  Motivated by the black hole firewall problem, we find highly entangled pairs
of spatially localized modes in quantum field theory. We demonstrate that
appropriately chosen wavepackets localized outside the horizon are nearly
purified by 'mirror' modes behind the horizon. In addition, we calculate the
entanglement entropy of a single localized wavepacket in the Minkowski vacuum.
In all cases we study, the quantum state of the system becomes pure in the
limit that the wavepackets delocalize; we quantify the trade-off between
localization and purity.
