Estimation of Shannon and Rényi entropies of unknown discrete distributions is a fundamental problem in statistical property testing and an active research topic in both theoretical computer science and information theory. Tight bounds on the number of samples to estimate these entropies have been established in the classical setting, while little is known about their quantum counterparts. In t...

A time-frequency distribution provides many advantages in the analysis of multicomponent nonstationary signals. The simultaneous signal representation with respect to the time and frequency axis defines the signal amplitude, frequency, bandwidth, and the number of components at each time moment. The Rényi entropy, applied to a time-frequency distribution, is shown to be a valuable indicator of ...

Relations between Shannon entropy and Rényi entropies of integer order are discussed. For any N–point discrete probability distribution for which the Rényi entropies of order two and three are known, we provide an lower and an upper bound for the Shannon entropy. The average of both bounds provide an explicit extrapolation for this quantity. These results imply relations between the von Neumann...

Two maximization problems of Rényi entropy rate are investigated: the maximization over all stochastic processes whose marginals satisfy a linear constraint, and the Burg-like maximization over all stochastic processes whose autocovariance function begins with some given values. The solutions are related to the solutions to the analogous maximization problems of Shannon entropy rate.

It has long been conjectured that the entropy of quantum fields across boundaries scales as the boundary area. This conjecture has not been easy to test in spacetime dimensions greater than four because of divergences in the von Neumann entropy. Here we show that the Rényi entropy provides a convergent alternative, yielding a quantitative measure of entanglement between quantum field theoretic ...

We consider a bipartite quantum conductor and discuss the joint probability distribution of particle number in a subsystem and the self-information associated with the reduced density matrix of the subsystem. By extending the multi-contour Keldysh Green function technique, we calculate the Rényi entropy of a positive integer order M subjected to the particle number constraint, from which we der...

In this paper, we propose a novel layering approach to achieve end-to-end exponential security without resorting to presumed physical layer conditions. The only requirement for such an exponentially secure system is existence of a common key source between legitimate users that is partially known by Eve. The novel framework includes a random cipher and key stream generating scheme constituting ...