Is entanglement entropy proportional to area?

Abstract

It is known that the entanglement entropy of a scalar field, found by tracing over its degrees of freedom inside a sphere of radius $\mathcal{R}$, is proportional to the area of the sphere (and not its volume). This suggests that the origin of black hole entropy, also proportional to its horizon area, may lie in the entanglement between the degrees of freedom inside and outside the horizon. We examine this proposal carefully by including excited states, to check probable deviations from the area law.

arXiv comment6 pages. Based on talk by S. Das at Theory Canada 1, Vancouver, 3 June, 2005. To be published in a special edition of the Canadian Journal of Physics. Minor changes to match published version

References in corpus (6)

• Microscopic Origin of the Bekenstein-Hawking Entropy
• Entropy and Area
• Quantum Geometry and Black Hole Entropy
• Black Hole Entropy from Conformal Field Theory in Any Dimension
• Entropy, entanglement, and area: analytical results for harmonic lattice systems
• Semiclassical quantisation of space-times with apparent horizons

Cited by in corpus (8)

• Holographic Entanglement Entropy in Lovelock Gravities
• Power-law corrections to entanglement entropy of horizons
• Left-Right Entanglement Entropy of Boundary States
• Where are the black hole entropy degrees of freedom ?
• Real-space quantum-to-classical transition of time dependent background fluctuations
• Dynamical scaling symmetry and asymptotic quantum correlations for time-dependent scalar fields
• Entanglement Entropy of Excited States in the Quantum Lifshitz Model
• Perturbative approach to the entanglement entropy and the area law in Fock and polymer quantization