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

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

[3] Ou Z Y. Fundamental quantum limit in precision phase measurement[J]. Physical Review A, 55, 2598-2609(1997).

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

[5] Chen G, Aharon N, Sun Y N et al. Heisenberg-scaling measurement of the single-photon Kerr non-linearity using mixed states[J]. Nature Communications, 9, 93(2018).

[6] Chen G, Zhang L J, Zhang W H et al. Achieving Heisenberg-scaling precision with projective measurement on single photons[J]. Physical Review Letters, 121, 060506(2018).

[7] Zhang L J, Datta A, Walmsley I A. Precision metrology using weak measurements[J]. Physical Review Letters, 114, 210801(2015).

[8] Xu L, Liu Z X, Datta A et al. Approaching quantum-limited metrology with imperfect detectors by using weak-value amplification[J]. Physical Review Letters, 125, 080501(2020).

[9] 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).

[10] 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).

[11] Degen C L, Reinhard F, Cappellaro P. Quantum sensing[J]. Reviews of Modern Physics, 89, 035002(2017).

[12] Pezzè L, Smerzi A, Oberthaler M K et al. Quantum metrology with nonclassical states of atomic ensembles[J]. Reviews of Modern Physics, 90, 035005(2018).

[13] Polino E, Valeri M, Spagnolo N et al. Photonic quantum metrology[J]. AVS Quantum Science, 2, 024703(2020).

[14] Liu J, Yuan H D, Lu X M et al. Quantum Fisher information matrix and multiparameter estimation[J]. Journal of Physics A: Mathematical and Theoretical, 53, 023001(2020).

[15] Braunstein S L, Caves C M. Statistical distance and the geometry of quantum states[J]. Physical Review Letters, 72, 3439-3443(1994).

[16] Fujiwara A. Strong consistency and asymptotic efficiency for adaptive quantum estimation problems[J]. Journal of Physics A: Mathematical and Theoretical, 44, 079501(2011).

[17] Gill R D, Massar S. State estimation for large ensembles[J]. Physical Review A, 61, 042312(2000).

[18] Hayashi M, Matsumoto K. Asymptotic performance of optimal state estimation in qubit system[J]. Journal of Mathematical Physics, 49, 102101(2008).

[19] Giovannetti V, Lloyd S, Maccone L. Quantum metrology[J]. Physical Review Letters, 96, 010401(2006).

[20] Giovannetti V, Lloyd S, Maccone L. Advances in quantum metrology[J]. Nature Photonics, 5, 222-229(2011).

[21] Hou Z B, Tang J F, Shang J W et al. Deterministic realization of collective measurements via photonic quantum walks[J]. Nature Communications, 9, 1414(2018).

[22] Perarnau-Llobet M, Bäumer E, Hovhannisyan K V et al. No-go theorem for the characterization of work fluctuations in coherent quantum systems[J]. Physical Review Letters, 118, 070601(2017).

[23] Wu K D, Bäumer E, Tang J F et al. Minimizing backaction through entangled measurements[J]. Physical Review Letters, 125, 210401(2020).

[24] Gisin N, Popescu S. Spin flips and quantum information for antiparallel spins[J]. Physical Review Letters, 83, 432-435(1999).

[25] Tang J F, Hou Z B, Shang J W et al. Experimental optimal orienteering via parallel and antiparallel spins[J]. Physical Review Letters, 124, 060502(2020).

[26] Demkowicz-Dobrzański R, Górecki W, Guţă M. Multi-parameter estimation beyond quantum Fisher information[J]. Journal of Physics A: Mathematical and Theoretical, 53, 363001(2020).

[27] Ji Z F, Wang G M, Duan R Y et al. Parameter estimation of quantum channels[J]. IEEE Transactions on Information Theory, 54, 5172-5185(2008).

[28] de Burgh M, Bartlett S D. Quantum methods for clock synchronization: beating the standard quantum limit without entanglement[J]. Physical Review A, 72, 042301(2005).

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

[30] Braun D, Adesso G, Benatti F et al. Quantum-enhanced measurements without entanglement[J]. Reviews of Modern Physics, 90, 035006(2018).

