Quantum teleportation of single-electron states

Abstract: Quantum teleportation is a way to transfer a quantum state between two locations, by utilizing a shared entangled state, measurements and the ability to communicate measurement outcomes between the two locations. This thesis consists of a theoretical investigation of an experiment that would implement quantum teleportation using single-electron states in mesoscopic architectures. First, we studied an idealized version, where it is assumed that single-electron states can be detected, which is yet to be demonstrated for certain types of implementations. There we find a teleportation efficiency of 25\% or 12.5\%, depending on whether a conditional unitary operation can be applied to the teleported state. We also show how to verify successful teleportation, by describing a way to perform state tomography on the teleported state. Next, we considered a more realistic setup where single-electron states called levitons are periodically injected. We show that at $T=0$ it is possible to perform state tomography using measurements of low-frequency current correlators up to order three. This opens the possibility to perform teleportation experiments that do not rely on single-electron detection. The correlators were calculated within the framework of Floquet scattering theory. Strictly speaking, the simple picture of single-electron state teleportation breaks down at finite temperatures. However, we find that the generalized observables can be interpreted in terms of noisy teleportation.