[1] Born M, Wolf E[J]. Principles of optics, 461, 93(1999).

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

[3] Braunstein S L, Caves C M, Milburn G J. Generalized uncertainty relations: theory, examples, and Lorentz invariance[J]. Annals of Physics, 247, 135-173(1996).

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

[5] Paris M G A. Quantum estimation for quantum technology[J]. International Journal of Quantum Information, 7, 125-137(2009).

[6] Boto A N, Kok P, Abrams D S et al. Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit[J]. Physical Review Letters, 85, 2733-2736(2000).

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

[8] Walther P, Pan J W, Aspelmeyer M et al. De Broglie wavelength of a non-local four-photon state[J]. Nature, 429, 158-161(2004).

[9] Chen Y A, Bao X H, Yuan Z S et al. Heralded generation of an atomic NOON state[J]. Physical Review Letters, 104, 043601(2010).

[10] Afek I, Ambar O, Silberberg Y. High-NOON states by mixing quantum and classical light[J]. Science, 328, 879-881(2010).

[11] Daniel B, Gerardo A, Fabio B et al. Quantum-enhanced measurements without entanglement[J]. Reviews of Modern Physics, 90, 035006(2018).

[12] Ono T, Okamoto R, Takeuchi S. An entanglement-enhanced microscope[J]. Nature Communications, 4, 2426(2013).

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

[14] Caves C M. Quantum-mechanical noise in an interferometer[J]. Physical Review D, 23, 1693(1981).

[15] Pezzé L, Smerzi A, Khoury G et al. Phase detection at the quantum limit with multiphoton Mach-Zehnder interferometry[J]. Physical Review Letters, 99, 223602(2007).

[16] Pezzé L, Smerzi A. Mach-Zehnder interferometry at the Heisenberg limit with coherent and squeezed-vacuum light[J]. Physical Review Letters, 100, 073601(2008).

[17] Hofmann H F, Ono T. High-photon-number path entanglement in the interference of spontaneously down-converted photon pairs with coherent laser light[J]. Physical Review A, 76, 031806(2007).

[18] 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).

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

[20] Shi Z Z, Zhou L K, Jin G R. Unambiguous phase measurement for twin-Fock states[J]. Acta Optica Sinica, 43, 0212006(2023).

[21] 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]. EPL (Europhysics Letters), 82, 024001(2008).

[22] Schäfermeier C, Ježek M, Madsen L S et al. Deterministic phase measurements exhibiting super-sensitivity and super-resolution[J]. Optica, 5, 60-64(2018).

[23] Feng X M, Jin G R, Yang W. Quantum interferometry with binary-outcome measurements in the presence of phase diffusion[J]. Physical Review A, 90, 013807(2014).

[24] Luca G, Ilaria S, Paolo B et al. Quantum metrology at level anticrossing[J]. Physical Review A, 97, 012120(2018).

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

[26] 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).

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

[28] Gerry C C, Campos R A. Generation of maximally entangled states of a Bose-Einstein condensate and Heisenberg-limited phase resolution[J]. Physical Review A, 68, 025602(2003).

[29] Anisimov P M, Raterman G M, Chiruvelli A et al. Quantum metrology with two-mode squeezed vacuum: parity detection beats the Heisenberg limit[J]. Physical Review Letters, 104, 103602(2010).

[30] Gao Y, Anisimov P M, Wildfeuer C F et al. Super-resolution at the shot-noise limit with coherent states and photon-number-resolving detectors[J]. Journal of the Optical Society of America B, 27, A170-A174(2010).

[31] Seshadreesan K P, Kim S, Dowling J P et al. Phase estimation at the quantum Cramér-Rao bound via parity detection[J]. Physical Review A, 87, 043833(2013).

[32] Xu J H, Chen A X, Yang W et al. Data processing over single-port homodyne detection to realize superresolution and supersensitivity[J]. Physical Review A, 100, 063839(2019).

[33] Zhou L K, Xu J H, Zhang W Z et al. Linear combination estimator of multiple-outcome detections with discrete measurement outcomes[J]. Physical Review A, 103, 043702(2021).

[34] Yuan Y, Niu Y P, Gong S Q et al. Performance of collective measurement to estimate quantum coherence[J]. Acta Optica Sinica, 42, 0327014(2022).

[35] Liu Y Z, Zuo X J, Yan Z H et al. Analysis of quantum interferometer based on optical parametric amplifier[J]. Acta Optica Sinica, 42, 0327013(2022).

[36] 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).

[37] Pezzé L, Smerzi A. Sub shot-noise interferometric phase sensitivity with beryllium ions Schrödinger cat states[J]. EPL (Europhysics Letters), 78, 030004(2007).

[38] Higgins B L, Berry D W, Bartlett S D et al. Entanglement-free Heisenberg-limited phase estimation[J]. Nature, 450, 393-396(2007).

[39] Berry D W, Higgins B L, Bartlett S D et al. How to perform the most accurate possible phase measurements[J]. Physical Review A, 80, 052114(2009).