论文标题
负香农信息隐藏网络
Negative Shannon Information Hides Networks
论文作者
论文摘要
Shannon信息的定义是为了表征经典概率分布的不确定性信息。作为一种不确定性度量，通常认为它是积极的。由于多膜公理，这将适用于两个随机变量的任何信息数量。但是，未知为什么在有限维空间上有两个以上随机变量有负信息。我们首先显示了否定的三方共同信息，暗示其联合分布的特定贝叶斯网络表示。然后，我们证明了否定的香农信息是从具有量子实现的一般三方贝叶斯网络获得的。这提供了不依赖于设备的香农信息的见证人。我们最终扩展了通用网络的结果。目前的结果显示了非香农信息不平等的网络兼容性中的新见解。
Shannon information was 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. We first show the negative tripartite Shannon mutual information implies specific Bayesian network representations of its joint distribution. We then show 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. We finally extend the result for general networks. The present result shows new insights in the network compatibility from non-Shannon information inequalities.
