[1] [1] HEISENBERGG W. ber den anschaulichen Inhalt der quantenmechanischen Kinematik und Mechanik[J]. Zeitschrift Physik, 1927, 43: 172-198. DOI: 10.1007/BF013972806.

[2] [2] KENNARD E H. Zur quantenmechanik einfacher bewegungstypen[J]. Zeitschrift Physik, 1927, 44(4): 326. DOI: 10.1007/BF01391200.

[3] [3] ROBERTSON H P. The Uncertainty Principle[J]. Physical Review, 1929, 34: 163. DOI: 10.1103/PhysRev.34.163.

[4] [4] RENES J M, BERTA M, CHRISTANDL M, et al. The Uncertainty Principle in the Presence of Quantum Memory[J]. Nature physics, 2009, 7(10): 757, DOI: 10.1038/nphys1734.

[5] [5] DEUTSCH D. Uncertainty in quantum measurements[J]. Physical Review Letters, 1983, 50(9): 631. DOI: 10.1103/PhysRevLett.50.631.

[7] [7] MAASSEN H, UFFINK J. Generalized entropic uncertainty relations[J]. Physical Review Letters, 1988, 60(12): 1103-1106. DOI:10.1103/PhysRevLett.60.1103.

[8] [8] RENES J M, BOILEAU J C. Conjectured strong complementary information tradeoff[J]. Physical Review Letters, 2009, 103: 020402. DOI: 10.1103/PhysRevLett.103.020402.

[9] [9] BERTA M, CHRISTANDL M, COLBECK R, et al. The uncertainty principle in the presence of quantum memory[J]. Nature Physics, 2010, 6: 659. DOI: 10.1038/nphys1734.

[10] [10] PREVEDEL R, HAMEL D R, COLBECK R, et al. Experimental investigation of the uncertainty principle in the presence of quantum memory and its application to witnessing entanglement[J]. Nature Physics, 2011, 7(10): 757-761. DOI:10.1038/nphys2048.

[11] [11] LI C F, XU J S, XU X Y, et al. Experimental investigation of the entanglement-assisted entropic uncertainty principle[J]. Nature Physics, 2011, 7: 752. DOI: 10.1038/nphys2047.

[12] [12] MING F, WANG D, FAN X G, et al. Improved tripartite uncertainty relation with quantum memory[J]. Physical Review A, 2020, 102: 012206. DOI: 10.1103/PhysRevA.102.012206.

[13] [13] NATAF P, DOGAN M, HUR K L. Heisenbergg Uncertainty Principle as a Probe of Entanglement Entropy: Application to Super Radiant Quantum Phase Transitions[J]. Phys Rev A, 2012, 86: 043807. DOI: 10.1103/physreva.86.043807.

[14] [14] BALLESTER M A, WEHNER S. Entropic Uncertainty Relations and Locking: Tight Bounds for Mutually Unbiased Basea[J]. Phys Rev A, 2007, 75(2): 441. DOI: 10.1103/PhysRevA.75.022319.

[15] [15] TOMAMICHEL M, RENNER R. The Uncertainty Relation for Smooth Entropies[J]. Physical Review Letters, 2012, 106(11): 110506. DOI: 10.1103/PhysRevLett.106.110506.

[16] [16] TOMAMICHEL M, LIM C C W, GISIN N, et al. Tight finite-key analysis for quantum cryptography[J]. Nature communications, 2012, 3: 634. DOI: 10.1038/ncomms1631.

[17] [17] XU Z Y, YANG W L, FENG M. Quantum-memory-assisted entropic uncertainty relation under noise[J]. Physical Review A, 2012, 86(1): 18515-18524. DOI: 10.1103/PhysRevA.86.012113.

[18] [18] HU M L, FAN H. Quantum-memory-assisted entropic uncertainty principle, teleportation and entanglement witness in structured reservoirs[J]. Physical Review A, 2012, 86(3): 9591-9598. DOI: 10.1103/PhysRevA.86.032338.

