Fonctionne avec Indico
v3.2.9
The Kitaev chain model exhibits a phase where two Majorana fermions at the edge of the chain pair up non-locally. From the pair emerges a zero-energy excitation with topological order justifying the application of anyon statistics to the Majorana fermions. An arbitrary large yet finite number of such Majorana fermion pairs can constitute a lattice of anyons, then referred to as Ising anyons, which have been extensively studied with respect to quantum transport and quantum computation. We study quantum teleportation in such fermionic systems of Majorana fermions without considering anyon statistics. Generally, quantum teleportation suggests the transfer of a quantum state by means of a bipartite resource state,
local operations and classical channels. While it is well-understood in qubit systems, many essential concepts, like quantum entanglement of the bipartite resource state, cannot be directly translated to fermionic systems. We present our own quantum teleportation protocol on the basis of fermionic linear optics and fermionic Gaussian resource states, which allow for an unambiguous definition of entanglement. This approach is unique to the best of our knowledge, and we argue that it supersedes other approaches as it includes the teleportation via a single non-local Majorana pair transferring only ’half an electron’. With the proposed protocol, we explore the capacity of quantum teleportation depending on a given fermionic Gaussian resource state and reproduce results found for qubit systems by Horodecki. In particular, we show that the maximal fidelity of a quantum teleportation channel only depends on the best attainable bipartite resource state by means of local operations and classical communication.