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We investigate the decoherence of a qubit coupled to either a quantumtwo-level system (TLS) again coupled to an environment, or a classicalfluctuator modeled by random telegraph noise. In order to do this we constructa model for the quantum TLS where we can adjust the temperature of itsenvironment, and the decoherence rate independently. The model has awell-defined classical limit at any temperature and this corresponds to theappropriate random telegraph process, which is symmetric at high temperaturesand becomes asymmetric at low temperatures. We find that the difference in thequbit decoherence rates predicted by the two models depends on the ratiobetween the qubit-TLS coupling and the decoherence rate in the pointer basis ofthe TLS. This is then the relevant parameter which determines whether the TLShas to be treated quantum mechanically or can be replaced by a classicaltelegraph process. We also compare the mutual information between the qubit andthe TLS in the classical and quantum cases.

Decoherence of a qubit due to a quantum fluctuator or to a classical telegraph noise