[1] Nonlinear waves in PT-symmetric systems. Rev. Mod. Phys., 88, 035002(2016). https://doi.org/10.1103/RevModPhys.88.035002

[2] Non-Hermitian physics. Adv. Phys., 69, 249-435(2020). https://doi.org/10.1080/00018732.2021.1876991

[3] Exceptional topology of non-Hermitian systems. Rev. Mod. Phys., 93, 015005(2021). https://doi.org/10.1103/RevModPhys.93.015005

[4] On the generators of quantum dynamical semigroups. Commun. Math. Phys., 48, 119-130(1976). https://doi.org/10.1007/BF01608499

[5] Localization transitions in non-Hermitian quantum mechanics. Phys. Rev. Lett., 77, 570-573(1996). https://doi.org/10.1103/PhysRevLett.77.570

[6] Theory of directed localization in one dimension. Phys. Rev. B, 56, R4333-R4335(1997). https://doi.org/10.1103/PhysRevB.56.R4333

[7] Directed quantum chaos. Phys. Rev. Lett., 79, 491-494(1997). https://doi.org/10.1103/PhysRevLett.79.491

[8] et alEffect of quantum jumps on non-Hermitian systems. Phys. Rev. A, 108, 032214(2023). https://doi.org/10.1103/PhysRevA.108.032214

[9] et alQuantum exceptional points of non-Hermitian Hamiltonians and Liouvillians: The effects of quantum jumps. Phys. Rev. A, 100, 062131(2019). https://doi.org/10.1103/PhysRevA.100.062131

[10] Real spectra in non-Hermitian Hamiltonians having PT symmetry. Phys. Rev. Lett., 80, 5243(1998). https://doi.org/10.1103/PhysRevLett.80.5243

[11] Complex extension of quantum mechanics. Phys. Rev. Lett., 89, 270401(2002). https://doi.org/10.1103/PhysRevLett.89.270401

[12] Making sense of non-Hermitian Hamiltonians. Rep. Prog. Phys., 70, 947(2007). https://doi.org/10.1088/0034-4885/70/6/R03

[13] Non-Hermitian photonics based on parity–time symmetry. Nat. Photonics, 11, 752-762(2017). https://doi.org/10.1038/s41566-017-0031-1

[14] Parity–time symmetric photonics. Natl. Sci. Rev., 5, 183-199(2018). https://doi.org/10.1093/nsr/nwy011

[15] et alNon-Hermitian physics and PT symmetry. Nat. Phys., 14, 11-19(2018). https://doi.org/10.1038/nphys4323

[16] et alParity–time symmetry and exceptional points in photonics. Nat. Mater., 18, 783-798(2019). https://doi.org/10.1038/s41563-019-0304-9

[17] -symmetric, non-Hermitian quantum many-body physics–a methodological perspective. Rep. Prog. Phys., 86, 124501(2023). https://doi.org/10.1088/1361-6633/ad05f3

[18] Information retrieval and criticality in parity-time-symmetric systems. Phys. Rev. Lett., 119, 190401(2017). https://doi.org/10.1103/PhysRevLett.119.190401

[19] et alObservation of critical phenomena in parity-time-symmetric quantum dynamics. Phys. Rev. Lett., 123, 230401(2019). https://doi.org/10.1103/PhysRevLett.123.230401

[20] et alObservation of parity-time symmetry breaking in a single-spin system. Science, 364, 878-880(2019). https://doi.org/10.1126/science.aaw8205

[21] et alObservation of emergent momentum–time skyrmions in parity–time-symmetric non-unitary quench dynamics. Nat. Commun., 10, 2293(2019). https://doi.org/10.1038/s41467-019-10252-7

[22] Invisibility and PT symmetry. Phys. Rev. A, 87, 012103(2013). https://doi.org/10.1103/PhysRevA.87.012103

[23] et alUnidirectional invisibility induced by PT-symmetric periodic structures. Phys. Rev. Lett., 106, 213901(2011). https://doi.org/10.1103/PhysRevLett.106.213901

[24] et alExperimental investigation of quantum -enhanced sensor. Phys. Rev. Lett., 125, 240506(2020). https://doi.org/10.1103/PhysRevLett.125.240506

[25] Negative refraction and planar focusing based on parity-time symmetric metasurfaces. Phys. Rev. Lett., 113, 023903(2014). https://doi.org/10.1103/PhysRevLett.113.023903

[26] et alPT-symmetric acoustics. Phys. Rev. X, 4, 031042(2014). https://doi.org/10.1103/PhysRevX.4.031042

[27] et alAnyonic-parity-time symmetry in complex-coupled lasers. Sci. Adv., 8, eabm7454(2022). https://doi.org/10.1126/sciadv.abm7454

[28] et alPT-symmetric quantum sensing: Advantages and restrictions. Phys. Rev. A, 109, 062611(2024). https://doi.org/10.1103/PhysRevA.109.062611

[29] et alEnhanced frequency conversion in parity-time symmetry line. Phys. Rev. Lett., 132, 256902(2024). https://doi.org/10.1103/PhysRevLett.132.256902

[30] et alExperimental investigation of the no-signalling principle in parity-time symmetric theory using an open quantum system. Nat. Photonics, 10, 642-646(2016). https://doi.org/10.1038/nphoton.2016.144

[31] Irreversibility across a nonreciprocal PT-symmetry-breaking phase transition. Phys. Rev. Lett., 131, 258301(2023). https://doi.org/10.1103/PhysRevLett.131.258301

[32] -symmetric laser absorber. Phys. Rev. A, 82, 031801(2010). https://doi.org/10.1103/PhysRevA.82.031801

[33] et al-symmetric phonon laser. Phys. Rev. Lett., 113, 053604(2014). https://doi.org/10.1103/PhysRevLett.113.053604

[34] Pseudo-Hermiticity versus PT symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian. J. Math. Phys., 43, 205-214(2002). https://doi.org/10.1063/1.1418246

[35] et alHomotopy, symmetry, and non-Hermitian band topology. Rep. Prog. Phys., 87, 078002(2024). https://doi.org/10.1088/1361-6633/ad4e64

[36] et alRevealing the missing dimension at an exceptional point. Nat. Phys., 16, 571-578(2020). https://doi.org/10.1038/s41567-020-0807-y

[37] et alEnhanced sensitivity at higher-order exceptional points. Nature, 548, 187-191(2017). https://doi.org/10.1038/nature23280

[38] et alExceptional points enhance sensing in an optical microcavity. Nature, 548, 192-196(2017). https://doi.org/10.1038/nature23281

[39] et alExceptional-point-based accelerometers with enhanced signal-to-noise ratio. Nature, 607, 697-702(2022). https://doi.org/10.1038/s41586-022-04904-w

[40] et alKnotted non-Hermitian metals. Phys. Rev. B, 99, 161115(2019). https://doi.org/10.1103/PhysRevB.99.161115

