Quantum precision measurement using perfect W state via two-body interacting operation

Abstract

We comprehensively investigate the metrological performance of perfect $W$ (PW) state in quantum phase measurement, including local operation and two-body interacting operation as the phase generator. The analytical precision limits are obtained in both cases and the decoherence effects are also considered. The results show that under local operation the precision limit is slightly lower than $W$ state. In amplitude damping channel the precision limit decreases first and then increases to the shot noise limit, whereas it is always decreased in phase damping channel. Alternatively, the optimal strategies are also provided. In the two-body interacting operations, Ising model and Lipkin–Meshkov–Glick (LMG) model are employed to explore the precision limit. It behaves similar in both cases that with increasing interacting strength $\gamma$ the precision limit surpasses the Heisenberg limit for linear phase estimation and gradually converges with $W$ state. However, the difference is also evident that the more qubits involved for achieving Heisenberg limit, the larger the $\gamma$ needed in Ising model but smaller in LMG model. Interestingly, in amplitude damping channel, with increasing $\gamma$ an expanding platform area of precision limit emerges in few-qubit PW state ($N<6$). This will be beneficial to the stable and tunable high-precision measurement, especially in the noisy circumstances.