Maximizing the divergence from a hierarchical model of quantum states
Stephan Weis, Andreas Knauf, Nihat Ay,and Ming-Jing Zhao
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Submission date: 06. Jun. 2014
published in: Open systems and information dynamics, 22 (2015) 1, art-no. 1550006
DOI number (of the published article): 10.1142/S1230161215500067
MSC-Numbers: 94A17, 81P45, 62F30
Keywords and phrases: mutual information, multi-information, higher-order correlations, hierarchical model, factoring, Gibbs family, maximum entropy, maximizers of correlation, separable state
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We quantify higher-order correlations in a composite quantum system in terms of the divergence from a family of Gibbs states with well-specified interaction patterns, known as hierarchical model. We begin with a review of factoring in a classical hierarchical model. This is just one aspect of our critical discussion of the divergence from a hierarchical model of quantum states. Then we turn to maximizers of the divergence from a Gibbs family. For example, we consider an upper bound on the support size of a local maximizer of higher-order correlation and we improve it to the square root, asymptotically for identical units. We compute the global maximizers of the mutual information of two separable qubits.