[41] et alSymmetry-protected nodal phases in non-Hermitian systems. Phys. Rev. B, 99, 041406(2019). https://doi.org/10.1103/PhysRevB.99.041406

[42] et alSimulating exceptional non-Hermitian metals with single-photon interferometry. Phys. Rev. Lett., 127, 026404(2021). https://doi.org/10.1103/PhysRevLett.127.026404

[43] et alNon-Hermitian spatial symmetries and their stabilized normal and exceptional topological semimetals. Phys. Rev. Lett., 128, 226401(2022). https://doi.org/10.1103/PhysRevLett.128.226401

[44] Fractal nodal band structures. Phys. Rev. Res., 5, 043043(2023). https://doi.org/10.1103/PhysRevResearch.5.043043

[45] et alObservation of a chiral state in a microwave cavity. Phys. Rev. Lett., 90, 034101(2003). https://doi.org/10.1103/PhysRevLett.90.034101

[46] et alDynamically encircling an exceptional point for asymmetric mode switching. Nature, 537, 76-79(2016). https://doi.org/10.1038/nature18605

[47] et alExceptional non-Abelian topology in multiband non-Hermitian systems. Phys. Rev. Lett., 130, 157201(2023). https://doi.org/10.1103/PhysRevLett.130.157201

[48] et alTopological energy braiding of non-Bloch bands. Phys. Rev. B, 106, 195425(2022). https://doi.org/10.1103/PhysRevB.106.195425

[49] et alTopological complex-energy braiding of non-Hermitian bands. Nature, 598, 59-64(2021). https://doi.org/10.1038/s41586-021-03848-x

[50] et alObservation of acoustic non-Hermitian Bloch braids and associated topological phase transitions. Phys. Rev. Lett., 130, 017201(2023). https://doi.org/10.1103/PhysRevLett.130.017201

[51] et alExperimental realization of stable exceptional chains protected by non-Hermitian latent symmetries unique to mechanical systems. Phys. Rev. Lett., 131, 237201(2023). https://doi.org/10.1103/PhysRevLett.131.237201

[52] et alExceptional nexus in Bose-Einstein condensates with collective dissipation. Phys. Rev. Lett., 132, 253401(2024). https://doi.org/10.1103/PhysRevLett.132.253401

[53] et alThird-order exceptional line in a nitrogen-vacancy spin system. Nat. Nanotech., 19, 160-165(2024). https://doi.org/10.1038/s41565-023-01583-0

[54] Symmetry and higher-order exceptional points. Phys. Rev. Lett., 127, 186601(2021). https://doi.org/10.1103/PhysRevLett.127.186601

[55] et alSymmetry-protected topological exceptional chains in non-Hermitian crystals. Commun. Phys., 6, 169(2023). https://doi.org/10.1038/s42005-023-01291-0

[56] et alExperimental simulation of symmetry-protected higher-order exceptional points with single photons. Sci. Adv., 9, eadi0732(2023). https://doi.org/10.1126/sciadv.adi0732

[57] Nonstandard symmetry classes in mesoscopic normal-superconducting hybrid structures. Phys. Rev. B, 55, 1142-1161(1997). https://doi.org/10.1103/PhysRevB.55.1142

[58] A classification of non-Hermitian random matrices. Statistical Field Theories, 207-214(2002).

[59] et alSymmetry and topology in non-Hermitian physics. Phys. Rev. X, 9, 041015(2019). https://doi.org/10.1103/PhysRevX.9.041015

[60] Colloquium: Topological insulators. Rev. Mod. Phys., 82, 3045-3067(2010). https://doi.org/10.1103/RevModPhys.82.3045

[61] Topological insulators and superconductors. Rev. Mod. Phys., 83, 1057-1110(2011). https://doi.org/10.1103/RevModPhys.83.1057

[62] Anomalous edge state in a non-Hermitian lattice. Phys. Rev. Lett., 116, 133903(2016). https://doi.org/10.1103/PhysRevLett.116.133903

[63] et alEdge modes, degeneracies, and topological numbers in non-Hermitian systems. Phys. Rev. Lett., 118, 040401(2017). https://doi.org/10.1103/PhysRevLett.118.040401

[64] et alGeometrical meaning of winding number and its characterization of topological phases in one-dimensional chiral non-Hermitian systems. Phys. Rev. A, 97, 052115(2018). https://doi.org/10.1103/PhysRevA.97.052115

[65] et alBiorthogonal bulk-boundary correspondence in non-Hermitian systems. Phys. Rev. Lett., 121, 026808(2018). https://doi.org/10.1103/PhysRevLett.121.026808

[66] Edge states and topological invariants of non-Hermitian systems. Phys. Rev. Lett., 121, 086803(2018). https://doi.org/10.1103/PhysRevLett.121.086803

[67] Non-Hermitian robust edge states in one dimension: Anomalous localization and eigenspace condensation at exceptional points. Phys. Rev. B, 97, 121401(2018). https://doi.org/10.1103/PhysRevB.97.121401

[68] et alTopological non-Hermitian skin effect. Front. Phys., 18, 53605(2023). https://doi.org/10.1007/s11467-023-1309-z

[69] Non-Bloch band theory of non-Hermitian systems. Phys. Rev. Lett., 123, 066404(2019). https://doi.org/10.1103/PhysRevLett.123.066404

[70] et alNon-Hermitian bulk-boundary correspondence and auxiliary generalized brillouin zone theory. Phys. Rev. Lett., 125, 226402(2020). https://doi.org/10.1103/PhysRevLett.125.226402

[71] et alTopological origin of non-Hermitian skin effects. Phys. Rev. Lett., 124, 086801(2020). https://doi.org/10.1103/PhysRevLett.124.086801

[72] Correspondence between winding numbers and skin modes in non-Hermitian systems. Phys. Rev. Lett., 125, 126402(2020). https://doi.org/10.1103/PhysRevLett.125.126402

[73] Universal non-Hermitian skin effect in two and higher dimensions. Nat. Commun., 13, 2496(2022). https://doi.org/10.1038/s41467-022-30161-6

[74] Non-Hermitian morphing of topological modes. Nature, 608, 50-55(2022). https://doi.org/10.1038/s41586-022-04929-1

[75] et alObservation of dynamic non-Hermitian skin effects. Nat. Commun., 15, 6544(2024). https://doi.org/10.1038/s41467-024-50776-1

[76] et alAcoustic non-Hermitian skin effect from twisted winding topology. Nat. Commun., 12, 6297(2021). https://doi.org/10.1038/s41467-021-26619-8

[77] et alProbing PT-symmetry breaking of non-Hermitian topological photonic states via strong photon-magnon coupling. Phys. Rev. Lett., 132, 156901(2024). https://doi.org/10.1103/PhysRevLett.132.156901

[78] Non-Hermitian physics in magnetic systems. J. Appl. Phys., 132, 220902(2022). https://doi.org/10.1063/5.0124841

[79] et alGain- and loss-induced topological insulating phase in a non-Hermitian electrical circuit. Phys. Rev. Appl., 13, 014047(2020). https://doi.org/10.1103/PhysRevApplied.13.014047

