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.

翻译：香农信息的定义是确定古典概率分布的不确定信息的特征。 作为一种不确定性的衡量标准,一般认为是肯定的。 这对于两个随机变量中的任何信息数量来说都是肯定的。 但是,由于多甲虫轴心, 尚不清楚为什么在有限维度空间上存在两个以上随机变量的负面信息。 我们首先显示, 负面的三方香农相互信息意味着具体的巴伊西亚网络对其联合分布的表示。 我们然后显示, 负面的香农信息是从一般三方巴伊西亚网络中获取的, 并且实现了量子化。 这为否定香农信息提供了一个设备独立的见证。 我们最终扩展了一般网络的结果。 目前的结果显示, 网络的兼容性因非桑农信息不平等而有了新的洞见。