9/2/2023 0 Comments Renyi entropy![]() ![]() The term and the concept are used in diverse fields, from classical thermodynamics, where it was first recognized, to the microscopic description of nature in statistical physics, and. They appear in the form of unconditional and conditional entropies, relative entropies, or mutual information, and have found many applications in information theory and beyond. We present simple and computationally efficient nonparametric estimators of Renyi entropy. Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. 1 Measuring second-order Rnyi entropies through randomized measurements. There are always a lot of issues about existence and well-posedness when one tries to do these anayltic continuations - but for someone like me who is brought up on a daily diet of Feynman path-integrals its a very common issue to deal with and we have a lot of tools to address these. The Rényi entropies constitute a family of information measures that generalizes the well-known Shannon entropy, inheriting many of its properties. 1.1 Shannon and Rnyi entropies The most commonly used measure of randomness of a distri- bution p over a set X is its Shannon entropy. monitored the build-up of the so-called Rnyi entropy in a. We enumerate the various possible behaviours of the Rnyi entropy and its singularities. This allows us to obtain the singularities in the Rnyi entropy from those of the thermodynamic potential, which is directly related to the free energy density of the model. After one has done such an integration one happily forgets about the manifold used and just tries to do the analytic continuation parametrically in the variable $q$. We calculate analytically the Renyi entropy for the zeta-urn model with a Gibbs measure definition of the micro-state probabilities. This is in analogy to the same question for the Shannon and von Neumann entropy (alpha1) which are known to satisfy several. We investigate the universal inequalities relating the alpha-Renyi entropies of the marginals of a multi-partite quantum state. Noah Linden, Milán Mosonyi, Andreas Winter. Most of us are familiar with - or at least have heard of - the Shannon entropy of a random variable, $H(X) = -\mathbb$, this I call "analytic" continuation because often enough one needs to do the interpolation via contours in the complex plane - and the continuation can depend on what contours one chooses through the poles and branch-cuts of the $S_q$ that one started with)Īt integral values of $q>1$ typically there is a always a very well-defined construction in terms of some integration of some function on some $q-$branched manifold. The structure of Renyi entropic inequalities. ![]()
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