Jianlian Cui, Ph.D. from the Institute of Mathematics of the Academy of Mathematics and Systems Science, Chinese Academy of Sciences, and postdoctoral researcher at the Institute of Mathematics, Peking University. Previously worked at the Department of Mathematics, Taiyuan University of Technology. Joined the Department of Mathematical Sciences, Tsinghua University in April 2004, promoted to Associate Professor in December 2005, to Professor in December 2023, and appointed Professor at the Teaching Center of Mathematics, Tsinghua University in April 2024. Visiting Scholar at the Department of Mathematics, College of William & Mary, USA; Seoul National University, South Korea; and The University of Hong Kong. Engaged in research on operator theory, operator algebras, and quantum information theory. Received second-class funding from the China Postdoctoral Science Foundation. Led or participated in five National Natural Science Foundation of China projects, one NSFC China-Korea International Cooperation and Exchange Project, four provincial or ministerial research projects, and five Tsinghua University undergraduate education reform projects. Co-authored the monograph Introduction to Linear Maps on Operator Algebras (Science Press) and co-authored the two-volume textbook Principles of Calculus (MIIT 14th Five-Year Plan Textbook). Supervised two Ph.D. students, both graduated and currently employed at research institutes.

Taught undergraduate courses including: Functional Analysis, Calculus I, Calculus II, Calculus III, Advanced Calculus B, Calculus A(1), Calculus B(1), and Calculus A(2), among others.

Led a small-class problem-solving seminar reform project, significantly enhancing student progress and talent development. Teaching methods are highly appreciated by students, consistently ranking in the top 5% of teaching evaluations for courses of similar scale at Tsinghua University since the spring semester of 2018.

Published two volumes of the MIIT 14th Five-Year Plan Textbook Principles of Calculus:

1. Principles of Calculus (Volume 1), Jianlian Cui and Yong Wang, Publishing House of Electronics Industry, July 2023;

2. Principles of Calculus (Volume 2), Jianlian Cui and Yong Wang, Publishing House of Electronics Industry, October 2023.

Achieved a series of significant and impactful research results in operator algebras and operator theory. Published over 60 academic papers, with more than 50 indexed in SCI. Obtained a complete classification of nonlinear numerical radius isometries on a class of important non-self-adjoint operator algebras, published in the prestigious Journal of Functional Analysis. Addressed a problem on invertibility preservation proposed by renowned mathematician Kaplansky in the 1970s on von Neumann algebras. Introduced the concept of tr-rank on finite von Neumann algebras for the first time and characterized the structure of linear maps that is completely tr-rank non-increasing. In recent years, applied research to quantum information, an emerging interdisciplinary field involving physics, computer science, and mathematics. Quantum entanglement enables quantum information transmission to surpass the speed of light, providing new principles and methods for the development of information science, and is a key direction for future technological advancements in China. Monogamy of entanglement in multi-body systems is central to various quantum information and communication protocols and is a critical component of quantum cryptographic security. Developed an entanglement measure for high-dimensional multi-body systems and proved the existence of monogamy in the 3-qutrit system for the first time, resolving a long-standing problem. This result was published in Scientific Reports, a Nature journal. Quantum error correction techniques were developed to address quantum decoherence. Constructed new quantum codes by designing matrix product codes satisfying Euclidean or Hermitian dual containment. Provided the first constructive methods for NSC quasi-orthogonal and NSC quasi-unitary matrices, with partial results published in the prestigious IEEE Communications Letters.

1. 2025, Recognized as a Favorite Teacher and Course by Tsinghua University’s 2025 Graduates

2.2024, Received the Gong Yuzhi Teaching Award from Tsinghua University

3. 2024, Received the Tsinghua University Annual Teaching Excellence Award

4. 2023, Received the Tsinghua University New Century Teaching Achievement Award

5. 2023, Received the 9th Tsinghua University Qingyun Candlelight "My Favorite Teacher"

6. 2023, Recognized as a Favorite Teacher and Course by Tsinghua University’s 2023 Graduates

7. 2021, Received the Baosteel Education Award for Outstanding Teacher

8. 2021, Received the Tsinghua University Annual Outstanding Worker Award

9. 2021, Received the Tsinghua University Annual Teaching Excellence Award

10. 2020, Received the Outstanding Teacher Award for Online Teaching During the Pandemic

11. 2020, Calculus B(1) was recognized as one of the first National First-Class Undergraduate Courses by the Ministry of Education (Key Member)

12. 2019, Received the Tsinghua University Annual Teaching Excellence Award

13. 2018, Received the Outstanding Advisor Award for the 29th Beijing University Student Mathematics Competition

