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

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 \(\varepsilon \), 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 \(\varepsilon =1\) 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.