpha}$-norm for $n$-ary probability vectors, $n \ge 2$. More precisely, we investigate the tight bounds of the $\ell_{\alpha}$-norm with a fixed Shannon entropy,…
In the recent years, information theory of quantum-mechanical systems have aroused the interest of many Theoretical Physicist. This due to the fact that it provides a deeper insight into the internal structure of the systems. Also, It is…
The striking differences between quantum and classical systems predicate disruptive quantum technologies. We peruse quantumness from a variety of viewpoints, concentrating on phase-space formulations because they can be applied beyond…
This PHD thesis is concerned with uncertainty relations in quantum probability theory, state estimation in quantum stochastics, and natural bundles in differential geometry. After some comments on the nature and necessity of decoherence in…
Complementarity relations between various characterizations of a probability distribution are at the core of information theory. In particular, lower and upper bounds for the entropic function are of great importance. In applied topics, we…
We formulate some properties of a set of several mutually unbiased measurements. These properties are used for deriving entropic uncertainty relations. Applications of mutually unbiased measurements in entanglement detection are also…
In the history of quantum mechanics, various types of uncertainty relationships have been introduced to accommodate different operational meanings of Heisenberg uncertainty principle. We derive an optimized entropic uncertainty relation…
The well-known Robertson-Schr\"odinger uncertainty relations have state-dependent lower bounds which are trivial for certain states. We present a general approach to deriving tight state-independent uncertainty relations for qubit…
The $D$-dimensional harmonic system (i.e., a particle moving under the action of a quadratic potential) is, together with the hydrogenic system, the main prototype of the physics of multidimensional quantum systems. In this work we…
A new method is proposed for analyzing complexity and studying the information in random geometric networks using Tsallis entropy tool. Tsallis entropy of the ensemble of random geometric networks is calculated based on the components of…
It is argued that the factorization of compound probability over subsystems is a consequence of the existence of thermodynamic equilibrium in the composite system having Tsallis entropy. So it should be respected by all exact calculations…
The spreading properties of the stationary states of the quantum multidimensional harmonic oscillator are analytically discussed by means of the main dispersion measures (radial expectation values) and the fundamental entropy-like…
We investigate the extremality of stabilizer states to reveal their exceptional role in the space of all $n$-qubit/qudit states. We establish uncertainty principles for the characteristic function and the Wigner function of states,…
Entropic uncertainty relations place nontrivial lower bounds to the sum of Shannon information entropies for noncommuting observables. Here we obtain a novel lower bound on the entropy sum for general pairs of observables in…
Entropic uncertainty is a well-known concept to formulate uncertainty relations for continuous variable quantum systems with finitely many degrees of freedom. Typically, the bounds of such relations scale with the number of oscillator…
Uncertainty relations based on information theory for both discrete and continuous distribution functions are briefly reviewed. We extend these results to account for (differential) R\'{e}nyi entropy and its related entropy power. This…
Uncertainty relations for more than two observables have found use in quantum information, though commonly known relations pertain to a pair of observables. We present novel uncertainty and certainty relations of state-independent form for…