论文标题
张量网络作为铃不平等优化工具集的热带收缩
Tropical contraction of tensor networks as a Bell inequality optimization toolset
论文作者
论文摘要
我们表明，发现贝尔贝族不平等的宽阔家族的经典界限可以自然地构建为相关张量网络的收缩，但是在热带代数中，该总和被最小值替换，并且产品被算术添加代替。我们用范式示例在多部分方案和两部分方案中以多个结果来说明我们的方法。我们展示了该方法如何扩展到某些翻译不变系统的热力学极限，并在热带特征值的概念与经典界限之间建立连接，作为热带重新分配过程的固定点。
We show that finding the classical bound of broad families of Bell inequalities can be naturally framed as the contraction of an associated tensor network, but in tropical algebra, where the sum is replaced by the minimum and the product is replaced by the arithmetic addition. We illustrate our method with paradigmatic examples both in the multipartite scenario and the bipartite scenario with multiple outcomes. We showcase how the method extends into the thermodynamic limit for some translationally invariant systems and establish a connection between the notions of tropical eigenvalue and the classical bound per particle as a fixed point of a tropical renormalization procedure.