[80] et alNon-Hermitian topolectrical circuit sensor with high sensitivity. Adv. Sci., 10, 2301128(2023). https://doi.org/10.1002/advs.202301128

[81] et alQuantum time reflection and refraction of ultracold atoms. Nat. Photonics, 18, 68-73(2024). https://doi.org/10.1038/s41566-023-01290-1

[82] Heralded magnetism in non-Hermitian atomic systems. Phys. Rev. X, 4, 041001(2014). https://doi.org/10.1103/PhysRevX.4.041001

[83] et alUniversal dissipative dynamics in strongly correlated quantum gases. Nat. Phys., 34, 1-6(2025). https://doi.org/10.1038/s41567-025-02800-4

[84] et alQuantum state tomography across the exceptional point in a single dissipative qubit. Nat. Phys., 15, 1232-1236(2019). https://doi.org/10.1038/s41567-019-0652-z

[85] et alQuantum jumps in the non-Hermitian dynamics of a superconducting qubit. Phys. Rev. Lett., 127, 140504(2021). https://doi.org/10.1103/PhysRevLett.127.140504

[86] et alParity–time symmetry and exceptional points in photonics. Nat. Mater., 18, 783-798(2019). https://doi.org/10.1038/s41563-019-0304-9

[87] et alNon-Hermitian optics and photonics: from classical to quantum. Adv. Opt. Photonics, 15, 442-523(2023). https://doi.org/10.1364/AOP.475477

[88] et alThe dawn of non-Hermitian optics. Commun. Phys., 2, 37(2019). https://doi.org/10.1038/s42005-019-0130-z

[89] et alParity–time synthetic photonic lattices. Nature, 488, 167-171(2012). https://doi.org/10.1038/nature11298

[90] et alObservation of an exceptional point in a chaotic optical microcavity. Phys. Rev. Lett., 103, 134101(2009). https://doi.org/10.1103/PhysRevLett.103.134101

[91] et alGenerating arbitrary topological windings of a non-Hermitian band. Science, 371, 1240-1245(2021). https://doi.org/10.1126/science.abf6568

[92] et alDynamical control of quantum heat engines using exceptional points. Nat. Commun., 13, 6225(2022). https://doi.org/10.1038/s41467-022-33667-1

[93] et alEnhancement of quantum heat engine by encircling a Liouvillian exceptional point. Phys. Rev. Lett., 130, 110402(2023). https://doi.org/10.1103/PhysRevLett.130.110402

[94] et alTopologically protected entanglement switching around exceptional points. Light Sci. Appl., 13, 167(2024). https://doi.org/10.1038/s41377-024-01514-1

[95] . The Theory of Open Quantum Systems(2002).

[96] . Open Quantum Systems(2012).

[97] . Quantum Theory for Mathematicians(2013).

[98] Das dämpfungsproblem in der wellenmechanik. Z. Phys., 45, 430-441(1927). https://doi.org/10.1007/BF01343064

[99] . Quantum Optics(1997).

[100] A short introduction to the Lindblad master equation. AIP Adv., 10(2020). https://doi.org/10.1063/1.5115323

[101] Completely positive dynamical semigroups of N-level systems. J. Math. Phys., 17, 821-825(1976). https://doi.org/10.1063/1.522979

[102] Quantum jump dynamics in cavity QED. J. Math. Phys., 43, 3511-3537(2002). https://doi.org/10.1063/1.1476392

[103] . Contribution to Entanglement Theory, Applications in Atomic Systems and Cavity QED(2011).

[104] Anderson localization in the non-Hermitian Aubry-André-Harper model with physical gain and loss. Phys. Rev. A, 95, 062118(2017). https://doi.org/10.1103/PhysRevA.95.062118

[105] et alGain-and loss-induced topological insulating phase in a non-Hermitian electrical circuit. Phys. Rev. Appl., 13, 014047(2020). https://doi.org/10.1103/PhysRevApplied.13.014047

[106] Critical exponents for the reggeon quantum spin model. Phys. Lett. B, 76, 213-219(1978). https://doi.org/10.1016/0370-2693(78)90279-4

[107] Complex energy spectra in reggeon quantum mechanics with quartic interactions. Nucl. Phys. B, 171, 392-412(1980). https://doi.org/10.1016/0550-3213(80)90377-6

[108] New structure in the energy spectrum of reggeon quantum mechanics with quartic couplings. Phys. Lett. B, 91, 291-295(1980). https://doi.org/10.1016/0370-2693(80)90452-9

[109] Perturbation theory of odd anharmonic oscillators. Commun. Math. Phys., 75, 51-66(1980). https://doi.org/10.1007/BF01962591

[110] The large N expansion as a local perturbation theory. Ann. Phys., 140, 82-100(1982). https://doi.org/10.1016/0003-4916(82)90336-0

[111] Solitons in affine toda field theories. Nucl. Phys. B, 384, 523-540(1992). https://doi.org/10.1016/0550-3213(92)90579-Z

[112] Quasi-Hermitian operators in quantum mechanics and the variational principle. Ann. Phys., 213, 74-101(1992). https://doi.org/10.1016/0003-4916(92)90284-S

[113] Pseudo-Hermiticity versus PT symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian. J. Math. Phys., 43, 205-214(2002). https://doi.org/10.1063/1.1418246

[114] Pseudo-Hermiticity versus PT-symmetry. ii. a complete characterization of non-Hermitian Hamiltonians with a real spectrum. J. Math. Phys., 43, 2814-2816(2002). https://doi.org/10.1063/1.1461427

[115] Pseudo-Hermiticity versus PT-symmetry iii: Equivalence of pseudo-Hermiticity and the presence of antilinear symmetries. J. Math. Phys., 43, 3944-3951(2002). https://doi.org/10.1063/1.1489072

[116] PT-symmetric quantum mechanics. J. Math. Phys., 40, 2201-2229(1999). https://doi.org/10.1063/1.532860

[117] Introduction to PT-symmetric quantum theory. Contemp. Phys., 46, 277-292(2005). https://doi.org/10.1080/00107500072632

[118] et alVariational ansatz for PT-symmetric quantum mechanics. Phys. Lett. A, 259, 224-231(1999). https://doi.org/10.1016/S0375-9601(99)00468-5

[119] et alComplex square well-a new exactly solvable quantum mechanical model. J. Phys. A: Math. Gen., 32, 6771(1999). https://doi.org/10.1088/0305-4470/32/39/305

[120] Complex periodic potentials with real band spectra. Phys. Lett. A, 252, 272-276(1999). https://doi.org/10.1016/S0375-9601(98)00960-8

[121] PT-symmetric Harmonic oscillators. Phys. Lett. A, 259, 220-223(1999). https://doi.org/10.1016/S0375-9601(99)00429-6

[122] Systematic search for PT-symmetric potentials with real energy spectra. J. Phys. A: Math. Gen., 33, 7165(2000). https://doi.org/10.1088/0305-4470/33/40/313

