Quantum metrological performance of WW¯-like state in Ising model

Abstract

We examine the metrological performance of $W\overline{W}$-like state ($\alpha {\left(W\right)}_N+\beta {\left(\overline{W}\right)}_N$) in quantum phase estimation. Based on the framework of quantum interferometry, we analytically derive the quantum Fisher information (QFI) and analyze the precision limits. In the noninteracting environment, the metrological power of $W\overline{W}$-like state is same as that of the $W$ state in few-qubit case but symmetrically enhanced (with respect to ${\beta }^2$) in large-qubit case. In the Ising model, with increasing interaction strength, the QFI of $N\le 6$ qubit $W\overline{W}$-like state is universally enhanced and displays different and exotic trends (with respect to ${\beta }^2$), particularly for 4- and 6-qubit cases where it respectively shows a reversible phenomenon and a reversal scenario. Regarding others ($N>6$), it exhibits a similar trend that the precision limit is always better than that of $W\overline{W}$ state in strong interaction.