Fidelity of asymmetric dephasing channels

We study the properties of the fidelity of one-qubit operations in a noisy channel and reveal its properties in dependence on coupling to the outer environment. We show that for an asymmetric qubit-environment coupling, the fidelity can be improved by a tuning of the external parameters acting on the qubit energy splitting. In particular, for the case of a spin qubit, the fidelity can be improved by an appropriate tuning of the external magnetic field. We observe that within tailored parameter regimes, the fidelity (typically being oscillatory) evolves monotonically and remains significant in the long-time regime, for both an environment prepared in vacuum and coherent states. This result holds true also for the entanglement fidelity of the two-qubit system.

Figure 1

(Color online) Time evolution of the averaged fidelity of asymmetric dephasing channel $T$: the influence of qubit level separation $\epsilon$ for fixed ${\lambda }_1=0.05$, ${\mu }_{\pm 1}=0.1$, and ${\lambda }_{-1}\approx 0.04$ (within this choice the monotonic fidelity with $\Omega =0$ occurs for ${\lambda }_1=0.05$ and $\epsilon =0.5$). The time unit is $100∕{\omega }_c$.

Figure 2

(Color online) Time evolution of the averaged fidelity of asymmetric dephasing channel $T$: the effect of asymmetry ${\lambda }_1\ne {\lambda }_{-1}$ resulting in controllable fidelity oscillations. Values of other parameters are the same as in Fig. 1.

Figure 3

(Color online) Time evolution of the averaged fidelity of asymmetric dephasing channel $T$: Initial oscillations of the averaged fidelity for sufficiently large asymmetry. Values of other parameters are the same as in Fig. 1.

Figure 4

(Color online) Time evolution of the averaged fidelity of asymmetry dephasing channel $T$: the effect of the initial coherent state, Eq. (52), for ${\mu }_{\alpha }=0.1$. Values of other parameters are the same as in Fig. 1.