The mutual information is a measure of classical and quantum correlations of great interest in quantum information. It is also relevant in quantum many-body physics, by virtue of satisfying an area law for thermal states and bounding all correlation functions. However, calculating it exactly or approximately is often challenging in practice. Here, we consider alternative definitions based on Rényi divergences. Their main advantage over their von Neumann counterpart is that they can be expressed as a variational problem whose cost function can be efficiently evaluated for families of states like matrix product operators while preserving all desirable properties of a measure of correlations. In particular, we show that they obey a thermal area law in great generality, and that they upper bound all correlation functions. We also investigate their behavior on certain tensor network states and on classical thermal distributions.

中文翻译：

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可计算的人一互信息：面积规律和相关性

互信息是对量子信息非常感兴趣的经典和量子相关性的度量。由于满足热态的面积定律并限制所有相关函数，它在量子多体物理学中也很重要。然而，精确或近似地计算它在实践中通常具有挑战性。在这里，我们考虑基于 Rényi 分歧的替代定义。与冯诺依曼对应物相比，它们的主要优点是它们可以表示为变分问题，其成本函数可以有效地评估状态族，如矩阵乘积算子，同时保留相关性度量的所有理想属性。特别是，我们证明了它们非常普遍地遵循热面积定律，并且它们对所有相关函数进行了上限。