标题： 从高一维中的熵效应获得的Renyi信息 显示英文标题

标题： Renyi information from entropic effects in one higher dimension

摘要： 计算纠缠熵及其相关量在最简单的连续和格点模型中通常具有挑战性，部分原因在于这些熵非平凡地依赖于纠缠区域的所有几何特性。 两个或多个区域之间的量子信息度量更加复杂，但包含更多且普遍的信息。 在本文中，我们专注于阶数为$n=2$的Rényi熵和信息。 对于一个自由场论，我们表明这些量通过引入在更高一维中满足狄利克雷和诺伊曼边界条件的边界而映射到热力学自由能的变化。 这种映射使我们能够利用热卡西米尔效应背景下可用的强大工具，特别是适用于计算任意形状区域之间Rényi信息的多极展开。 特别是，我们计算了两个圆盘状区域在任意分离距离下的Rényi信息。 我们将Rényi信息表示为闭合环状聚合物的求和，这建立了与纯熵效应的联系，并在推导信息不等式时很有用。 最后，我们讨论了我们的结果在自由场理论之外的扩展。 显示英文摘要

摘要： Computing entanglement entropy and its cousins is often challenging even in the simplest continuum and lattice models, partly because such entropies depend nontrivially on all geometric characteristics of the entangling region. Quantum information measures between two or more regions are even more complicated, but contain more, and universal, information. In this paper, we focus on R\'{e}nyi entropy and information of the order $n=2$. For a free field theory, we show that these quantities are mapped to the change of the thermodynamic free energy by introducing boundaries subject to Dirichlet and Neumann boundary conditions in one higher dimension. This mapping allows us to exploit the powerful tools available in the context of thermal Casimir effect, specifically a multipole expansion suited for computing the R\'{e}nyi information between arbitrarily-shaped regions. In particular, we compute the R\'{e}nyi information between two disk-shaped regions at an arbitrary separation distance. We provide an alternative representation of the R\'{e}nyi information as a sum over closed-loop polymers, which establishes a connection to purely entropic effects, and proves useful in deriving information inequalities. Finally, we discuss extensions of our results beyond free field theories.