[31] Escher B M, de Matos Filho R L, Davidovich L. General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology[J]. Nature Physics, 7, 406-411(2011).

[32] Escher B M, de Matos Filho R L, Davidovich L. Quantum metrology for noisy systems[J]. Brazilian Journal of Physics, 41, 229-247(2011).

[33] Demkowicz-Dobrzański R, Kołodyński J, Guţă M. The elusive Heisenberg limit in quantum-enhanced metrology[J]. Nature Communications, 3, 1063(2012).

[34] Walmsley I A. Quantum optics: science and technology in a new light[J]. Science, 348, 525-530(2015).

[35] Pan J W, Chen Z B, Lu C Y et al. Multiphoton entanglement and interferometry[J]. Reviews of Modern Physics, 84, 777-838(2012).

[36] O’Brien J L, Furusawa A, Vučković J. Photonic quantum technologies[J]. Nature Photonics, 3, 687-695(2009).

[37] Kwiat P G, Mattle K, Weinfurter H et al. New high-intensity source of polarization-entangled photon pairs[J]. Physical Review Letters, 75, 4337-4341(1995).

[38] Ou Z Y, Pereira S F, Kimble H J et al. Realization of the Einstein-Podolsky-Rosen paradox for continuous variables[J]. Physical Review Letters, 68, 3663-3666(1992).

[39] Bouwmeester D, Pan J W, Mattle K et al. Experimental quantum teleportation[J]. Nature, 390, 575-579(1997).

[40] Furusawa A, Sorensen J L, Braunstein S L et al. Unconditional quantum teleportation[J]. Science, 282, 706-709(1998).

[41] Flamini F, Spagnolo N, Sciarrino F. Photonic quantum information processing: a review[J]. Reports on Progress in Physics, 82, 016001(2019).

[42] Slussarenko S, Pryde G J. Photonic quantum information processing: a concise review[J]. Applied Physics Reviews, 6, 041303(2019).

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

[44] Brambilla E, Caspani L, Jedrkiewicz O et al. High-sensitivity imaging with multi-mode twin beams[J]. Physical Review A, 77, 053807(2008).

[45] Gregory T, Moreau P A, Toninelli E et al. Imaging through noise with quantum illumination[J]. Science Advances, 6, eaay2652(2020).

[46] Moreau P A, Toninelli E, Gregory T et al. Imaging with quantum states of light[J]. Nature Reviews Physics, 1, 367-380(2019).

[47] Berchera I R, Degiovanni I P. Quantum imaging with sub-Poissonian light: challenges and perspectives in optical metrology[J]. Metrologia, 56, 024001(2019).

[48] Genovese M. Real applications of quantum imaging[J]. Journal of Optics, 18, 073002(2016).

[49] Samantaray N, Ruo-Berchera I, Meda A et al. Realization of the first sub-shot-noise wide field microscope[J]. Light, Science & Applications, 6, e17005(2017).

[50] Giovannetti V, Lloyd S, Maccone L et al. Sub-Rayleigh-diffraction-bound quantum imaging[J]. Physical Review A, 79, 013827(2009).

[51] Tenne R, Rossman U, Rephael B et al. Super-resolution enhancement by quantum image scanning microscopy[J]. Nature Photonics, 13, 116-122(2019).

[52] Treps N, Andersen U, Buchler B et al. Surpassing the standard quantum limit for optical imaging using nonclassical multimode light[J]. Physical Review Letters, 88, 203601(2002).

[53] Kolobov M I. The spatial behavior of nonclassical light[J]. Reviews of Modern Physics, 71, 1539-1589(1999).

[54] Caves C M. Quantum-mechanical noise in an interferometer[J]. Physical Review D, 23, 1693-1708(1981).

[55] Braunstein S L, van Loock P. Quantum information with continuous variables[J]. Reviews of Modern Physics, 77, 513-577(2005).

[56] Pirandola S, Bardhan B R, Gehring T et al. Advances in photonic quantum sensing[J]. Nature Photonics, 12, 724-733(2018).

