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Showing 1 to 6 of 6 for “"Entropy inequalities"”.
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Saturating Quantum Relative Entropy Inequalities
… data processing inequality for quantum relative entropy. The data processing inequality describes how knowledge about quantum states (that describe a quantum system) cannot increase whenever the states undergo some noisy action (or a local operation). In chapter 3, we give a detailed explanation …
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Two Studies of Constraints in High Dimensions: Entropy Inequalities and the Randomized Symmetric Binary Perceptron
… a high dimensional inequality for the binary entropy. The perceptron is a natural model in high-dimensional probability, and a toy shallow neural network which stores random patterns; we also study a randomized variant of the symmetric binary perceptron. We first consider the (k + 1)-th …
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On equivalence of additive-combinatorial inequalities for Shannon entropy and differential entropy
Entropy inequalities are very important in information theory and they play a crucial role in various communication-theoretic problems, for example, in the study of the degrees of freedom of interference channels. In this thesis, we are concerned with the additive-combinatorial entropy inequalities …
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Analysis of a Spacetime Discontinuous Galerkin Method for Systems of Conservation Laws
… naturally suggests a discrete version of the Lax entropy condition. The CSDG method is an explicit method, that is, a direct element-by-element solution procedure is possible. We investigate existence, uniqueness and continuous dependence on the initial data of a CSDG solution for general …
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On the nature and decay of quantum relative entropy
… core of thermodynamics and information theory, entropy's use in quantum information extends to diverse topics including high-energy physics and operator algebras. Entropy can gauge the extent to which a quantum system departs from classicality, including by measuring entanglement and coherence, …
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Algorithms for Gibbs states of quantum many-body systems
… hierarchy for the free energy called Markov Entropy Decomposition. We prove a convergence criterion for this hierarchy based on the so-called effective interaction, a quantity that is related to the parent Hamiltonian of marginals of the Gibbs state. The criterion is known to hold in 1D and …