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

TL;DR

This paper investigates how a qubit coupled to a noisy control register exhibits partial decoherence, with certain symmetric conditions preserving some quantum coherence even at long times.

Contribution

It demonstrates that under symmetric Hamiltonian conditions, the qubit retains partial coherence asymptotically, revealing noise protection mechanisms.

Findings

Asymptotic density matrix retains partial coherence under symmetry.

Partial coherence depends on initial real part of off-diagonal density matrix.

Symmetry can protect quantum information from decoherence.

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 $\rho$ of an electron which starts in some coherent state on the qubit. At infinite time, $\rho$ usually approaches the fully decoherent state, with $\rho^{}_{nm}=\delta^{}_{nm}/3$. However, when the Hamiltonian is symmetric under $1\leftrightarrow 2$, the element $\rho^{}_{12}$ approaches a non-zero real value, implying a partial coherence of the asymptotic state. The asymptotic density matrix depends only on ${\rm Re}[\rho^{}_{12}(t=0)]$. In several cases, the information stored on the qubit is protected from the noise.