Quantum teleportation by particle-hole annihilation in the Fermi sea

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.