[123] et alQuantum complex Hénon–Heiles potentials. Phys. Lett. A, 281, 311-316(2001). https://doi.org/10.1016/S0375-9601(01)00146-3

[124] Non-Hermitian Hamiltonians with real and complex eigenvalues in a Lie-algebraic framework. Phys. Lett. A, 300, 18-26(2002). https://doi.org/10.1016/S0375-9601(02)00689-8

[125] Generalized PT symmetry and real spectra. J. Phys. A: Math. Gen., 35, L467(2002). https://doi.org/10.1088/0305-4470/35/31/101

[126] On the eigenproblems of PT-symmetric oscillators. J. Math. Phys., 42, 2513-2530(2001). https://doi.org/10.1063/1.1366328

[127] Eigenvalues of-symmetric oscillators with polynomial potentials. J. Phys. A: Math. Gen., 38, 6147(2005). https://doi.org/10.1088/0305-4470/38/27/005

[128] Eigenvalues of complex Hamiltonians with PT-symmetry. Phys. Lett. A, 250, 25-28(1998). https://doi.org/10.1016/S0375-9601(98)00791-9

[129] Eigenvalues of complex Hamiltonians with PT-symmetry. Phys. Lett. A, 250, 29-32(1998). https://doi.org/10.1016/S0375-9601(98)00792-0

[130] Spectral analysis of the complex cubic oscillator. J. Phys. A: Math. Gen., 33, 8771(2000). https://doi.org/10.1088/0305-4470/33/48/314

[131] PT-symmetry and its spontaneous breakdown explained by anti-linearity. J. Opt. B: Quantum Semiclass. Opt., 5, S416(2003). https://doi.org/10.1088/1464-4266/5/3/380

[132] An algorithmic test for diagonalizability of finite-dimensional PT-invariant systems. J. Phys. A: Math. Gen., 39, 235(2005). https://doi.org/10.1088/0305-4470/39/1/017

[133] Detecting PT broken-symmetry. J. Phys. A: Math. Gen., 39, 10239(2006). https://doi.org/10.1088/0305-4470/39/32/S22

[134] Conjecture on the interlacing of zeros in complex Sturm–Liouville problems. J. Math. Phys., 41, 6381-6387(2000). https://doi.org/10.1063/1.1288247

[135] Some properties of eigenvalues and eigenfunctions of the cubic oscillator with imaginary coupling constant. J. Phys. A: Math. Gen., 33, 4911(2000). https://doi.org/10.1088/0305-4470/33/27/308

[136] Comment on a recent paper by Mezincescu. J. Phys. A: Math. Gen., 34, 3325(2001). https://doi.org/10.1088/0305-4470/34/15/401

[137] et alTwo-point Green’s function in PT-symmetric theories. Phys. Lett. A, 302, 286-290(2002). https://doi.org/10.1016/S0375-9601(02)01196-9

[138] Completeness and orthonormality in PT-symmetric quantum systems. Phys. Rev. A, 68, 062111(2003). https://doi.org/10.1103/PhysRevA.68.062111

[139] Generalized continuity equation and modified normalization in PT symmetric quantum mechanics. Mod. Phys. Lett. A, 16, 2047(2001). https://doi.org/10.1142/S0217732301005333

[140] . PCT, Spin and Statistics, and all that(2000).

[141] Complex extension of quantum mechanics. Phys. Rev. Lett., 89, 270401(2002). https://doi.org/10.1103/PhysRevLett.89.270401

[142] On pseudo-Hermitian Hamiltonians and their Hermitian counterparts. J. Phys. A: Math. Gen., 38, 1741(2005). https://doi.org/10.1088/0305-4470/38/8/010

[143] Results on certain non-Hermitian Hamiltonians. J. Math. Phys., 8, 2039(1967). https://doi.org/10.1063/1.1705118

[144] Time-dependent theory of non-Hermitian Schrodinger equation: Application to multiphoton-induced ionisation decay of atoms. J. Phys. B: At. Mol. Phys., 14, 3603(1981). https://doi.org/10.1088/0022-3700/14/19/012

[145] Biorthogonal quantum systems. J. Math. Phys., 48(2007). https://doi.org/10.1063/1.2196243

[146] Biorthogonal quantum mechanics. J. Phys. A: Math. Theor., 47, 035305(2013). https://doi.org/10.1088/1751-8113/47/3/035305

[147] Pseudo-Hermitian representation of quantum mechanics. Int. J. Geom. Methods Mod. Phys., 7, 1191-1306(2010). https://doi.org/10.1142/S0219887810004816

[148] The physical interpretation of the quantum dynamics. Proc. R. Soc. A, 113, 621-641(1927).

[149] The physics of exceptional points. J. Phys. A: Math. Theor., 45, 444016(2012). https://doi.org/10.1088/1751-8113/45/44/444016

[150] et alObservation of anti-parity-time-symmetry, phase transitions and exceptional points in an optical fibre. Nat. Commun., 12, 486(2021). https://doi.org/10.1038/s41467-020-20797-7

[151] Exceptional points and phase transitions in non-Hermitian nonlinear binary systems. Phys. Rev. B, 109, 085311(2024). https://doi.org/10.1103/PhysRevB.109.085311

[152] Phases of wave functions and level repulsion. Eur. Phys. J. D, 7, 1-4(1999). https://doi.org/10.1007/s100530050339

[153] Repulsion of resonance states and exceptional points. Phys. Rev. E, 61, 929(2000). https://doi.org/10.1103/PhysRevE.61.929

[154] The chirality of exceptional points. Eur. Phys. J. D, 17, 149-151(2001). https://doi.org/10.1007/s100530170017

[155] . Non-Hermitian Quantum Mechanics(2011).

[156] . Multiparameter Stability Theory with Mechanical Applications(2003).

[157] Signatures of three coalescing eigenfunctions. J. Phys. A: Math. Theor., 45, 025303(2011). https://doi.org/10.1088/1751-8113/45/2/025303

[158] Non-Hermitian adiabatic transport in spaces of exceptional points. Phys. Rev. A, 102, 032216(2020). https://doi.org/10.1103/PhysRevA.102.032216

[159] et alEnhanced sensitivity at higher-order exceptional points. Nature, 548, 187-191(2017). https://doi.org/10.1038/nature23280

[160] et alExceptional points enhance sensing in an optical microcavity. Nature, 548, 192-196(2017). https://doi.org/10.1038/nature23281

[161] et alObserving exceptional point degeneracy of radiation with electrically pumped photonic crystal coupled-nanocavity lasers. Optica, 8, 184-192(2021). https://doi.org/10.1364/OPTICA.412596

[162] et alExperimental observation of non-Hermitian higher-order skin interface states in topological electric circuits. Phys. Rev. Res., 5, 043034(2023). https://link.aps.org/doi/10.1103/PhysRevResearch.5.043034

[163] PT symmetric harmonic oscillators. Phys. Lett. A, 285, 7-10(2001). https://doi.org/10.1016/S0375-9601(01)00301-2

