Finally, I examine the possibility to interpret the Bekenstein-Hawking entropy entirely as the entanglement entropy. The holographic description of the entanglement entropy of the blackhole horizon is illustrated on the two- and four-dimensional examples. Keywords and phrases: quantum statistics, information, spin half, qubit, two level system. The puzzling behavior of the entanglement entropy due to fields, which non-minimally couple to gravity, is emphasized. AMS subject classifications: 62F12, 62P35. The relations to other known approaches such as 't Hooft's brick-wall model and the Euclidean path integral in the optical metric are discussed in detail. The focus in the review is on the systematic use of the conical singularity method. I review a variety of aspects of this calculation: the useful mathematical tools such as the geometry of spaces with conical singularities and the heat kernel method, the UV divergences in the entropy and their renormalization, the logarithmic terms in the entanglement entropy in four and six dimensions and their relation to the conformal anomalies. functions of singular v The entropy of entanglement (or entanglement entropy) is a measure of the. The geometrical nature of entanglement-entropy calculation is particularly intriguing when applied to black holes when the entangling surface is the black-hole horizon. The von Neumann entropy is also strongly subadditive. For two sub-systems separated by a surface the entanglement entropy is proportional to the area of the surface and depends on the UV cutoff, which regulates the short-distance correlations. The entanglement entropy is a fundamental quantity, which characterizes the correlations between sub-systems in a larger quantum-mechanical system.
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