by spin exchange regime may exceedingly prolong the lifetimes of the W state even up to several hours [@prl_nuclear; @spin; @ofer_noble-gas].

The $W$ state with phase informations encoded in billions of atoms exists in the form of a spin wave, which resemble a tremendous networked quantum sensors with entanglement between each elements. The phase informations of spin wave are not only related to the position informations of motional atoms, but also sensitive to some other physical parameters related to atomic internal states, like magnetic field [@interfermeter_prl], which makes the $W$ state become a promising candidate for quantum sensing. Due to the collective enhancement effects in the readout of spin wave, the huge scale will become an advantage in enhanced metrology. The nonclassical correlations contained in the $W$ state among huge entangled particles may endow the meteorological gain over classical states [@PRL_Wgain], such as being beneficial to interferometry measurement for beating standard quantum limit [@review_quantum; @metrology]. Interestingly, $W$ state is also robust for the purpose of metrology, because the remaining particles are still entangled while one particle is trace out. Furthermore, the multipartite entanglement constructed between these quantum sensors may significantly enhance the precision of multiparameter estimation [@PRL_MPE].

Acknowledgments. {#acknowledgments. .unnumbered}