[57] Ono T, Hofmann H F. Effects of photon losses on phase estimation near the Heisenberg limit using coherent light and squeezed vacuum[J]. Physical Review A, 81, 033819(2010).

[58] Jarzyna M, Demkowicz-Dobrzański R. Quantum interferometry with and without an external phase reference[J]. Physical Review A, 85, 011801(2012).

[59] Seshadreesan K P, Anisimov P M, Lee H et al. Parity detection achieves the Heisenberg limit in interferometry with coherent mixed with squeezed vacuum light[J]. New Journal of Physics, 13, 083026(2011).

[60] D’Ariano G M, Leonhardt U, Paul H. Homodyne detection of the density matrix of the radiation field[J]. Physical Review A, 52, R1801-R1804(1995).

[61] Demkowicz-Dobrzański R, Jarzyna M, Kołodyński J. Quantum limits in optical interferometry[M]. Progress in optics, 345-435(2015).

[62] Treps N, Grosse N, Bowen W et al. A quantum laser pointer[J]. Science, 301, 940-943(2003).

[63] Grangier P, Slusher R E, Yurke B et al. Squeezed-light-enhanced polarization interferometer[J]. Physical Review Letters, 59, 2153-2156(1987).

[64] Xiao M, Wu L A, Kimble H J. Precision measurement beyond the shot-noise limit[J]. Physical Review Letters, 59, 278-281(1987).

[65] McKenzie K, Shaddock D A, McClelland D E et al. Experimental demonstration of a squeezing-enhanced power-recycled Michelson interferometer for gravitational wave detection[J]. Physical Review Letters, 88, 231102(2002).

[66] Vahlbruch H, Chelkowski S, Hage B et al. Demonstration of a squeezed-light-enhanced power- and signal-recycled Michelson interferometer[J]. Physical Review Letters, 95, 211102(2005).

[67] Goda K, Miyakawa O, Mikhailov E E et al. A quantum-enhanced prototype gravitational-wave detector[J]. Nature Physics, 4, 472-476(2008).

[68] Plick W N, Dowling J P, Agarwal G S. Coherent-light-boosted, sub-shot noise, quantum interferometry[J]. New Journal of Physics, 12, 083014(2010).

[69] Ou Z Y. Enhancement of the phase-measurement sensitivity beyond the standard quantum limit by a nonlinear interferometer[J]. Physical Review A, 85, 023815(2012).

[70] Jing J T, Liu C J, Zhou Z F et al. Realization of a nonlinear interferometer with parametric amplifiers[J]. Applied Physics Letters, 99, 011110(2011).

[71] Hudelist F, Kong J, Liu C J et al. Quantum metrology with parametric amplifier-based photon correlation interferometers[J]. Nature Communications, 5, 3049(2014).

[72] Anderson B E, Gupta P, Schmittberger B L et al. Phase sensing beyond the standard quantum limit with a variation on the SU(1,1) interferometer[J]. Optica, 4, 752-756(2017).

[73] Manceau M, Leuchs G, Khalili F et al. Detection loss tolerant supersensitive phase measurement with an SU(1,1) interferometer[J]. Physical Review Letters, 119, 223604(2017).

[74] Guo X S, Li X Y, Liu N N et al. Quantum information tapping using a fiber optical parametric amplifier with noise figure improved by correlated inputs[J]. Scientific Reports, 6, 30214(2016).

[75] Lukens J M, Pooser R C, Peters N A. A broadband fiber-optic nonlinear interferometer[J]. Applied Physics Letters, 113, 091103(2018).

[76] Liu Y H, Li J M, Cui L et al. Loss-tolerant quantum dense metrology with SU(1,1) interferometer[J]. Optics Express, 26, 27705-27715(2018).

[77] Lukens J M, Peters N A, Pooser R C. Naturally stable Sagnac-Michelson nonlinear interferometer[J]. Optics Letters, 41, 5438-5441(2016).

[78] Wang W, Chen Z J, Liu X et al. Quantum-enhanced radiometry via approximate quantum error correction[J]. Nature Communications, 13, 3214(2022).