[164] Real spectra in non-Hermitian Hamiltonians having pt symmetry. Phys. Rev. Lett., 80, 5243-5246(1998). https://doi.org/10.1103/PhysRevLett.80.5243

[165] Topological protection from exceptional points in Weyl and nodal-line semimetals. Phys. Rev. B, 96, 045437(2017). https://doi.org/10.1103/PhysRevB.96.045437

[166] Exceptional points in optics and photonics. Science, 363, eaar7709(2019). https://doi.org/10.1126/science.aar7709

[167] et alExceptional points and non-Hermitian photonics at the nanoscale. Nat. Nanotechnol., 18, 1748-3395(2023). https://doi.org/10.1038/s41565-023-01408-0

[168] Quantum Fisher information perspective on sensing in anti-PT symmetric systems. Phys. Rev. Res., 4, 013131(2022). https://link.aps.org/doi/10.1103/PhysRevResearch.4.013131

[169] et alTime scaling and quantum speed limit in non-Hermitian Hamiltonians. Phys. Rev. A, 104, 052620(2021). http://10.48550/arXiv.2106.05155

[170] . Mechanics(1960).

[171] . The Classical Theory of Fields(2013).

[172] et alConserved quantities in parity-time symmetric systems. Phys. Rev. Res., 2, 022039(2020). https://doi.org/10.1103/PhysRevResearch.2.022039

[173] et alComplex skin modes in non-Hermitian coupled laser arrays. Light Sci. Appl., 11, 336(2022). https://doi.org/10.1038/s41377-022-01030-0

[174] et alTwo-dimensional reconfigurable non-Hermitian gauged laser array. Phys. Rev. Lett., 130, 263801(2023). https://doi.org/10.1103/PhysRevLett.130.263801

[175] et alNon-Hermitian hybrid silicon photonic switching. Nat. Photonics, 19, 264-270(2025). https://doi.org/10.1038/s41566-024-01579-9

[176] et alTopological insulator laser: experiments. Science, 359(2018). https://doi.org/10.1126/science.aar4005

[177] et alNon-Hermitian topological light steering. Science, 365, 1163-1166(2019). https://doi.org/10.1126/science.aay1064

[178] Visualization of branch points in PT-symmetric waveguides. Phys. Rev. Lett., 101, 080402(2008). https://doi.org/10.1103/PhysRevLett.101.080402

[179] et alObservation of PT-symmetry breaking in complex optical potentials. Phys. Rev. Lett., 103, 093902(2009). https://doi.org/10.1103/PhysRevLett.103.093902

[180] et alObservation of parity–time symmetry in optics. Nat. Phys., 6, 192-195(2010). https://doi.org/10.1038/nphys1515

[181] PT-symmetry breaking and laser-absorber modes in optical scattering systems. Phys. Rev. Lett., 106, 093902(2011). https://doi.org/10.1103/PhysRevLett.106.093902

[182] et alPump-induced exceptional points in lasers. Phys. Rev. Lett., 108, 173901(2012). https://doi.org/10.1103/PhysRevLett.108.173901

[183] Topologically protected midgap states in complex photonic lattices. Opt. Lett., 38, 1912-1914(2013). http://10.1364/ol.38.001912

[184] et alReversing the pump dependence of a laser at an exceptional point. Nat. Commun., 5, 1-7(2014). https://doi.org/10.1038/ncomms5034

[185] et alSelective enhancement of topologically induced interface states in a dielectric resonator chain. Nat. Commun., 6, 1-5(2015). https://doi.org/10.1038/ncomms7710

[186] et alObservation of a topological transition in the bulk of a non-Hermitian system. Phys. Rev. Lett., 115, 040402(2015). https://doi.org/10.1103/PhysRevLett.115.040402

[187] et alTopologically protected bound states in photonic parity–time-symmetric crystals. Nat. Mater., 16, 433-438(2017). https://doi.org/10.1038/nmat4811

[188] et alNonreciprocal light propagation in a silicon photonic circuit. Science, 333, 729-733(2011). https://doi.org/10.1126/science.1206038

[189] et alExperimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies. Nat. Mater., 12, 108-113(2013). https://doi.org/10.1038/nmat3495

[190] et alParity–time-symmetric whispering-gallery microcavities. Nat. Phys., 10, 394-398(2014). https://doi.org/10.1038/nphys2927

[191] et alParity–time symmetry and variable optical isolation in active–passive-coupled microresonators. Nat. Photonics, 8, 524-529(2014). https://doi.org/10.1038/nphoton.2014.133

[192] et alSingle-mode laser by parity-time symmetry breaking. Science, 346, 972-975(2014). https://doi.org/10.1126/science.1258479

[193] et alParity-time–symmetric microring lasers. Science, 346, 975-978(2014). https://doi.org/10.1126/science.1258480

[194] et alA 2D quantum walk simulation of two-particle dynamics. Science, 336, 55-58(2012). https://doi.org/10.1126/science.1218448

[195] Universal computation by multiparticle quantum walk. Science, 339, 791-794(2013). https://doi.org/10.1126/science.1229957

[196] et alDecoherence and disorder in quantum walks: From ballistic spread to localization. Phys. Rev. Lett., 106, 180403(2011). https://doi.org/10.1103/PhysRevLett.106.180403

[197] et alObservation of topologically protected bound states in photonic quantum walks. Nat. Commun., 3, 1-7(2012). https://doi.org/10.1038/ncomms1872

[198] et alElectric quantum walks with individual atoms. Phys. Rev. Lett., 110, 190601(2013). https://doi.org/10.1103/PhysRevLett.110.190601

[199] et alExperimental quantum-walk revival with a time-dependent coin. Phys. Rev. Lett., 114, 140502(2015). https://doi.org/10.1103/PhysRevLett.114.140502

[200] et alObservation of topological edge states in parity–time-symmetric quantum walks. Nat. Phys., 13, 1117-1123(2017). https://doi.org/10.1038/nphys4204

[201] et alDetecting topological invariants in nonunitary discrete-time quantum walks. Phys. Rev. Lett., 119, 130501(2017). https://doi.org/10.1103/PhysRevLett.119.130501

[202] et alSimulating dynamic quantum phase transitions in photonic quantum walks. Phys. Rev. Lett., 122, 020501(2019). https://doi.org/10.1103/PhysRevLett.122.020501

[203] et alObservation of non-Bloch parity-time symmetry and exceptional points. Phys. Rev. Lett., 126, 230402(2021). https://doi.org/10.1103/PhysRevLett.126.230402

[204] et alObservation of non-Hermitian edge burst in quantum dynamics. Phys. Rev. Lett., 133, 070801(2024). https://doi.org/10.1103/PhysRevLett.133.070801

[205] et alPhotons walking the line: A quantum walk with adjustable coin operations. Phys. Rev. Lett., 104, 050502(2010). https://doi.org/10.1103/PhysRevLett.104.050502

