Tuesday, October 04, 2005

Entanglement entropy

New paper! Available on arxiv.org:

Slides for a related talk.

Entanglement entropy, black holes and holography
Authors: R. Buniy, S. Hsu

We observe that the entanglement entropy resulting from tracing over a subregion of an initially pure state can grow faster than the surface area of the subregion (indeed, proportional to the volume), in contrast to examples studied previously. The pure states with this property have long-range correlations between interior and exterior modes and are constructed by purification of the desired density matrix. We show that imposing a no-gravitational collapse condition on the pure state is sufficient to exclude faster than area law entropy scaling. This observation leads to an interpretation of holography as an upper bound on the realizable entropy (entanglement or von Neumann) of a region, rather than on the dimension of its Hilbert space.


Anonymous said...

Nice paper, and I find the results intuitively appealing.

Cute how "beta" starts as a Lagrange multiplier, and ends up as the inverse temperature - is that original? Or did I just miss that day in Stat Mech?

Steve Hsu said...


Yes, it is standard. I think Sakurai even discusses it when covering density matrices.

We came to it by accident, but then realized it had to work out that way.

The magic is in the form of the v.N. entropy = - tr rho ln rho. It always gives you a thermal result if you extremize it subject to, e.g., an energy constraint.


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