[79] Lee H, Kok P, Dowling J P. A quantum Rosetta Stone for interferometry[J]. Journal of Modern Optics, 49, 2325-2338(2002).

[80] 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).

[81] Hong C K, Ou Z Y, Mandel L. Measurement of subpicosecond time intervals between two photons by interference[J]. Physical Review Letters, 59, 2044-2046(1987).

[82] Ou Z Y, Zou X Y, Wang L J et al. Experiment on nonclassical fourth-order interference[J]. Physical Review A, 42, 2957-2965(1990).

[83] Rarity J G, Tapster P R, Jakeman E et al. Two-photon interference in a Mach-Zehnder interferometer[J]. Physical Review Letters, 65, 1348-1351(1990).

[84] Kuzmich A, Mandel L. Sub-shot-noise interferometric measurements with two-photon states[J]. Quantum and Semiclassical Optics: Journal of the European Optical Society Part B, 10, 493-500(1998).

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

[86] Nagata T, Okamoto R, O’Brien J L et al. Beating the standard quantum limit with four-entangled photons[J]. Science, 316, 726-729(2007).

[87] 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).

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

[89] Schnabel R, Mavalvala N, McClelland D E et al. Quantum metrology for gravitational wave astronomy[J]. Nature Communications, 1, 121(2010).

[90] Abbott B P, Abbott R, Abbott T D et al. Observation of gravitational waves from a binary black hole merger[J]. Physical Review Letters, 116, 061102(2016).

[91] Abbott B P, Abbott R, Abbott T D et al. GW151226: observation of gravitational waves from a 22-solar-mass binary black hole coalescence[J]. Physical Review Letters, 116, 241103(2016).

[92] Vahlbruch H, Wilken D, Mehmet M et al. Laser power stabilization beyond the shot noise limit using squeezed light[J]. Physical Review Letters, 121, 173601(2018).

[93] 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).

[94] Tse M, Yu H C, Kijbunchoo N et al. Quantum-enhanced advanced LIGO detectors in the era of gravitational-wave astronomy[J]. Physical Review Letters, 123, 231107(2019).

[95] Wang W, Xia J L, Xu Y X. Research on integrated optical gyroscope[C](2008).

[96] Khial P P, White A D, Hajimiri A. Nanophotonic optical gyroscope with reciprocal sensitivity enhancement[J]. Nature Photonics, 12, 671-675(2018).

[97] Post E J. Sagnac effect[J]. Reviews of Modern Physics, 39, 475-493(1967).

[98] Mehmet M, Eberle T, Steinlechner S et al. Demonstration of a quantum-enhanced fiber Sagnac interferometer[J]. Optics Letters, 35, 1665-1667(2010).

[99] Jiao L, An J-H. Noisy quantum gyroscope[J]. Photonics Research, 11, 150(2023).

[100] Zhao W, Tang X, Guo X S et al. Quantum entangled Sagnac interferometer[J]. Applied Physics Letters, 122, 064003(2023).

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

[102] Demkowicz-Dobrzanski R, Dorner U, Smith B J et al. Quantum phase estimation with lossy interferometers[J]. Physical Review A, 80, 013825(2009).

[103] Kacprowicz M, Demkowicz-Dobrzański R, Wasilewski W et al. Experimental quantum-enhanced estimation of a lossy phase shift[J]. Nature Photonics, 4, 357-360(2010).

[104] Datta A, Zhang L J, Thomas-Peter N et al. Quantum metrology with imperfect states and detectors[J]. Physical Review A, 83, 063836(2011).

[105] Spagnolo N, Vitelli C, Lucivero V G et al. Phase estimation via quantum interferometry for noisy detectors[J]. Physical Review Letters, 108, 233602(2012).

[106] Resch K J, Pregnell K L, Prevedel R et al. Time-reversal and super-resolving phase measurements[J]. Physical Review Letters, 98, 223601(2007).