[19] [19] XU Z Y, ZHU S Q, YANG W L. Quantum-memory-assisted entropic uncertainty relation with a single nitrogen-vacancy center in diamond[J]. Applied Physics Letters, 2012, 101(24): 172. DOI: 10.1063/1.4771988.

[20] [20] WANG D, HUANG A J, HOEHN R D, et al. Entropic uncertainty relations for Markovian and non-Markovian processes under a structured bosonic reservoir[J]. Scientific Reports, 2017, 7(1): 1066. DOI: 10.1038/s41598-017-01094-8.

[21] [21] ZOU H M, FANG M F, YANG B Y, et al. The quantum entropic uncertainty relation and entanglement witness in the two-atom system coupling with the non-Markovian environments[J]. Physica Scripta, 2014, 89(11): 115101. DOI: 10.1088/0031-8949/89/11/115101.

[22] [22] KARPAT G, PIILO J, MANISCALCO S. Controlling entropic uncertainty bound through memory effects[J]. Europhysics Letters, 2015, 111(5): 50006. DOI: 10.1209/0295-5075/111/50006.

[23] [23] BAI X M, WANG N, LI J Q, et al. The creation of quantum correlation and entropic uncertainty relation in photonic crystals[J]. Quantum Information Processing, 2016, 15(7): 1-14. DOI: 10.1007/s11128-016-1299-7.

[24] [24] ZHENG X, ZHANG G F. The effects of mixedness and entanglement on the properties of the entropic uncertainty in Heisenberg model with Dzyaloshinski-Moriya interaction[J]. Quantum Information Processing, 2017, 16: 1. DOI: 10.1007/s11128-016-1481-y.

[25] [25] WANG D, MING F, HUANG A J, et al. Entropic uncertainty for spin-1/2 XXX chains in the presence of inhomogeneous magnetic fields and its steering via weak measurement reversals[J]. Laser Physics Letters, 2017, 14: 095204. DOI: 10.1088/1612-202X/aa7b4e.

[26] [26] ZHANG Y L, ZHOU Q P, XU H Z, et al. Quantum-Memory-Assisted Entropic Uncertainty in Two-Qubit Heisenbergg XX Spin Chain Model[J]. International Journal of Theoretical Physics, 2019, 58(12): 4194-4207. DOI: 10.1007/s10773-019-04287-1.

[27] [27] SEKI S, YU X Z, ISHIWATA S, et al. Observation of Skyrmions in a Multiferroic Material[J]. Science, 2012, 336: 198. DOI: 10.1126/science.1214143.

[28] [28] ADAMS T, CHACON A, WAGNER M, et al. Long wavelength helimagnetic order and skyrmion lattice phase in Cu2OSeO3[J]. Physical Review Letters, 2012, 108(23): 237204. DOI: 10.1103/PhysRevLett.108.237204.

[29] [29] YANG J H, LI Z L, LU X Z, et al. Strong Dzyaloshinskii-Moriya Interaction and Origin of Ferroelectricity in Cu2OSeO3[J]. Physical Review Letters, 2012, 109(10): 1-6. DOI: 10.1103/PhysRevLett.109.107203.

[30] [30] YANG Y Y, SUN W Y, SHI W N, et al. Dynamical characteristic of measurement uncertainty under Heisenbergg spin models with Dzyaloshinskii-Moriya interactions[J]. Frontiers of Physics, 2019, 14(3): 31601. DOI: 10.1007/s11467-018-0880-1.

[31] [31] HUANG J H, CHEN Z Y, YU T B, et al. Dynamics of three-qubit entanglement in photonic crystals[J]. Physical Review A, 2012, 85: 014301. DOI: 10.1103/PhysRevA.85.014301.

[32] [32] CHEN P F, SUN W Y, MING F, et al. Observation of quantum-memory-assisted entropic uncertainty relation under open systems, and its steering[J]. Laser Physics Letter, 2018, 15(1): 015206. DOI: 10.1088/1612-202X/aa9639.