Entanglement Entropy of Two Spheres
High Energy Physics - Theory
2012-07-25 v4 High Energy Astrophysical Phenomena
General Relativity and Quantum Cosmology
Quantum Physics
Abstract
We study the entanglement entropy S_{AB} of a massless free scalar field on two spheres A and B whose radii are R_1 and R_2, respectively, and the distance between the centers of them is r. The state of the massless free scalar field is the vacuum state. We obtain the result that the mutual information S_{A;B}:=S_A+S_B-S_{AB} is independent of the ultraviolet cutoff and proportional to the product of the areas of the two spheres when r>>R_1,R_2, where S_A and S_B are the entanglement entropy on the inside region of A and B, respectively. We discuss possible connections of this result with the physics of black holes.
Keywords
Cite
@article{arxiv.1201.4865,
title = {Entanglement Entropy of Two Spheres},
author = {Noburo Shiba},
journal= {arXiv preprint arXiv:1201.4865},
year = {2012}
}
Comments
17 pages, 9 figures; v4, added references, revised argument in section V, a typo in eq.(25) corrected, published version