[206] et alObservation of non-Hermitian topological Anderson insulator in quantum dynamics. Nat. Commun., 13, 1-8(2022). https://doi.org/10.1038/s41467-022-30938-9

[207] et alTopological phase transitions and mobility edges in non-Hermitian quasicrystals. Phys. Rev. Lett., 129, 113601(2022). https://doi.org/10.1103/PhysRevLett.129.113601

[208] Manipulating directional flow in a two-dimensional photonic quantum walk under a synthetic magnetic field. Nat. Commun., 14, 1-8(2023). https://doi.org/10.1038/s41467-023-42045-4

[209] et alSelf acceleration from spectral geometry in dissipative quantum-walk dynamics. Nat. Commun., 15, 1-11(2024). https://doi.org/10.1038/s41467-024-48815-y

[210] et alAnderson localization of entangled photons in an integrated quantum walk. Nat. Photonics, 7, 322-328(2013). https://doi.org/10.1038/nphoton.2013.26

[211] et alDirect observation of topology from single-photon dynamics. Phys. Rev. Lett., 122, 193903(2019). https://doi.org/10.1103/PhysRevLett.122.193903

[212] et alBreaking and resurgence of symmetry in the non-Hermitian Su-Schrieffer-Heeger model in photonic waveguides. Phys. Rev. Res., 6, 023140(2024). https://doi.org/10.1103/PhysRevResearch.6.023140

[213] et alNon-Abelian thouless pumping in photonic waveguides. Nat. Phys., 18, 1080-1085(2022). https://doi.org/10.1038/s41567-022-01669-x

[214] et alPhotonic Floquet skin-topological effect. Phys. Rev. Lett., 132, 063804(2024). https://doi.org/10.1103/PhysRevLett.132.063804

[215] et alGeneral rules governing the dynamical encircling of an arbitrary number of exceptional points. Phys. Rev. Lett., 127, 253901(2021). https://doi.org/10.1103/PhysRevLett.127.253901

[216] et alMobility transition from ballistic to diffusive transport in non-Hermitian lattices. Nat. Commun., 4, 1-7(2013). https://doi.org/10.1038/ncomms3533

[217] et alTransport and Anderson localization in disordered two-dimensional photonic lattices. Nature, 446, 52-55(2007). https://doi.org/10.1038/nature05623

[218] et alDisorder-enhanced transport in photonic quasicrystals. Science, 332, 1541-1544(2011). https://doi.org/10.1126/science.1202977

[219] et alA disordered insulator in an optical lattice. Nat. Phys., 6, 677-680(2010). https://doi.org/10.1038/nphys1726

[220] et alEinstein-Podolsky-Rosen spatial entanglement in ordered and Anderson photonic lattices. Phys. Rev. Lett., 110, 150503(2013). https://doi.org/10.1103/PhysRevLett.110.150503

[221] et alAmorphous photonic lattices: Band gaps, effective mass, and suppressed transport. Phys. Rev. Lett., 106, 193904(2011). https://doi.org/10.1103/PhysRevLett.106.193904

[222] A photonic thermalization gap in disordered lattices. Nat. Phys., 11, 930-935(2015). https://doi.org/10.1038/nphys3482

[223] et alExceptional points enhance sensing in an optical microcavity. Nature, 548, 192-196(2017). https://doi.org/10.1038/nature23281

[224] Dielectric microcavities: Model systems for wave chaos and non-Hermitian physics. Rev. Mod. Phys., 87, 61-111(2015). https://doi.org/10.1103/RevModPhys.87.61

[225] et alSynthetic anti-PT symmetry in a single microcavity. Phys. Rev. Lett., 124, 053901(2020). https://doi.org/10.1103/PhysRevLett.124.053901

[226] et alCoherent control of chaotic optical microcavity with reflectionless scattering modes. Nat. Phys., 20, 109-115(2024). https://doi.org/10.1038/s41567-023-02242-w

[227] et alPicotesla-sensitivity microcavity optomechanical magnetometry. Light Sci. Appl., 13, 279(2024). https://doi.org/10.1038/s41377-024-01643-7

[228] et alTopological states of non-Hermitian systems. Eur. Phys. J. Spec. Top., 227, 1295-1308(2018). https://doi.org/10.1140/epjst/e2018-800091-5

[229] New topological invariants in non-Hermitian systems. J. Phys.: Condens. Matter, 31, 263001(2019). https://doi.org/10.1088/1361-648X/ab11b3

[230] Non-Hermitian boundary modes and topology. Phys. Rev. Lett., 124, 056802(2020). https://doi.org/10.1103/PhysRevLett.124.056802

[231] Non-Hermitian robust edge states in one dimension: Anomalous localization and eigenspace condensation at exceptional points. Phys. Rev. B, 97, 121401(2018). https://doi.org/10.1103/PhysRevB.97.121401

[232] et alNon-Hermitian bulk–boundary correspondence in quantum dynamics. Nat. Phys., 16, 761-766(2020). https://doi.org/10.1038/s41567-020-0836-6

[233] et alDetecting non-Bloch topological invariants in quantum dynamics. Phys. Rev. Lett., 127, 270602(2021). https://doi.org/10.1103/PhysRevLett.127.270602

[234] et alNon-Hermitian edge burst. Phys. Rev. Lett., 128, 120401(2022). https://doi.org/10.1103/PhysRevLett.128.120401

[235] et alObservation of non-Hermitian edge burst effect in one-dimensional photonic quantum walk. Phys. Rev. Lett., 132, 203801(2024). https://doi.org/10.1103/PhysRevLett.132.203801

[236] Colloquium: Topological band theory. Rev. Mod. Phys., 88, 021004(2016). https://doi.org/10.1103/RevModPhys.88.021004

[237] Weyl and Dirac semimetals in three-dimensional solids. Rev. Mod. Phys., 90, 015001(2018). https://doi.org/10.1103/RevModPhys.90.015001

[238] et alClassification of topological quantum matter with symmetries. Rev. Mod. Phys., 88, 035005(2016). https://doi.org/10.1103/RevModPhys.88.035005

[239] Majorana fermions in density-modulated p-wave superconducting wires. Phys, Rev, B, 86, 205135(2012). https://doi.org/10.1103/PhysRevB.86.205135

[240] et alTopological states and adiabatic pumping in quasicrystals. Phys. Rev. Lett., 109, 106402(2012). https://doi.org/10.1103/PhysRevLett.109.106402

[241] Topological zero-energy modes in gapless commensurate Aubry-André-Harper models. Phys. Rev. Lett., 110, 180403(2013). https://doi.org/10.1103/PhysRevLett.110.180403

[242] Quantum spin hall effect in graphene. Phys. Rev. Lett., 95, 226801(2005). https://doi.org/10.1103/PhysRevLett.95.226801

[243] Quantum spin Hall effect and topological phase transition in HgTe quantum wells. Science, 314, 1757-1761(2006). https://doi.org/10.1126/science.1133734