[107] Slussarenko S, Weston M M, Chrzanowski H M et al. Unconditional violation of the shot-noise limit in photonic quantum metrology[J]. Nature Photonics, 11, 700-703(2017).

[108] 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).

[109] 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).

[110] Jin R B, Fujiwara M, Shimizu R et al. Detection-dependent six-photon Holland-Burnett state interference[J]. Scientific Reports, 6, 36914(2016).

[111] Crowley P J D, Datta A, Barbieri M et al. Tradeoff in simultaneous quantum-limited phase and loss estimation in interferometry[J]. Physical Review A, 89, 023845(2014).

[112] Szczykulska M, Baumgratz T, Datta A. Multi-parameter quantum metrology[J]. Advances in Physics: X, 1, 621-639(2016).

[113] Humphreys P C, Barbieri M, Datta A et al. Quantum enhanced multiple phase estimation[J]. Physical Review Letters, 111, 070403(2013).

[114] Hong S, Ur Rehman J, Kim Y S et al. Quantum enhanced multiple-phase estimation with multi-mode N00N states[J]. Nature Communications, 12, 5211(2021).

[115] Hong S, Rehman J U, Kim Y S et al. Practical sensitivity bound for multiple phase estimation with multi-mode N00N$N00N$ states[J]. Laser & Photonics Reviews, 16, 2100682(2022).

[116] Polino E, Riva M, Valeri M et al. Experimental multiphase estimation on a chip[J]. Optica, 6, 288-295(2019).

[117] Valeri M, Polino E, Poderini D et al. Experimental adaptive Bayesian estimation of multiple phases with limited data[J]. NPJ Quantum Information, 6, 92(2020).

[118] Zhang Z S, Zhuang Q T. Distributed quantum sensing[J]. Quantum Science and Technology, 6, 043001(2021).

[119] Ge W C, Jacobs K, Eldredge Z et al. Distributed quantum metrology with linear networks and separable inputs[J]. Physical Review Letters, 121, 043604(2018).

[120] Gross J A, Caves C M. One from many: estimating a function of many parameters[J]. Journal of Physics A: Mathematical and Theoretical, 54, 014001(2021).

[121] Liu L Z, Zhang Y Z, Li Z D et al. Distributed quantum phase estimation with entangled photons[J]. Nature Photonics, 15, 137-142(2021).

[122] Guo X S, Breum C R, Borregaard J et al. Distributed quantum sensing in a continuous-variable entangled network[J]. Nature Physics, 16, 281-284(2020).

[123] Zhuang Q T, Zhang Z S, Shapiro J H. Distributed quantum sensing using continuous-variable multipartite entanglement[J]. Physical Review A, 97, 032329(2018).

[124] Rubio J, Knott P A, Proctor T J et al. Quantum sensing networks for the estimation of linear functions[J]. Journal of Physics A: Mathematical and Theoretical, 53, 344001(2020).

[125] Albarelli F, Friel J F, Datta A. Evaluating the Holevo Cramér-Rao bound for multiparameter quantum metrology[J]. Physical Review Letters, 123, 200503(2019).

[126] Matsumoto K. A new approach to the Cramér-Rao-type bound of the pure-state model[J]. Journal of Physics A: Mathematical and General, 35, 3111-3123(2002).

[127] Yang Y X, Chiribella G, Hayashi M. Attaining the ultimate precision limit in quantum state estimation[J]. Communications in Mathematical Physics, 368, 223-293(2019).

[128] Jun S. Explicit formula for the Holevo bound for two-parameter qubit-state estimation problem[J]. Journal of Mathematical Physics, 57, 042201(2016).

[129] Sidhu J S, Ouyang Y K, Campbell E T et al. Tight bounds on the simultaneous estimation of incompatible parameters[J]. Physical Review X, 11, 011028(2021).

[130] Linden N, Massar S, Popescu S. Purifying noisy entanglement requires collective measurements[J]. Physical Review Letters, 81, 3279-3282(1998).

[131] Yuan Y, Hou Z B, Tang J F et al. Direct estimation of quantum coherence by collective measurements[J]. NPJ Quantum Information, 6, 46(2020).

