  We consider (2+1)-dimensional topological quantum states which possess edge
states described by a chiral (1+1)-dimensional Conformal Field Theory (CFT),
such as e.g. a general quantum Hall state. We demonstrate that for such states
the reduced density matrix of a finite spatial region of the gapped topological
state is a thermal density matrix of the chiral edge state CFT which would
appear at the spatial boundary of that region. We obtain this result by
applying a physical instantaneous cut to the gapped system, and by viewing the
cutting process as a sudden "quantum quench" into a CFT, using the tools of
boundary conformal field theory. We thus provide a demonstration of the
observation made by Li and Haldane about the relationship between the
entanglement spectrum and the spectrum of a physical edge state.
