Eur. Phys. J. Plus (2022) 137: 476
https://doi.org/10.1140/epjp/s13360-022-02701-y

Regular Article

Quantum Fisher information of N-qubit W and GHZ superposition state under nonlocal operation

¹ Department of Physics, Taiyuan Normal University, 030619, Jinzhong, China
² Institute of Computational and Applied Physics, Taiyuan Normal University, 030619, Jinzhong, China

^a li8989971@163.com

Received: 17 December 2021
Accepted: 6 April 2022
Published online: 17 April 2022

Abstract

From the perspective of nonlocal operation, we investigate the quantum Fisher information of N-qubit W and GHZ superposition state. Taking advantage of the general Ising model and Lipkin–Meshkov–Glick model, we analytically present the QFI of N-qubit superposition state. Evidently the traditional fixed QFI is changed and largely increased. As an paradigm, we numerically study the QFI of 3-qubit superposition state with respect to ratio $\alpha$ and interaction strength $\epsilon$, and find the trends of QFI in both models are similar. There always exists a turning point for QFI, and the $\alpha$ is around 0.7. Interestingly, for the interaction strength $\epsilon =1$ in the Ising model, the well-known Heisenberg limit is almost achieved for all $\alpha$. Moreover, under the same interaction strength, we compare the QFI of N-qubit superposition state in both models. With the increasing qubits involved, the $\alpha$ for maximal QFI in the Ising model is changed from close to 1 to the middle region, while it is different in Lipkin–Meshkov–Glick model and the $\alpha$ is close to 1.