Direct Calculation of Mutual Information of Distant Regions

Noburo Shiba

doi:10.1007/JHEP09(2020)182

paper

Direct Calculation of Mutual Information of Distant Regions

arXiv:1907.07155 · doi:10.1007/JHEP09(2020)182

Abstract

We consider the (Renyi) mutual information, $I^{(n)} (A, B) = S_{A}^{(n)} + S_{B}^{(n)} - S_{A \cup B}^{(n)}$ , 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 $I^{(n)} (A, B) \sim C_{A B}^{(n)} ⟨ 0∣ ϕ (r) ϕ (0) ∣0 ⟩^{2}$ . We obtain the direct expression of $C_{A B}^{(n)}$ 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.

arXiv comment17 pages; v2, added references, minor corrections in eq.(3.20). arXiv admin note: text overlap with arXiv:1408.0637

Direct Calculation of Mutual Information of Distant Regions

Abstract

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