Enhancement of parameter-estimation precision in noisy systems by dynamical decoupling pulses

We present a scheme to enhance the precision of parameter estimation (PPE) in noisy systems by employing dynamical decoupling pulses. An exact analytical expression for the estimation precision of an unknown parameter is obtained by using the transfer matrix and time-dependent Kraus operators. We show that the PPE in noisy systems can be preserved in the Heisenberg limit by control of the dynamical decoupling pulses. It is found that a larger number of pulses and longer reservoir correlation time can greatly protect the PPE.

Figure 1

Schematic representation of parameter estimation for an $N$-qubit noisy system in the presence of dynamical decoupling. The total evolution procedure can be described by the tensor product ${\mathcal{E}}_{\phi }^{\otimes N}$.

Figure 2

Mean QFI $\overline{F}$ (a) as a function of time ${\gamma }_{0}t$ with $N=5$, and (b) with respect to the pulse number $n$ at a given time ${\gamma }_{0}t=10$ and $N=20$.

Figure 3

Comparison of the values of $\Delta {\phi }_{\text{min}}$ at fixed time ${\gamma }_{0}t=10$ with different $\lambda$ with respect to the number of (a) qubits $N$ and (b) control pulses $n$. The shaded area indicates the region between the HL and SQL.