  A tunnel barrier in a degenerate electron gas was recently discovered as a
source of entangled particle-hole excitations. The entanglement is produced by
elastic tunneling events, without requiring electron-electron interactions.
Here we investigate the inverse process, the annihilation of an electron and a
hole by elastic scattering. We find that this process leads to teleportation of
the (unknown) state of the annihilated electron to a second, distant electron
-- if the latter was previously entangled with the annihilated hole. We propose
an experiment, involving low-frequency noise measurements on a two-dimensional
electron gas in a high magnetic field, to detect teleportation of electrons and
holes in the two lowest Landau levels.
