  We investigate quantum entanglement of gravitational configurations in 3D AdS
gravity using the AdS/CFT correspondence. We derive explicit formulas for the
holographic entanglement entropy (EE) of the BTZ black hole, conical
singularities and regularized AdS$_{3}$. The leading term in the large
temperature expansion of the holographic EE of the BTZ black hole reproduces
exactly its Bekenstein-Hawking entropy S_BH, whereas the subleading term
behaves as ln S_BH. We also show that the leading term of the holographic EE
for the BTZ black hole can be obtained from the large temperature expansion of
the partition function of a broad class of 2D CFTs on the torus. This result
indicates that black hole EE is not a fundamental feature of the underlying
theory of quantum gravity but emerges when the semiclassical notion of
spacetime geometry is used to describe the black hole.