14. 2017, Received the Tsinghua University Outstanding Class Advisor Second Prize

15. 2015, Received the Tsinghua University Outstanding Class Advisor Second Prize

16. 2014, Received the Outstanding Advisor Award for the 25th Beijing University Student Mathematics Competition

17. 2010, Received the Shanxi Province Science and Technology Second Prize (Collaboration)

18. 2003, Received the Shanxi Province Science and Technology Progress First Prize (Collaboration)

19. 2002, Received the Chinese Academy of Sciences President’s Outstanding Award

20. 2002, Received the Chinese Academy of Sciences Procter & Gamble Outstanding Award

1. Cao M, Wang H X, Cui J L*, Construction of quantum codes from matrix-product codes. IEEE Communications Letters, 2020, 24(4):706-710.

2. Cao M, Cui J L*, New stabilizer codes from the construction of dual-containing matrix-product codes. Finite Fields and Their Applications, 2020, 63:101643.

3. Cao M, Cui J L*, Construction of new quantum codes via Hermitian dual-containing matrix-product codes. Quantum Information Processing 19 (2020): 1-26.

4. T. Xin, S.J. Wei, J.L. Cui, J.X. Xiao, I. Arrazola, L. Lamata, X.Y. Kong, D.W. Lu, E. Solano, G.L. Long, Quantum algorithm for solving linear differential equations: Theory and experiment, PHYSICAL REVIEW A (ISSN: 2469-9926), Vol 101(3), 2020, WOS: 000518434700002.

5. Q.T. Li, J.L. Cui*, S.H. Wang, G.L. Long, Entanglement monogamy in three qutrit systems, Scientific Reports 7, Article number: 1946(2017), doi: 10.1038/s41598-017-02066-8.

6. J.L. Cui,*, C.K. Li, N.S. Sze, Unitary similarity invariant function preservers of skew products of operators. J. Math. Anal. Appl., 454 (2017), No. 2, 716–729.

7. J.L. Cui, C.K. Li, N.S. Sze, Products of positive semi-definite matrices. Lin. Alg. Appl., 528(2017), 17-24.

8. Q.T. Li, J.L. Cui*, S.H. Wang, G.L. Long, Study of a monogamous entanglement measure for three-qubit quantum systems, Quantum Information Processing, 2016, 15(6), 2405-2424. DOI: 10.1007/s11128-016-1285-0.

9. J.L. Cui, C.K. Li, Y.T. Poon, Preservers of Unitary Similarity Functions on Lie Products of Matrices, Lin. Alg. Appl., Vol. 498, 2016, 160-180.

10. X.F. Qi, J.C. Hou, J.L. Cui, Additive maps preserving zero skew *-Lie products (in Chinese). Sci. Sin. Math, 2015, 45: 151-165, doi: 10.1360/012014-69.

11. J.L. Cui, C.K. Li, Y.T. Poon, Pseudospectra of special operators and pseudospectrum preservers, J. Math. Anal. Appl., 419 (2014) 1261–1273.

12. J.L. Cui, Q.T. Li, J.C. Hou, X.F. Qi, Some unitary similarity invariant sets preservers of skew Lie products, Lin. Alg. Appl., 457 (2014), 76–92.

13. C. Park, J.L. Cui, Madjid Eshaghi Gordji, Orthogonality and quintic functional equations, Acta Math. Sinica, Vol 29(7), 2013, 1381-1390.

14. H. Li, S.H. Wang, J.L. Cui, G.L. Long, Quantifying entanglement of arbitrary-dimensional multipartite pure states in terms of the singular values of coefficient matrices, Phys, Rev. A 87, 042335 (2013).

15. S.H. Wang, Y. Lu, M. Gao, J.L. Cui, J.L. Li, Classification of arbitrary-dimensional multipartite pure states under stochastic local operations and classical communication using the rank of coefficient matrix, J. Phys. A: Math. Theor. 46(2013), 105303(10pp).

16. J.L. Cui, C.K. Li, Maps preserving peripheral-spectrum of Jordan products of operators, Operators and Matrices, Vol.6, No.1, (2012), 129-146.

17. J.L. Cui, C. Park, Maps preserving strong skew Lie products on factor von Neumann algebras, Acta Math. Scientia, 2012, 32B(2), 531-538.

18. J.L. Cui, Forstall, Li, Yall, Property and preservers of the pseudospectrum, Lin. Alg. Appl., 436, (2012), pp. 316-325.

19. X.F. Qi, J.L. Cui, J.C. Hou, Additive maps (generalized) $\xi$-Lie derivable at zero point on prime algebras, Lin. Alg. Appl, (434)2011, 669-682.

