Figure 2
Proposed realization of the teleportation scheme of Fig. 1, using edge channels in the quantum Hall effect. The thick black lines indicate the boundaries of a two-dimensional electron gas, connected by Ohmic contacts (black rectangles) to a voltage source
or to ground. A strong perpendicular magnetic field ensures that the transport in an energy range
above the Fermi level takes place in two edge channels, extended along a pair of equipotentials (thin solid lines and dashed lines, with arrows that give the direction of propagation). These edge channels realize the two-channel conductors of Fig. 1, with the Landau level index
playing the role of the spin index
. Solid lines signify predominantly filled edge channels with hole excitations (open circles), while dashed lines signify predominantly empty edge channels with particle excitations (black dots). The beam splitters of Fig. 1 are formed by split gate electrodes (shaded rectangles), through which the edge channels may tunnel (dashed arrows, scattering matrices
). The annihilation of the particle-hole excitation at the central beam splitter is detected through the currents
and
. Entanglement swapping resulting from two-way teleportation is detected by the violation of a Bell inequality. This requires two gate electrodes to locally mix the edge channels (scattering matrices
,
) and two pairs of contacts
to separately measure the current in each transmitted and reflected edge channel. Notice that there are no phase-coherent paths connecting the left and the right ends of the conductor (because of the intervening dephasing contacts
and
), so a demonstration of entanglement between the two ends is indeed a demonstration of teleportation.
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