  It is well known that quantum effects can produce negative energy densities,
though for limited times. Here we show in the context of two-dimensional CFT
that such negative energy densities are present in any non-trivial conformal
vacuum and can be interpreted in terms of the entanglement structure of such
states. We derive an exact identity relating the outgoing energy flux and the
entanglement entropy in the in-vacuum. When applied to two-dimensional models
of black hole evaporation, this identity implies that unitarity is incompatible
with monotonic mass loss.
