Abstract We study the metrological performance of the superposition of Greenberger-Horne-Zeilinger state and Twin Fock state (SGT) in quantum phase estimation. The analytical quantum Fisher information (QFI) of an Nqubit SGT state in noninteracting environment has been derived and with the increasing ratio β in SGT state it emerges a turning point at βt = q 1 − 1 N · q2 3 , where the smallest QFI FQ = (N 2 + 2N)/3 is achieved. Interestingly, we find the 4-qubit SGT state performs better than TF state in all ratio region and further achieves the Heisenberg limit at β = √ 3/2. Working in the Mach-Zehnder interferometry, we have provided the optimal metrology schemes saturated by quantum CRLB for all kinds of SGT states and found the same βt also existed in the selection of phase generator and measured parity operator. Moreover, we have considered the decoherence effects and with the increasing decay the QFI in amplitude damping and phase damping channel decreases to the number of qubits involved, while it decreases to zero in depolarizing channel. Specially, the 4-qubit SGT state of β = √ 3/2 is found to perform better than GHZ state in phase damping channel. Our work enriches the metrological useful quantum resources.
We study the reciprocal of the mean quantum Fisher information (RMQFI),
χ2 for general three qubit states, having graph and hypergraph states as special cases, for identifying genuine multi party entanglement characterized by
χ2<1. We demonstrate that the most symmetric graph state and the GHZ state have the lowest RMQFI values leading to the highest statistical speed showing that both these states attain the Heisenberg limit in phase sensitivity. Unlike the GHZ state, graph states have the same RMQFI values for measurement through different parameters, a property shared by the hypergraph states. Three qubit graph and hypergraph states can violate Bell's inequality as
FQ>N. Both the GHZ state and the most symmetric graph state have the highest concurrence equalling 3 and the maximum QFI values.