Negative Shannon Information Hides Networks. Issue 12 (17th October 2022) - Luo, Ming‐Xing
Abstract: Shannon information is defined for characterizing the uncertainty information of classical probabilistic distributions. As an uncertainty measure it is generally believed to be positive. This holds for any information quantity from two random variables because of the polymatroidal axioms. However, it is unknown why there is negative information for more than two random variables on finite dimensional spaces. It is first shown that the negative tripartite Shannon mutual information implies specific Bayesian network representations of its joint distribution. Then it is shown that the negative Shannon information is obtained from general tripartite Bayesian networks with quantum realizations. This provides a device‐independent witness of negative Shannon information. Finally the result is extended for general networks. The present result shows new insights in the network compatibility from non‐Shannon information inequalities. Abstract : Shannon information as an uncertainty information measure for classical probabilistic distributions is generally believed to be positive because of the polymatroidal axioms. However, there is negative information for more than two random variables. It is proven the network compatibility of specific joint distribution with negative tripartite Shannon mutual information.