[1] LandauL.LifshitzE., Quantum Mechanics: Non Relativistic Theory (Pergamon, 1977), Vol. 3.

[2] C. M. Bender, S. Boettcher. Real spectra in non-Hermitian Hamiltonians having PT symmetry. Phys. Rev. Lett., 1998, 80: 5243-5246.

[3] Y. N. Joglekar, C. Thompson, D. D. Scott, G. Gautam. Optical waveguide arrays: quantum effects and PT symmetry breaking. Eur. Phys. J., 2013, 63: 30001.

[4] L. Feng, R. El-Ganainy, L. Ge. Non-Hermitian photonics based on parity-time symmetry. Nat. Photonics, 2017, 11: 752-762.

[5] R. El-Ganainy, K. G. Makris, M. Khajavikhan, Z. H. Musslimani, S. Rotter, D. N. Christodoulides. Non-Hermitian physics and PT symmetry. Nat. Phys., 2018, 14: 11-19.

[6] M. Mueller, I. Rotter. Exceptional points in open quantum systems. J. Phys. A, 2008, 41: 244018.

[7] W. D. Heiss. The physics of exceptional points. J. Phys. A, 2012, 45: 444016.

[8] KatoT., Perturbation Theory for Linear Operators (Springer Science & Business Media, 2013), Vol. 132.

[9] A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, D. N. Christodoulides. Observation of PT-symmetry breaking in complex optical potentials. Phys. Rev. Lett., 2009, 103: 093902.

[10] K. Ding, G. Ma, M. Xiao, Z. Q. Zhang, C. T. Chan. Emergence, coalescence, and topological properties of multiple exceptional points and their experimental realization. Phys. Rev. X, 2016, 6: 021007.

[11] NaghilooM.AbbasiM.JoglekarY. N.MurchK., “Quantum state tomography across the exceptional point in a single dissipative qubit,” arXiv:1901.07968 (2019).

[12] J. Li, A. K. Harter, J. Liu, L. de Melo, Y. N. Joglekar, L. Luo. Observation of parity-time symmetry breaking transitions in a dissipative Floquet system of ultracold atoms. Nat. Commun., 2019, 10: 855.

[13] BianZ.XiaoL.WangK.ZhanX.OnangaF. A.RuzickaF.YiW.JoglekarY. N.XueP., “Time invariants across a fourth-order exceptional point in a parity-time-symmetric qudit,” arXiv:1903.09806 (2019).

[14] J. Doppler, A. A. Mailybaev, J. Bohm, U. Kuhl, A. Girschik, F. Libisch, T. J. Milburn, P. Rabl, N. Moiseyev, S. Rotter. Dynamically encircling an exceptional point for asymmetric mode switching. Nature, 2016, 537: 76-79.

[15] H. Xu, D. Mason, L. Jiang, J. G. E. Harris. Topological energy transfer in an optomechanical system with exceptional points. Nature, 2016, 537: 80-83.

[16] S. Assawaworrarit, X. Yu, S. Fan. Robust wireless power transfer using a nonlinear parity-time-symmetric circuit. Nature, 2017, 546: 387-390.

[17] J. Wiersig. Enhancing the sensitivity of frequency and energy splitting detection by using exceptional points: application to microcavity sensors for single-particle detection. Phys. Rev. Lett., 2014, 112: 203901.

[18] J. Wiersig. Sensors operating at exceptional points: general theory. Phys. Rev. A, 2016, 93: 033809.

[19] H. Hodaei, A. U. Hassan, S. Wittek, H. Garcia-Gracia, R. El-Ganainy, D. N. Christodoulides, M. Khajavikhan. Enhanced sensitivity at higher-order exceptional points. Nature, 2017, 548: 187-191.

[20] W. Chen, S. Kaya Ozdemir, G. Zhao, J. Wiersig, L. Yang. Exceptional points enhance sensing in an optical microcavity. Nature, 2017, 548: 192-196.

[21] H. Zhao, Z. Chen, R. Zhao, L. Feng. Exceptional point engineered glass slide for microscopic thermal mapping. Nat. Commun., 2018, 9: 1764.

[22] Q. Zhong, D. N. Christodoulides, M. Khajavikhan, K. G. Makris, R. El-Ganainy. Power-law scaling of extreme dynamics near higher-order exceptional points. Phys. Rev. A, 2018, 97: 020105.

[23] S. Wang, B. Hou, W. Lu, Y. Chen, Z. Q. Zhang, C. T. Chan. Arbitrary order exceptional point induced by photonic spin-orbit interaction in coupled resonators. Nat. Commun., 2019, 10: 832.