[132] Wu K D, Yuan Y, Xiang G Y et al. Experimentally reducing the quantum measurement back action in work distributions by a collective measurement[J]. Science Advances, 5, eaav4944(2019).

[133] Conlon L O, Vogl T, Marciniak C D et al. Approaching optimal entangling collective measurements on quantum computing platforms[J]. Nature Physics, 19, 351-357(2023).

[134] Cox K C, Greve G P, Weiner J M et al. Deterministic squeezed states with collective measurements and feedback[J]. Physical Review Letters, 116, 093602(2016).

[135] Conlon L O, Suzuki J, Lam P K et al. Efficient computation of the Nagaoka-Hayashi bound for multiparameter estimation with separable measurements[J]. NPJ Quantum Information, 7, 110(2021).

[136] Ragy S, Jarzyna M, Demkowicz-Dobrzański R. Compatibility in multiparameter quantum metrology[J]. Physical Review A, 94, 052108(2016).

[137] Altorio M, Genoni M G, Vidrighin M D et al. Weak measurements and the joint estimation of phase and phase diffusion[J]. Physical Review A, 92, 032114(2015).

[138] Szczykulska M, Baumgratz T, Datta A. Reaching for the quantum limits in the simultaneous estimation of phase and phase diffusion[J]. Quantum Science and Technology, 2, 044004(2017).

[139] Knysh S I, Durkin G A. Estimation of phase and diffusion: combining quantum statistics and classical noise[EB/OL]. https:∥arxiv.org/abs/1307.0470

[140] Vidrighin M D, Donati G, Genoni M G et al. Joint estimation of phase and phase diffusion for quantum metrology[J]. Nature Communications, 5, 3532(2014).

[141] Roccia E, Gianani I, Mancino L et al. Entangling measurements for multiparameter estimation with two qubits[J]. Quantum Science and Technology, 3, 01LT01(2018).

[142] Qassim H, Miatto F M, Torres J P et al. Limitations to the determination of a Laguerre-Gauss spectrum via projective, phase-flattening measurement[J]. Journal of the Optical Society of America B, 31, A20-A23(2014).

[143] Bouchard F, Valencia N H, Brandt F et al. Measuring azimuthal and radial modes of photons[J]. Optics Express, 26, 31925-31941(2018).

[144] Bavaresco J, Herrera Valencia N, Klöckl C et al. Measurements in two bases are sufficient for certifying high-dimensional entanglement[J]. Nature Physics, 14, 1032-1037(2018).

[145] Marcikic I, de Riedmatten H, Tittel W et al. Long-distance teleportation of qubits at telecommunication wavelengths[J]. Nature, 421, 509-513(2003).

[146] Schreiber A, Gábris A, Rohde P P et al. A 2D quantum walk simulation of two-particle dynamics[J]. Science, 336, 55-58(2012).

[147] Lorz L, Meyer-Scott E, Nitsche T et al. Photonic quantum walks with four-dimensional coins[J]. Physical Review Research, 1, 033036(2019).

[148] Zhong T, Zhou H C, Horansky R D et al. Photon-efficient quantum key distribution using time-energy entanglement with high-dimensional encoding[J]. New Journal of Physics, 17, 022002(2015).

[149] Nunn J, Wright L J, Söller C et al. Large-alphabet time-frequency entangled quantum key distribution by means of time-to-frequency conversion[J]. Optics Express, 21, 15959-15973(2013).

[150] Steinlechner F, Ecker S, Fink M et al. Distribution of high-dimensional entanglement via an intra-city free-space link[J]. Nature Communications, 8, 15971(2017).

[151] Gianani I, Sbroscia M, Barbieri M. Measuring the time-frequency properties of photon pairs: a short review[J]. AVS Quantum Science, 2, 011701(2020).

[152] Eriksson M, Goldberg A Z, Hiekkamäki M et al. Sensing rotations with multiplane light conversion[J]. Physical Review Applied, 20, 024052(2023).

[153] Xia B K, Huang J Z, Li H J et al. Toward incompatible quantum limits on multiparameter estimation[J]. Nature Communications, 14, 1021(2023).

