Electron teleportation in a $p$-wave superconducting Kitaev wire with Coulomb interaction.

We study the problem of electron teleportation in a $p$-wave superconducting wire [1] as a function of the Coulomb interaction strength. We calculate the change in the probability $delta ho$ of finding an electron at one edge of the wire when another electron is injected at the other edge site. In the absence of Coulomb interaction there is no change in this probability. Including the global charging energy for the wire [2] makes $delta ho$ finite but length-dependent, tending to zero with increasing wire length. We also investigate a modified model in which the Coulomb charging energy is included only between the two edge sites. For this model the change in the probability becomes length-independent. However unlike the canonical spin-teleportation i) this effect is transient (time-dependent) ii) it relies on existence of instantaneous Coulomb correlation between edge sites iii) the value of $delta ho$ is lower than the corresponding normal metal wire. These limitations argue for impossibility of teleportation via Majorana fermions even in the presence of Coulomb interactions.

[1] G. W. Semenoff and P. Sodano, arXiv preprint cond-mat/0605147 (2006)

[2] L. Fu, Physical review letters 104, 056402 (2010