Decoherence Patterns of Topological Qubits from Majorana Modes

We investigate the decoherence patterns of topological qubits in contact with the environment. Each topological qubit is made of two Majorana modes of a 1D Kitaev's chain. These two Majorana modes weakly interact with the fermionic/bosonic environments. We find the topological qubits decohere completely in the Ohmic and sub-Ohmic environments but not in the super-Ohmic ones. Though the fermion parities of the topological qubits cannot prevent the qubit states from decoherence in the sub-Ohmic environments, it can prevent the qubits turning into Gibbs state. We also study the cases in which each Majorana mode couples to different Ohmic-like environments and the time dependence of concurrence for two topological qubits.