[244] Topological insulators with inversion symmetry. Phys. Rev. B, 76, 045302(2007). https://doi.org/10.1103/PhysRevB.76.045302

[245] et alQuantum spin Hall insulator state in HgTe quantum wells. Science, 318, 766-770(2007). https://www.science.org/doi/10.1126/science.1148047

[246] et alQuantized Hall conductance in a two-dimensional periodic potential. Phys. Rev. Lett., 49, 405(1982). https://doi.org/10.1103/PhysRevLett.49.405

[247] Topological invariant and the quantization of the Hall conductance. Ann. Phys., 160, 343-354(1985). https://doi.org/10.1016/0003-4916(85)90148-4

[248] Topological insulators in three dimensions. Phys. Rev. Lett., 98, 106803(2007). https://doi.org/10.1103/PhysRevLett.98.106803

[249] Topological invariants of time-reversal-invariant band structures. Phys. Rev. B, 75, 121306(2007). https://doi.org/10.1103/PhysRevB.75.121306

[250] et alTopological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface. Nat. Phys., 5, 438-442(2009). https://doi.org/10.1038/nphys1270

[251] et alNon-Hermitian topological Anderson insulators. Sci. China Phys. Mech. Astron., 63, 267062(2020). https://doi.org/10.1007/s11433-020-1521-9

[252] Non-Hermitian semi-Dirac semi-metals. J. Phys.: Condens. Matter, 33, 225401(2021). https://doi.org/10.1088/1361-648X/abe796

[253] Topological band theory for non-Hermitian Hamiltonians. Phys. Rev. Lett., 120, 146402(2018). https://doi.org/10.1103/PhysRevLett.120.146402

[254] et alTopological phases of non-Hermitian systems. Phys. Rev. X, 8, 031079(2018). https://doi.org/10.1103/PhysRevX.8.031079

[255] et alHall conductance of a non-Hermitian Weyl semimetal. New J. Phy., 26, 023057(2024). https://doi.org/10.1088/1367-2630/ad2b0e

[256] et alMetallic phase with long-range orientational order and no translational symmetry. Phys. Rev. Lett., 53, 1951(1984). https://doi.org/10.1103/PhysRevLett.53.1951

[257] . Crystallography of Quasicrystals: Concepts, Methods and Structures(2009).

[258] Topological phase transition in non-Hermitian quasicrystals. Phys. Rev. Lett., 122, 237601(2019). https://doi.org/10.1103/PhysRevLett.122.237601

[259] et alGeneralized Aubry-André self-duality and mobility edges in non-Hermitian quasiperiodic lattices. Phys. Rev. B, 102, 024205(2020). https://doi.org/10.1103/PhysRevB.102.024205

[260] et alTopological triple phase transition in non-Hermitian Floquet quasicrystals. Nature, 601, 354-359(2022). https://doi.org/10.1038/s41586-021-04253-0

[261] et alTopological phase transitions and mobility edges in non-Hermitian quasicrystals. Phys. Rev. Lett., 129, 113601(2022). https://doi.org/10.1103/PhysRevLett.129.113601

[262] et alExponentially enhanced non-Hermitian cooling. Phys. Rev. Lett., 132, 110402(2024). https://doi.org/10.1103/PhysRevLett.132.110402

[263] et alChiral quantum heating and cooling with an optically controlled ion. Light Sci. Appl., 13, 143(2024). https://doi.org/10.1038/s41377-024-01483-5

[264] Anatomy of skin modes and topology in non-Hermitian systems. Phys. Rev. B, 99, 201103(2019). https://doi.org/10.1103/PhysRevB.99.201103

[265] et alObservation of non-Hermitian topology and its bulk–edge correspondence in an active mechanical metamaterial. Proc. Natl. Acad. Sci. U.S.A., 117, 29561-29568(2020). https://doi.org/10.1073/pnas.2010580117

[266] et alGeneralized bulk-boundary correspondence in non-Hermitian topolectrical circuits. Nat. Phys., 16, 747-750(2020). https://www.nature.com/articles/s41567-020-0922-9

[267] et alTopological funneling of light. Science, 368, 311-314(2020). https://doi.org/10.1126/science.aaz8727

[268] New topological invariants in non-Hermitian systems. J. Phys. Condens. Matter, 31, 263001(2019). https://doi.org/10.1088/1361-648X/ab11b3

[269] Why does bulk boundary correspondence fail in some non-Hermitian topological models. J. Phys. Commun., 2, 035043(2018). https://doi.org/10.1088/2399-6528/aab64a

[270] Solitons in polyacetylene. Phys. Rev. Lett., 42, 1698-1701(1979). https://doi.org/10.1103/PhysRevLett.42.1698

[271] Absence of diffusion in certain random lattices. Phys. Rev., 109, 1492-1505(1958). https://doi.org/10.1103/PhysRev.109.1492

[272] et alGeneral dynamical description of quasi-adiabatically encircling exceptional points. Phys. Rev. A, 92, 052124(2015). https://doi.org/10.1103/PhysRevA.92.052124

[273] et alDynamically encircling exceptional points: in situ control of encircling loops and the role of the starting point. Phys. Rev. X, 8, 021066(2018). https://doi.org/10.1103/PhysRevX.8.021066

[274] et alPlasmonic topological metasurface by encircling an exceptional point. Science, 373, 1133-1137(2021). https://doi.org/10.1126/science.abj3179

[275] et alDecoherence-induced exceptional points in a dissipative superconducting qubit. Phys. Rev. Lett., 128, 110402(2022). https://doi.org/10.1103/PhysRevLett.128.110402

[276] et alInformation retrieval and eigenstate coalescence in a non-Hermitian quantum system with anti-PT symmetry. Phys. Rev. A, 105, L010204(2022). https://doi.org/10.1103/PhysRevA.105.L010204

[277] et alDynamically encircling an exceptional point in a real quantum system. Phys. Rev. Lett., 126, 170506(2021). https://doi.org/10.1103/PhysRevLett.126.170506

[278] et alChiral control of quantum states in non-Hermitian spin–orbit-coupled fermions. Nat. Phys., 18, 385-389(2022). https://doi.org/10.1038/s41567-021-01491-x

[279] Chiral state transfer under dephasing. Phys. Rev. A, 108, 013302(2023). https://doi.org/10.1103/PhysRevA.108.013302

[280] On the observability and asymmetry of adiabatic state flips generated by exceptional points. J. Phys. A: Math. Theor., 44, 435302(2011). https://doi.org/10.1088/1751-8113/44/43/435302

[281] Quantum metrology. Phys. Rev. Lett., 96, 010401(2006). https://doi.org/10.1103/PhysRevLett.96.010401

[282] et alQuantum metrology with nonclassical states of atomic ensembles. Rev. Mod. Phys., 90, 035005(2018). https://doi.org/10.1103/RevModPhys.90.035005

[283] et alQuantum-enhanced measurements without entanglement. Rev. Mod. Phys., 90, 035006(2018). https://doi.org/10.1103/RevModPhys.90.035006

