远距离区域互信息的直接计算
Direct Calculation of Mutual Information of Distant Regions
摘要：
本文研究了自由标量场真空态下远距离紧致空间区域A和B的（Renyi）互信息$I^{(n)}(A,B) = S^{(n)}_A+S^{(n)}_{B} - S^{(n)}_{A \cup B}$。A和B之间的距离r远大于它们的尺寸$R_{A,B}$。已知$I^{(n)}(A,B) \sim C^{(n)}_{AB} \left<0| ϕ(r)ϕ(0) |0\right>^2$ .我们得到了任意区域A和B的$C^{(n)}_{AB}$的直接表达式。对$n$进行解析延拓，得到互信息。直接表达式对数值计算是有用的。利用直接表达式，可以直接计算$I(A,B)$，而不需要分别计算$S_A, S_B$和$S_{A \cup B}$，大大减少了计算量。
英文摘要：
We consider the (Renyi) mutual information, $I^{(n)}(A,B) = S^{(n)}_A+S^{(n)}_{B} - S^{(n)}_{A \cup B}$, of distant compact spatial regions A and B in the vacuum state of a free scalar field. The distance r between A and B is much greater than their sizes $R_{A,B}$. It is known that $I^{(n)}(A,B) \sim C^{(n)}_{AB} \left<0| ϕ(r)ϕ(0) |0\right>^2$ . We obtain the direct expression of $C^{(n)}_{AB}$ for arbitrary regions A and B. We perform the analytical continuation of $n$ and obtain the mutual information. The direct expression is useful for the numerical computation. By using the direct expression, we can compute directly $I(A,B)$ without computing $S_A, S_B$ and $S_{A \cup B}$ respectively, so it reduces significantly the amount of computation.
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