[24] H.-K. Lau, A. A. Clerk. Fundamental limits and non-reciprocal approaches in non-Hermitian quantum sensing. Nat. Commun., 2018, 9: 4320.

[25] G. Harder, T. J. Bartley, A. E. Lita, S. W. Nam, T. Gerrits, C. Silberhorn. Single-mode parametric-down-conversion states with 50 photons as a source for mesoscopic quantum optics. Phys. Rev. Lett., 2016, 116: 143601.

[26] L. Banchi, W. S. Kolthammer, M. S. Kim. Multiphoton tomography with linear optics and photon counting. Phys. Rev. Lett., 2018, 121: 250402.

[27] Magaña-LoaizaO. S.León-MontielR. de J.Perez-LeijaA.U’RenA. B.YouC.BuschK.LitaA. E.NamS. W.MirinR. P.GerritsT., “Multiphoton quantum-state engineering using conditional measurements,” arXiv:1901.00122 (2019).

[28] W. K. Lai, V. Buek, P. L. Knight. Nonclassical fields in a linear directional coupler. Phys. Rev. A, 1991, 43: 6323-6336.

[29] K. Tschernig, R. de J. León-Montiel, O. S. Magaña-Loaiza, A. Szameit, K. Busch, A. Perez-Leija. Multiphoton discrete fractional Fourier dynamics in waveguide beam splitters. J. Opt. Soc. Am. B, 2018, 35: 1985-1989.

[30] E. M. Graefe, U. Gnther, H. J. Korsch, A. E. Niederle. A non-Hermitian PT symmetric Bose-Hubbard model: eigenvalue rings from unfolding higher-order exceptional points. J. Phys. A, 2008, 41: 255206.

[31] M. Christandl, N. Datta, A. Ekert, A. J. Landahl. Perfect state transfer in quantum spin networks. Phys. Rev. Lett., 2004, 92: 187902.

[32] A. Perez-Leija, R. Keil, A. Kay, H. Moya-Cessa, S. Nolte, L.-C. Kwek, B. M. Rodriguez-Lara, A. Szameit, D. N. Christodoulides. Coherent quantum transport in photonic lattices. Phys. Rev. A, 2013, 87: 012309.

[33] A. Perez-Leija, R. Keil, H. Moya-Cessa, A. Szameit, D. N. Christodoulides. Perfect transfer of path-entangled photons in J_x photonic lattices. Phys. Rev. A, 2013, 87: 022303.

[34] Y. N. Joglekar, A. Saxena. Robust PT-symmetric chain and properties of its Hermitian counterpart. Phys. Rev. A, 2011, 83: 050101.

[35] Y. N. Joglekar, C. Thompson, G. Vemuri. Tunable waveguide lattices with nonuniform parity-symmetric tunneling. Phys. Rev. A, 2011, 83: 063817.

[36] R. J. Chapman, M. Santandrea, Z. Huang, G. Corrielli, A. Crespi, M.-H. Yung, R. Osellame, A. Peruzzo. Experimental perfect state transfer of an entangled photonic qubit. Nat. Commun., 2016, 7: 11339.

[37] R. de J. León-Montiel, M. A. Quiroz-Juárez, J. L. Domínguez-Juárez, R. Quintero-Torres, J. L. Aragón, A. K. Harter, Y. N. Joglekar. Observation of slowly decaying eigenmodes without exceptional points in Floquet dissipative synthetic circuits. Commun. Phys., 2018, 1: 88.

[38] N. A. Mortensen, P. A. D. Gonçalves, M. Khajavikhan, D. N. Christodoulides, C. Tserkezis, C. Wolff. Fluctuations and noise-limited sensing near the exceptional point of parity-time-symmetric resonator systems. Optica, 2018, 5: 1342-1346.

[39] LonghiS., “Loschmidt echo and fidelity decay near an exceptional point,” arXiv:1905.03553 (2019).

[40] J. Wei, E. Norman. Lie algebraic solution of linear differential equations. J. Math. Phys., 1963, 4: 575-581.

[41] LouisellW. H., Quantum Statistical Properties of Radiation (Wiley, 1973), Vol. 7.

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

[43] J. Zhang, M. Um, D. Lv, J.-N. Zhang, L.-M. Duan, K. Kim. NOON states of nine quantized vibrations in two radial modes of a trapped ion. Phys. Rev. Lett., 2018, 121: 160502.

[44] TeimourpourM.ZhongQ.KhajavikhanM.El-GanainyR., “Higher order exceptional points in discrete photonics platforms,” in Parity-Time Symmetry and Its Applications (Springer, 2018), pp. 261–275.

[45] A. E. Lita, A. J. Miller, S. W. Nam. Counting near-infrared single-photons with 95% efficiency. Opt. Express, 2008, 16: 3032-3040.