Related papers: On a generalized entropic uncertainty relation in …
A geometric approach to formulate the uncertainty principle between quantum observables acting on an $N$-dimensional Hilbert space is proposed. We consider the fidelity between a density operator associated with a quantum system and a…
We derive an optimal bound on the sum of entropic uncertainties of two or more observables when they are sequentially measured on the same ensemble of systems. This optimal bound is shown to be greater than or equal to the bounds derived in…
The entropy of probability distribution defined by Shannon has several extensions. R\'enyi entropy is one of the general extensions of Shannon entropy and is widely used in engineering, physics, and so on. On the other hand, the quantum…
A comparative study of one-dimensional quantum structures which allow analytic expressions for the position and momentum R\'{e}nyi $R(\alpha)$ and Tsallis $T(\alpha)$ entropies, focuses on extracting the most characteristic physical…
Recently, an entropic uncertainty relation for multiple measurements has been proposed by Liu et al. in [Phys. Rev. A 91, 042133 (2015)]. However, the lower bound of the relation is not always tight with respect to different measurements.…
The uncertainty principle is an inherent characteristic of quantum mechanics. This principle can be formulated in various form. Fundamentally, this principle can be expressed in terms of the standard deviation of the measured observables.…
The uncertainty principle restricts potential information one gains about physical properties of the measured particle. However, if the particle is prepared in entanglement with a quantum memory, the corresponding entropic uncertainty…
We investigate bounds in the transmission of classical information through quantum systems. Our focus lies in the generalized Holevo theorem, which provides a single-letter Holevo-like inequality from arbitrary quantum distance measures.…
Bounds on information combining are a fundamental tool in coding theory, in particular when analyzing polar codes and belief propagation. They usually bound the evolution of random variables with respect to their Shannon entropy. In recent…
R\'enyi entropies are conceptually valuable and experimentally relevant generalisations of the celebrated von Neumann entanglement entropy. After a quantum quench in a clean quantum many-body system they generically display a universal…
For certain families of finite quantum graphs, we study the question of how eigenfunctions are distributed over the graph. To characterize properties of the distribution, generalized entropies of the R\'{e}nyi and Tsallis types are…
The uncertainty principle is one of the key concepts in quantum theory. This principle states that it is not possible to measure two incompatible observables simultaneously and accurately. In quantum information theory, the uncertainty…
We discuss some properties of the generalized entropies, called Renyi entropies and their application to the case of continuous distributions. In particular it is shown that these measures of complexity can be divergent, however, their…
We derive a strengthened monotonicity inequality for quantum relative entropy by employing properties of $\alpha$-R\'{e}nyi relative entropy. We develop a unifying treatment towards the improvement of some quantum entropy inequalities. In…
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 introduce a biparametric Fisher-R\'enyi complexity measure for general probability distributions and we discuss its properties. This notion, which is composed of two entropy-like components (the R\'enyi entropy and the biparametric…
Quantum information-theoretic approach has been identified as a way to understand the foundations of quantum mechanics as early as 1950 due to Shannon. However there hasn't been enough advancement or rigorous development of the subject. In…
We investigate the large-time asymptotics of nonlinear diffusion equations $u_t = \Delta u^p$ in dimension $n \ge 1$, in the exponent interval $p > n/(n+2)$, when the initial datum $u_0$ is of bounded second moment. Precise rates of…
We prove R\'enyi entropic inequalities in a holographic setup based on the recent proposal for the holographic formula of R\'enyi entropies when the bulk is stable against any perturbation. Regarding the R\'enyi parameter as an inverse…
Entropies are fundamental measures of uncertainty with central importance in information theory and statistics and applications across all the quantitative sciences. Under a natural set of operational axioms, the most general form of…