[154] Tsang M, Nair R, Lu X M. Quantum theory of superresolution for two incoherent optical point sources[J]. Physical Review X, 6, 031033(2016).

[155] Yu Z X, Prasad S. Quantum limited superresolution of an incoherent source pair in three dimensions[J]. Physical Review Letters, 121, 180504(2018).

[156] Napoli C, Piano S, Leach R et al. Towards superresolution surface metrology: quantum estimation of angular and axial separations[J]. Physical Review Letters, 122, 140505(2019).

[157] Wang B, Xu L, Li J C et al. Quantum-limited localization and resolution in three dimensions[J]. Photonics Research, 9, 1522-1530(2021).

[158] Prasad S, Yu Z X. Quantum-limited superlocalization and superresolution of a source pair in three dimensions[J]. Physical Review A, 99, 022116(2019).

[159] Řehaček J, Hradil Z, Stoklasa B et al. Multiparameter quantum metrology of incoherent point sources: towards realistic superresolution[J]. Physical Review A, 96, 062107(2017).

[160] Řeháček J, Hradil Z, Koutný D et al. Optimal measurements for quantum spatial superresolution[J]. Physical Review A, 98, 012103(2018).

[161] Prasad S. Quantum limited super-resolution of an unequal-brightness source pair in three dimensions[J]. Physica Scripta, 95, 054004(2020).

[162] Bisketzi E, Branford D, Datta A. Quantum limits of localisation microscopy[J]. New Journal of Physics, 21, 123032(2019).

[163] Hradil Z, Řeháček J, Sánchez-Soto L et al. Quantum Fisher information with coherence[J]. Optica, 6, 1437-1440(2019).

[164] Larson W, Saleh B E A. Resurgence of Rayleigh’s curse in the presence of partial coherence[J]. Optica, 5, 1382-1389(2018).

[165] Tsang M, Nair R. Resurgence of Rayleigh’s curse in the presence of partial coherence: comment[J]. Optica, 6, 400-401(2019).

[166] Larson W, Saleh B E A. Resurgence of Rayleigh’s curse in the presence of partial coherence: reply[J]. Optica, 6, 402-403(2019).

[167] Wang B, Xu L, Xia H K et al. Quantum-limited resolution of partially coherent sources[J]. Chinese Optics Letters, 21, 042601(2023).

[168] Paúr M, Stoklasa B, Hradil Z et al. Achieving the ultimate optical resolution[J]. Optica, 3, 1144-1147(2016).

[169] Tham W-K, Ferretti H, Steinberg A M. Beating Rayleigh’s curse by imaging using phase information[J]. Physical Review Letters, 118, 070801(2017).

[170] Parniak M, Borówka S, Boroszko K et al. Beating the Rayleigh limit using two-photon interference[J]. Physical Review Letters, 121, 250503(2018).

[171] Yang F, Tashchilina A, Moiseev E S et al. Far-field linear optical superresolution via heterodyne detection in a higher-order local oscillator mode[J]. Optica, 3, 1148-1152(2016).

[172] Tang Z S, Durak K, Ling A. Fault-tolerant and finite-error localization for point emitters within the diffraction limit[J]. Optics Express, 24, 22004(2016).

[173] Rouvière C, Rana D B, Grateau A et al. Ultra-sensitive separation estimation of optical sources[EB/OL]. https:∥arxiv.org/abs/2306.11916

[174] Boucher P, Fabre C, Labroille G et al. Spatial optical mode demultiplexing as a practical tool for optimal transverse distance estimation[J]. Optica, 7, 1621-1626(2020).

[175] Hou Z B, Wang R J, Tang J F et al. Control-enhanced sequential scheme for general quantum parameter estimation at the Heisenberg limit[J]. Physical Review Letters, 123, 040501(2019).

[176] Hou Z B, Tang J F, Chen H Z et al. Zero-trade-off multiparameter quantum estimation via simultaneously saturating multiple Heisenberg uncertainty relations[J]. Science Advances, 7, eabd2986(2021).