The Renyi entropy coprises a group of data estimates that sums up the well-known Shannon entropy, acquiring considerable lot its properties. It appears as unqualified and restrictive relative or common data, has found numerous applications in information theory. Renyi's argument, area law black hole plays significant role. However, total can be modified by some quantum effects, motivated random...

We investigate the Rényi entropy of sums independent integer-valued random variables through Fourier theoretic means, and give sharp comparisons between variance for Bernoulli variables. As applications, we prove that a discrete “min-entropy power” is superadditive with respect to convolution modulo universal constant, new bounds on an entropic generalization Littlewood-Offord problem are in “P...

Distributions derived from the maximization of Rényi-Tsallis entropy are often called Tsallis’ distributions. We first indicate that these distributions can arise as mixtures, and can be interpreted as the solution of a standard maximum entropy problem with fluctuating constraints. Considering that Tsallis’ distributions appear for systems with displaced or fluctuating equilibriums, we show tha...

We consider the maximum entropy problems associated with Rényi Q-entropy, subject to two kinds of constraints on expected values. The constraints considered are a constraint on the standard expectation, and a constraint on the generalized expectation as encountered in nonextensive statistics. The optimum maximum entropy probability distributions, which can exhibit a power-law behaviour, are der...

In this paper, we show that in order to obtain the Tsallis entropy rate for stochastic processes, we can use the limit of conditional entropy, as it was done for the case of Shannon and Renyi entropy rates. Using that we can obtain Tsallis entropy rate for stationary Gaussian processes. Finally, we derive the relation between Renyi, Shannon and Tsallis entropy rates for stationary Gaussian proc...

We consider a two-parameter family of Rényi relative entropies Dα,z(ρ||σ) that are quantum generalisations of the classical Rényi divergence Dα(p||q). This family includes many known relative entropies (or divergences) such as the quantum relative entropy, the recently defined quantum Rényi divergences, as well as the quantum Rényi relative entropies. All its members satisfy the quantum general...

The conditional quantum mutual information I(A;B|C) of a tripartite state ρABC is an information quantity which lies at the center of many problems in quantum information theory. Three of its main properties are that it is non-negative for any tripartite state, that it decreases under local operations applied to systems A and B, and that it obeys the duality relation I(A;B|C) = I(A;B|D) for a f...

It is known that the security evaluation can be done by smoothing of Rényi entropy of order 2 in the classical and quantum settings when we apply universal2 hash functions. Using the smoothing of Rényi entropy of order 2, we derive security bounds for L1 distinguishability and modified mutual information criterion under the classical and quantum setting, and have derived these exponential decre...