[1] Mitchell M W, Lundeen J S, Steinberg A M. Super-resolving phase measurements with a multiphoton entangled state[J]. Nature, 429, 161-164(2004).

[2] Dowling J P. Quantum optical metrology-the lowdown on high-NOON states[J]. Contemporary Physics, 49, 125-143(2008).

[3] Abadie J, Abbott B P, Abbott R et al. A gravitational wave observatory operating beyond the quantum shot-noise limit[J]. Nature Physics, 7, 962-965(2011).

[4] Aasi J, Abadie J, Abbott B P et al. Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light[J]. Nature Photonics, 7, 613-619(2013).

[5] Taylor M A, Bowen W P. Quantum metrology and its application in biology[J]. Physics Reports, 615, 1-59(2016).

[6] Mauranyapin N P, Madsen L S, Taylor M A et al. Evanescent single-molecule biosensing with quantum-limited precision[J]. Nature Photonics, 11, 477-481(2017).

[7] Ludlow A D, Boyd M M, Ye J et al. Optical atomic clocks[J]. Reviews of Modern Physics, 87, 637-701(2015).

[8] Katori H. Optical lattice clocks and quantum metrology[J]. Nature Photonics, 5, 203-210(2011).

[9] Dorner U, Demkowicz-Dobrzanski R, Smith B J et al. Optimal quantum phase estimation[J]. Physical Review Letters, 102, 040403(2009).

[10] Zhang Z, Duan L M. Quantum metrology with Dicke squeezed states[J]. New Journal of Physics, 16, 103037(2014).

[11] Xiang G Y, Hofmann H F, Pryde G J. Optimal multi-photon phase sensing with a single interference fringe[J]. Scientific Reports, 3, 2684(2013).

[12] Sun F W, Liu B H, Gong Y X et al. Experimental demonstration of phase measurement precision beating standard quantum limit by projection measurement[J]. Europhysics Letters, 82, 24001(2008).

[13] Jin G R, Yang W, Sun C P. Quantum-enhanced microscopy with binary-outcome photon[J]. Physical Review A, 95, 013835(2017).

[14] Bollinger J J, Itano W M, Wineland D J et al. Optimal frequency measurements with maximally correlated states[J]. Physical Review A, 54, R4649-R4652(1996).

[15] Gerry C C. Heisenberg-limit interferometry with four-wave mixers operating in a nonlinear regime[J]. Physical Review A, 61, 043811(2000).

[16] Israel Y, Rosen S, Silberberg Y. Supersensitive polarization microscopy using NOON states of light[J]. Physical Review Letters, 112, 103604(2014).

[17] Lücke B, Scherer M, Kruse J et al. Twin matter waves for interferometry beyond the classical limit[J]. Science, 334, 773-776(2011).

[18] Kim T, Pfister O, Holland M J et al. Influence of decorrelation on Heisenberg-limited interferometry with quantum correlated photons[J]. Physical Review A, 57, 4004-4013(1998).

[19] Xu J H, Wang J Z, Chen A X et al. Optimal phase estimation with photon-number difference measurement using twin-Fock states of light[J]. Chinese Physics B, 28, 120303(2019).

[20] Pezzé L, Smerzi A. Sub shot-noise interferometric phase sensitivity with beryllium ions Schrödinger cat states[J]. Europhysics Letters, 78, 30004(2007).

[21] Xiang G Y, Higgins B L, Berry D W et al. Entanglement-enhanced measurement of a completely unknown optical phase[J]. Nature Photonics, 5, 43-47(2011).

[22] Gkortsilas N, Cooper J J, Dunningham J A. Measuring a completely unknown phase with sub-shot-noise precision in the presence of loss[J]. Physical Review A, 85, 063827(2012).

[23] Yurke B, McCall S L, Klauder J R. SU(2) and SU(1,1) interferometers[J]. Physical Review A, 33, 4033-4054(1986).

[24] Holland M J, Burnett K. Interferometric detection of optical phase shifts at the Heisenberg limit[J]. Physical Review Letters, 71, 1355-1358(1993).

[25] Feng X M, Wang P, Yang W et al. High-precision evaluation of Wigner′s d matrix by exact diagonalization[J]. Physical Review E, 92, 043307(2015).

[26] Helstrom C W. Quantum detection and estimation theory[J]. Journal of Statistical Physics, 1, 231-252(1969).

[27] Giovannetti V, Lloyd S, Maccone L. Quantum-enhanced measurements: beating the standard quantum limit[J]. Science, 306, 1330-1336(2004).

[28] Huang X, Ni M, Ji Y et al. Simulation on boson sampling with photon partial distinguishability and photon losses[J]. Acta Optica Sinica, 41, 1227001(2021).

[29] Zhao Y C, Zhao B Y, Zheng J H et al. Design of superconducting nanowire single-photon detector with broadband light absorption characteristics in 3-5 μm[J]. Laser＆Optoelectronics Progress, 59, 0104001(2022).

[30] Zou Y Q, Wu L N, Liu Q et al. Beating the classical precision limit with spin-1 Dicke states of more than 10000 atoms[J]. Proceedings of the National Academy of Sciences of the United States of America, 115, 6381-6385(2018).