[1] [1] NIELSEN M A, CHUANG I L. Quantum Computation and Quantum Information[M]. Cambridge: Cambridge University Press, 2000:343-345.

[2] [2] STRELTSOV A, RANA S, BOES P, et al. Structure of the resource theory of quantum coherence[J]. Phys Rev Lett, 2017, 119(14):140402. DOI: 10.1103/PhysRevLett.119.140402.

[3] [3] STRELTSOV A, ADESSO G, PLENIO M B. Colloquium: quantum coherence as a resource[J]. Rev Mod Phys, 2017, 89(4): 041003. DOI: 10.1103/ RevModPhys.89.041003.

[4] [4] MA J J, YADIN B, GIROLAMI D, et al. Converting coherence to quantum correlations[J]. Phys Rev Lett, 2016, 116(16): 160407. DOI: 10.1103/ PhysRevLett.116.160407.

[5] [5] HU M L, HU X Y, WANG J C, et al. Quantum coherence and geometric quantum discord[J]. Phys Rep, 2018, 762:1-100. DOI: 10.1016/j.physrep.2018.07.004.

[6] [6] RADHAKRISHNAN C, PARTHASARATHY M, JAMBULINGAM S, et al. Distribution of quantum coherence in multi-partite systems[J]. Phys Rev Lett, 2016, 116(15):150504. DOI: 10.1103/PhysRevLett.116.150504.

[7] [7] RADHAKRISHNAN C, DING Z, SHI F Z, et al. Basis-independent quantum coherence and its distribution[J]. Ann Phys (NY), 2019, 409:167906. DOI: 10.1016/j.aop.2019.04.020.

[8] [8] RADHAKRISHNAN C, Lü Z G, JING J, et al. Dynamics of quantum coherence in a spin-star system: Bipartite initial state and coherence distribution[J]. Phys Rev A, 2019, 100(4):042333. DOI: 10.1103/PhysRevA.100.042333.

[9] [9] RADHAKRISHNAN C, CHEN P W, JAMBULINGAM S, et al. Time dynamics of quantum coherence and monogamy in a non-Markovian environment[J]. Sci Rep, 2019, 9:2363. DOI: 10.1038/s41598-019-39027-2.

[10] [10] DING Z, LIU R, RADHAKRISHNAN C, et al. Experimental study of quantum coherence decomposition and trade-off rela-tions in a tripartite system[J]. npj Quantum Inf, 2021, 7(1):145. DOI: 10.1038/s41534-021-00485-0.

[11] [11] BAUMGRATZ T, CRAMER M, PLENIO M B. Quantifying coherence[J]. Phys Rev Lett, 2014, 113(14):140401. DOI: 10. 1103/PhysRevLett.113.140401.

[12] [12] GIROLAMI D. Observable measure of quantum coherence in finite dimensional systems[J]. Phys Rev Lett, 2014, 113(17):170401. DOI: 10.1103/ PhysRevLett.113.170401.

[13] [13] SHAO L H, XI Z J, FAN H, et al. The Fidelity and trace-norm distances for quantifying coherence[J]. Phys Rev A, 2015, 91(4):042120. DOI: 10.1103/PhysRevA.91.042120.

[14] [14] YUAN X, ZHOU H Y, CAO Z, et al. Intrinsic randomness as a measure of quantum coherence[J]. Phys Rev A, 2015, 92(2): 022124. DOI: 10.1103/PhysRevA.92.022124.

[15] [15] STRELTSOV A, SINGH U, DHAR H S, et al. Measuring quantum coherence with entanglement[J]. Phys Rev Lett, 2015, 115(2):020403. DOI: 10.1103/PhysRevLett.115.020403.

[16] [16] YU X D, ZHANG D J, XU G F, et al. Alternative framework for quantifying coherence[J]. Phys Rev A, 2016, 94(6):060302. DOI: 10.1103/Phys RevA.94.060302.

[17] [17] YU C S. Quantum coherence via skew information and its polygamy[J]. Phys Rev A, 2017, 95(4):042337. DOI: 10.1103/Phys-RevA.95.042337.

[18] [18] MANDAL S, NAROZNIAK M, RADHAKRISHNAN C, et al. Characterizing coherence with quantum observables[J]. Phys Rev Research, 2020, 2(1):013157. DOI: 10.1103/PhysRevResearch.2.013157.

[19] [19] STRELTSOV A, CHITAMBAR E, RANA S, et al. Entanglement and coherence in quantum state merging[J]. Phys Rev Lett, 2016, 116(24):240405. DOI: 10.1103/PhysRevLett.116.240405.

[20] [20] NAPOLI C, BROMLEY T R, CIANCIARUSO M, et al. Robustness of coherence: an operational and observable measure of quantum coherence[J]. Phys Rev Lett, 2016, 116(15):150502. DOI: 10.1103/PhysRevLett.116.150502.

[21] [21] WINTER A, YANG D. Operational resource theory of coherence[J]. Phys Rev Lett, 2016, 116(12):120404. DOI: 10.1103/PhysRevLett.116.120404.

[22] [22] ROMERO E, AUGULIS R, NOVODEREZHKIN V I, et al. Quantum coherence in photosynthesis for efficient solar-energy conversion[J]. Nat Phys, 2014, 10(9):677. DOI: 10.1038/nphys3017.

[23] [23] KARPAT G, CAKMAK B, FANCHINI F F. Quantum coherence and uncertainty in the anisotropic XY chain[J]. Phys Rev B, 2014, 90(10):104431. DOI: 10.1103/PhysRevB.90.104431.

