Quantum Metrology with Superposition of GHZ state and Twin-Fock state

Abstract We study the metrological performance of the superposition of Greenberger-Horne-Zeilinger state and Twin Fock state (SGT) in quantum phase estimation. We have derived the analytical quantum Fisher information (QFI) of an N-qubit SGT state in noninteracting environment and it emerges a turning point at the critical βₜ=√1-1/N·√2/3. Working in the Mach-Zehnder interferometry, we have provided the optimal metrology schemes saturated by quantum CRLB for all kinds of SGT states, including the specified phase generator and measured parity operator. Moreover, the decoherence effects are also considered and with the increasing decay the QFI in amplitude damping and phase damping channel decreases to the number of qubits involved, implying the standard quantum limit. Specially, the $4$-qubit SGT state (β=√3/2) is found to perform better than GHZ state in phase damping channel. Our work enriches the metrological useful quantum resources.