Exact solution of a model of qubit decoherence due to telegraph noise

We present a general and exact formalism for finding the evolution of a quantum system subject to external telegraph noise. The various qubit decoherence rates are determined by the eigenvalues of a transfer matrix. The formalism can be applied to a qubit subject to an arbitrary combination of dephasing and relaxational telegraph noise, in contrast to existing non-perturbative methods that treat only one or the other of these limits. As the applications: 1) We obtain the full qubit dynamics on time scales short compared with the enviromenal correlation times. In the strong coupling cases this reveals unexpected oscillations and induced magnetization components; 2) We find in strong coupling case strong violations of the widely used relation 1/T2 = 1/2T1 + 1/Tφ, which is a result of perturbation theory; 3) We discuss the effects of bang-bang and spin-echo controls of the qubit dynamics in general settings of the telegraph noises. Finally, we discuss the extension of the method to the cases of many telegraph noise sources and multiple qubits. The method still works when white noise is also present.