نتایج جستجو برای: conditional entropy

تعداد نتایج: 122651  

2006
Ben Ibinson Noah Linden Andreas Winter

If the conditional information of a classical probability distribution of three random variables is zero, then it obeys a Markov chain condition. If the conditional information is close to zero, then it is known that the distance (minimum relative entropy) of the distribution to the nearest Markov chain distribution is precisely the conditional information. We prove here that this simple situat...

Journal: :Journal of Mathematical Physics 2022

We prove a simple uniform continuity bound for the sandwiched Rényi conditional entropy α ∈ [1/2, 1) ∪ (1, ∞], which is independent of dimension conditioning system.

2015
Masahito Hayashi Marco Tomamichel

Recently, a variety of new measures of quantum Rényi mutual information and quantum Rényi conditional entropy have been proposed, and some of their mathematical properties explored. Here, we show that the Rényi mutual information attains operational meaning in the context of composite hypothesis testing, when the null hypothesis is a fixed bipartite state and the alternate hypothesis consists o...

Journal: :CoRR 2018
Yuta Sakai

This study investigates generalized Fano-type inequalities in the following senses: (i) the alphabet X of a random variable X is countably infinite; (ii) instead of a fixed finite cardinality of X, a fixed X-marginal distribution PX is given; (iii) information measures are generalized from the conditional Shannon entropy H(X | Y ) to a general type of conditional information measures without ex...

2016
John Preskill

Contents 10 Quantum Shannon Theory 1 10.1 Shannon for Dummies 2 10.1.1 Shannon entropy and data compression 2 10.1.2 Joint typicality, conditional entropy, and mutual information 6 10.1.3 Distributed source coding 8 10.1.4 The noisy channel coding theorem 9 10.2 Von Neumann Entropy 16 10.2.1 Mathematical properties of H(ρ) 18 10.2.2 Mixing, measurement, and entropy 20 10.2.3 Strong subadditivit...

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