[24] [24] MALVEZZI A L, KARPAT G, CAKMAK B, et al. Quantum correlations and coherence in spin-1 Heisenberg chains[J]. Phys Rev B, 2016, 93(18):184428. DOI: 10.1103/PhysRevB.93.184428.

[25] [25] LI Y C, LIN H Q. Quantum coherence and quantum phase transitions[J]. Sci Rep, 2016, 6:26365. DOI: 10.1038/srep26365.

[26] [26] CHEN J J, CUI J, ZHANG Y R, et al. Coherence susceptibility as a probe of quantum phase transitions[J]. Phys Rev A, 2016, 94(2):022112. DOI: 10.1103/PhysRevA.94.022112.

[27] [27] YOU W L, WANG Y M, YI T C, et al. Quantum coherence in a compass chain under an alternating magnetic field[J]. Phys Rev B, 2018, 97(22):224420. DOI: 10.1103/PhysRevB.97.224420.

[28] [28] QIN M, WANG L, HE M L, et al. The dynamical behavior of quantum coherence in one-dimensional transverse-field Ising model[J]. Physica A, 2020, 540:122944. DOI: 10.1016/j.physa.2019.122944.

[29] [29] SACHDEV S. Quantum Phase Transition[M]. Cambridge: Cambridge University Press, 2011:10-14.

[30] [30] MAHMOUDI M, MAHDAVIFAR S, MOHAMMAD ALI ZADEH T, et al. Non-Markovian dynamics in the extended clus-ter spin-1/2 XX chain[J]. Phys Rev A, 2017, 95(1):012336. DOI: 10.1103/physreva.95.012336.

[31] [31] SHA Y T, WANG Y, SUN Z H, et al. Thermal quantum coherence and correlation in the extended XY spin chain[J]. Ann Phys (NY), 2018, 392:229-241. DOI: 10.1016/j.aop.2018.03.015.

[32] [32] LI S P, SUN Z H. Local and intrinsic quantum coherence in critical systems[J]. Phys Rev A, 2018, 98(2):022317. DOI: 10. 1103/PhysRevA.98.022317.

[33] [33] HU M L, GAO Y Y, FAN H. Steered quantum coherence as a signature of quantum phase transitions in spin chains[J]. Phys Rev A, 2020, 101(3):032305. DOI: 10.1103/PhysRevA.101.032305.

[34] [34] YIN S Y, SONG J, LIU S T, et al. Quantum coherence and topological quantum phase transitions in the extended XY chain[J]. Phys Lett A, 2021, 389:127089. DOI: 10.1016/j.physleta.2020.127089.

[35] [35] RADHAKRISHNAN C, ERMAKOV I, BYRNES T. Quantum coherence of planar spin models with Dzyaloshinsky-Moriy interaction[J]. Phys Rev A, 2017, 96(1):012341. DOI: 10.1103/PhysRevA.96.012341.

[36] [36] RADHAKRISHNAN C, PARTHASARATHY M, JAMBULINGAM S, et al. Quantum coherence of the Heisenberg spin models with Dzyaloshinsky-Moriya interactions[J]. Sci Rep, 2017, 7:13865. DOI: 10.1038/s41598-017- 13871-6.

[37] [37] YE B L, LI B, WANG Z X, et al. Quantum Fisher information and coherence in one-dimensional XY spin models with Dzyaloshinsky-Moriya interactions[J]. Sci China-Phys Mech Astron, 2018, 61(11):110312. DOI: 10.1007/s11433-018- 9262-9.

[38] [38] YI T C, YOU W L, WU N, et al. Criticality and factorization in the Heisenberg chain with Dzyaloshinskii-Moriya interac-tion[J]. Phys Rev B, 2019, 100(2):024423. DOI: 10.1103/PhysRevB.100.024423.

[39] [39] HUI N J, XU Y Y, WANG J C, et al. Quantum coherence and quantum phase transition in the XY model with staggered Dzyaloshinsky-Moriya interaction[J]. Physica B, 2017, 510:7-12. DOI: 10.1016/j.physb.2017.01.009.

[40] [40] YIN S Y, LIU S T, SONG J, et al. Markovian and non-Markovian dynamics of quantum coherence in the extended XX chain[J]. Phys Rev A, 2022, 106(3):032220. DOI: 10.1103/PhysRevA.106.032220.

[41] [41] YIN S Y, SONG J, WANG Y Y, et al. Quantum coherence and its distribution in the extended Ising chain[J]. Quantum Inf Process, 2021, 20(10):326. DOI: 10.1007/s11128-021-03266-y.

[42] [42] YIN S Y, SONG J, LIU S T, et al. Basis-independent quantum coherence and its distribution in spin chains with three-site interaction[J]. Physica A, 2022, 597:127239. DOI: 10.1016/j.physa.2022.127239.

[43] [43] DZYALOSHINSKY I. A thermodynamic theory of “weak” ferromagnetism of antiferromagnetics[J]. J Phys Chem Solids, 1958, 4(4):241-255. DOI: 10.1016/0022-3697(58)90076-3.

[44] [44] MORIYA T. New mechanism of anisotropic superexchange interaction[J]. Phys Rev Lett, 1960, 4(5): 228. DOI: 10.1103/PhysRevLett.4.228.

[45] [45] PERK J H H, CAPEL H W. Autocorrelation function of the x-component of the magnetization in the one-dimensional XY-model[J]. Physica A, 1976, 87(2):211-242. DOI: 10.1016/0378-4371(77)90014-0.