We study the connection between mixing properties for bipartite graphs and materialization of the mutual information in one-shot settings. We show that mixing properties of a graph imply impossibility to extract the mutual information shared by the ends of an edge randomly sampled in the graph. We apply these impossibility results to some questions motivated by information-theoretic cryptography. In particular, we show that communication complexity of a secret key agreement in one-shot setting is inherently uneven: for some inputs, almost all communication complexity inevitably falls on only one party.

翻译：我们研究二分图的混合性质与单次设置中互信息实现之间的联系。我们证明图的混合性质意味着无法提取图中随机采样边的两端共享的互信息。我们将这些不可能性结果应用于信息论密码学中的若干问题。特别地，我们证明单次设置下密钥协商的通信复杂度本质上是不均衡的：对于某些输入，几乎所有的通信复杂度不可避免地仅由一方承担。