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

TL;DR

This paper introduces an exact formalism for analyzing qubit decoherence under telegraph noise, revealing complex dynamics, violations of common relations, and limitations of control methods, applicable to multiple noise sources and qubits.

Contribution

The authors develop a comprehensive exact approach for qubit evolution under combined dephasing and relaxational telegraph noise, surpassing previous perturbative methods.

Findings

Revealed unexpected oscillations and magnetization components in strong coupling regimes.

Identified violations of the relation 1/T₂ = 1/2T₁ + 1/T_φ in strong coupling.

Showed limited effectiveness of bang-bang and spin-echo controls against telegraph noise.

Abstract

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. We present 3 applications: 1) We obtain the full qubit dynamics on time scales short compared with the enviromental 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/T$_2$ = 1/2T$_1$ + 1/T$_{\phi}$, 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. %The result shows that these methods are not very effective in %reducing decoherence arising from a single telegraph noise. 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.