Partial decoherence in a qubit coupled to a control register subject to telegraph noise

Abstract

A qubit (containing two quantum states, 1 and 2), is coupled to a control register (state 3), which is subject to telegraph noise. We study the time evolution of the density matrix ρ of an electron which starts in some coherent state on the qubit. At infinite time, ρ usually approaches the fully decoherent state, with ρ_nm = δ_nm/3. However, when the Hamiltonian is symmetric under 1 ↔ 2, the element ρ₁₂ approaches a non-zero real value, implying a partial coherence of the asymptotic state. The asymptotic density matrix depends only on Re[ρ₁₂(t = 0)]. In several cases, the information stored on the qubit is protected from the noise.