[284] et alAt the limits of criticality-based quantum metrology: Apparent super-Heisenberg scaling revisited. Phys. Rev. X, 8, 021022(2018). https://doi.org/10.1103/PhysRevX.8.021022

[285] Quantum sensing. Rev. Mod. Phys., 89, 035002(2017). https://doi.org/10.1103/RevModPhys.89.035002

[286] et alSensitivity optimization for NV-diamond magnetometry. Rev. Mod. Phys., 92, 015004(2020). https://doi.org/10.1103/RevModPhys.92.015004

[287] et alNon-Hermitian physics and PT symmetry. Nat. Phys., 14, 11(2018). https://doi.org/10.1038/nphys4323

[288] Quantum squeezing and sensing with pseudo-anti-parity-time symmetry. Phys. Rev. Lett., 128, 173602(2022). https://doi.org/10.1103/PhysRevLett.128.173602

[289] Non-Hermitian topological sensors. Phys. Rev. Lett., 125, 180403(2020). https://doi.org/10.1103/PhysRevLett.125.180403

[290] Quantum non-Hermitian topological sensors. Phys. Rev. Res., 4, 013113(2022). https://doi.org/10.1103/PhysRevResearch.4.013113

[291] Exponentially-enhanced quantum sensing with non-Hermitian lattice dynamics. Nat. Commun., 11, 5382(2020). https://doi.org/10.1038/s41467-020-19090-4

[292] Enhancing the sensitivity of frequency and energy splitting detection by using exceptional points: Application to microcavity sensors for single-particle detection. Phys. Rev. Lett., 112, 203901(2014). https://doi.org/10.1103/PhysRevLett.112.203901

[293] Sensors operating at exceptional points: General theory. Phys. Rev. A, 93, 033809(2016). https://doi.org/10.1103/PhysRevA.93.033809

[294] et alUltrasensitive micro-scale parity-time-symmetric ring laser gyroscope. Opt. Lett., 42, 1556(2017). https://doi.org/10.1364/OL.42.001556

[295] Large sagnac frequency splitting in a ring resonator operating at an exceptional point. Phys. Rev. A, 96, 033842(2017). https://doi.org/10.1103/PhysRevA.96.033842

[296] et alMetrology with PT-symmetric cavities: enhanced sensitivity near the PT-phase transition. Phys. Rev. Lett., 117, 110802(2016). https://doi.org/10.1103/PhysRevLett.117.110802

[297] et alObservation of the exceptional-point-enhanced sagnac effect. Nature, 576, 65(2019). https://doi.org/10.1038/s41586-019-1777-z

[298] et alPetermann-factor sensitivity limit near an exceptional point in a Brillouin ring laser gyroscope. Nat. Commun., 11, 1(2020). https://doi.org/10.1038/s41467-020-15341-6

[299] Physics of non-Hermitian degeneracies. Czech. J. Phys., 54, 1039-1047(2004). https://doi.org/10.1023/B:CJOP.0000044002.05657.04

[300] Exceptional points of non-Hermitian operators. J. Phys. Math. Gen., 37, 2455(2004). https://doi.org/10.1088/0305-4470/37/6/034

[301] et alNon-Hermitian sensing in the absence of exceptional points. Phys. Rev. Lett., 133, 180801(2024). https://doi.org/10.1103/PhysRevLett.133.180801

[302] No exceptional precision of exceptional-point sensors. Phys. Rev. A, 98, 023805(2018). https://doi.org/10.1103/PhysRevA.98.023805

[303] Fundamental limits and non-reciprocal approaches in non-Hermitian quantum sensing. Nat. Commun., 9, 1(2018). https://doi.org/10.1038/s41467-018-06477-7

[304] et alQuantum noise theory of exceptional point amplifying sensors. Phys. Rev. Lett., 123, 180501(2019). https://doi.org/10.1103/PhysRevLett.123.180501

[305] Sensitivity of parameter estimation near the exceptional point of a non-Hermitian system. New J. Phys., 21, 083002(2019). https://doi.org/10.1088/1367-2630/ab32ab

[306] Limitations of sensing at an exceptional point. ACS Photonics, 9, 1554(2022). https://doi.org/10.1021/acsphotonics.1c01535

[307] Review of exceptional point-based sensors. Photonics Res., 8, 1457(2020). https://doi.org/10.1364/PRJ.396115

[308] Fundamental sensitivity limits for non-Hermitian quantum sensors. Phys. Rev. Lett., 131, 160801(2023). https://doi.org/10.1103/PhysRevLett.131.160801

[309] et alExperimental determination of PT-symmetric exceptional points in a single trapped ion. Phys. Rev. Lett., 126, 083604(2021). https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.126.08360

[310] et alObservation of parity-time symmetry breaking transitions in a dissipative Floquet system of ultracold atoms. Nat. Commun., 10, 855(2019). https://doi.org/10.1038/s41467-019-08596-1

[311] et alQuantum sensing with a single-qubit pseudo-Hermitian system. Phys. Rev. Lett., 124, 020501(2020). https://doi.org/10.1103/PhysRevLett.124.020501

[312] et alQuantum walks on graphs, 50(2001).

[313] et alSpatial search by quantum walk is optimal for almost all graphs. Phys. Rev. Lett., 116, 100501(2016). https://doi.org/10.1103/PhysRevLett.116.100501

[314] Universal computation by quantum walk. Phys. Rev. Lett., 102, 180501(2009). https://doi.org/10.1103/PhysRevLett.102.180501

[315] Universal computation by multi-particle quantum walk. Science, 339, 791-794(2013). https://doi.org/10.1126/science.1229957

[316] Quantum-walk-based search and centrality. Phys. Rev. A, 82, 042333(2010). https://doi.org/10.1103/PhysRevA.82.042333

[317] et alCentrality measure based on continuous-time quantum walks and experimental realization. Phys. Rev. A, 95, 032318(2017). https://doi.org/10.1103/PhysRevA.95.032318

[318] et alExperimental realization of continuous-time quantum walks on directed graphs and their application in PageRank. Optica, 7, 1524-1530(2020). https://doi.org/10.1364/OPTICA.396228

[319] . Computer Networks and ISDN Systems, 107(1998).

[320] Normal dilations and extensions of operators. Summ. Bras. Math., 2, 125-134(1950).

[321] et alSimulating the vibrational quantum dynamics of molecules using photonics. Nature, 557, 660-667(2018). https://doi.org/10.1038/s41586-018-0152-9

[322] et alDynamic framework for criticality-enhanced quantum sensing. Phys. Rev. Lett., 126, 010502(2021). https://doi.org/10.1103/PhysRevLett.126.010502

[323] et alExponentially enhanced non-Hermitian cooling. Phys. Rev. Lett., 132, 110402(2024). https://doi.org/10.1103/PhysRevLett.132.110402

[324] et alSpeeding up entanglement generation by proximity to higher-order exceptional points. Phys. Rev. Lett., 131, 100202(2023). https://doi.org/10.1103/PhysRevLett.131.100202