20. J.L. Cui, Nonlinear preserver problems on B(H), Acta Math. Sinica, 2011, No. 27(1), 193-202.

21. C. Park, J.L. Cui, Fixed Points and Stability of the Cauchy Functional Equation in Lie C*-Algebras, Nonlinear analysis and Variational problems, Springer Optimization and Its Applications, 35(2010), 111-124.

22. J.L. Cui, C.K. Li, Maps preserving product $XY-YX^*$ on factor von Neumann algebras, Lin. Alg. Appl., 431 (2009) 833-842.

23. J.S. An, J.L. Cui, C. Park, Jordan *-derivations on C*-algebras and JC*-algebras, Abstract and Applied Analysis, Vol. 2008, Article ID 410437, 12 pages, doi: 10.1155/2008/410437.

24. J.L. Cui, J.C. Hou, Choonkil Park, Additive maps preserving commutativity up to a factor, Chinese Ann. of Math., 29A(5)(2008), 583-590.

25. J.L. Cui, J.C. Hou, Maps leaving functional values of operator products invariant, Lin. Alg. Appl., 428(2008), 1649-1663.

26. J.L. Cui, Additive Drazin inverse preservers, Lin. Alg. Appl., 426(2007), 448-453.

27. J.L. Cui, Linear maps leaving zeros of a polynomial invariant, Acta Math. Sinica, 50(3), 2007, 493-496.

28. J.C. Hou, J.L. Cui, Linear aps preserving essential spectral functions and closeness of operator ranges, Bulletin of London Math Soc., 39(2007), 575-582.

29. Choonkil Park, J.L. Cui, Generalized stability of C*-ternary quadratic mappings, Abstract and Applied Analysis, Vol 2007, Article ID23282, doi: 10.1155/2007/23282.

30. J.L. Cui, J.C. Hou, Additive maps preserving rank-1 nilpotency on nest algebras, Acta Mathematica Scientia, 27A(2), 2007, 193-203.

31. Choonkil Park, J.L. Cui, Approximately Linear Mappings in Banach Modules over a $C^*$-algebra, Acta Math. sinica, 2007, Vol.23(11), 1919-1936.

32. C. Park, J.S. An, J.L. Cui, Isomorphisms and derivations in Lie C*-algebras, Abstract and Applied Analysis, Vol 2007, Article ID 85737, 14 pages, doi: 10.1155/2007/85737.

33. J.L. Cui, J.C. Hou, Linear maps preserving elements annihilated by the polynomial $XY-YX^\dagger$, Studia Math., 2006, vol. 174(2), 183-199.

34. J.L Cui, J.C. Hou, An algebraic invariant for Jordan automorphisms on B(H): the set of idempotents, Science in China, 2005, Vol. 48(12), 1585-1596.

35. J.L. Cui, J.C. Hou, Non-linear numerical radius isometries on atomic nest algebras and diagonal algebras, Journal of Functional Analysis, 206 (2004), 414-448.

36. J.L. Cui, J.C. Hou, Chun-Gil Park, Indefinite orthogonality preserving additive maps. Archiv der Mathematik, 83 (2004), 548-557.

37. J.L. Cui, M.Z. Guo, J.C. Hou, Linear maps preserving rank-1 nilpotency on nest algebras, Lin. Alg. Appl., Vol 377(2004), 267-290.

38. J.L. Cui, J.C. Hou, Linear maps preserving idempotence on nest algebras, Acta Math. Sinica, Vol. 20 (5) (2004), 807-820.

39. J.L. Cui, J.C. Hou, Linear maps compressing the certain spectral functions on Banach algebras, Rocky Moun. J. Math., Vol. 34, no. 2 (2004), 565-584.

40. J.L. Cui, J.C. Hou, A Characterization of Homomorphisms Between Banach Algebras, Acta Math. Sinica, Vol. 20 (4) (2004), 761-768.

41. J.L. Cui, J.C. Hou, Linear maps preserving indefinite orthogonality on C$^*$-algebras, Chinese Ann. Math., Ser. A, Vol. 25, no. 4 (2004), 437-444.

42. J.C. Hou, J.L. Cui, Completely rank nonincreasing linear maps on nest algebras, Procceding of Amer. Math. Soc., Vol. 132 (2004), 1419-1428.

43. J.L. Cui, J.C. Hou, Linear maps preserving the closure of numerical range on nest algebras with maximal atomic nest, Integ. Equa.Oper. Theo., Vol. 46(3), (2003), 253-266.

44. J.L. Cui, J.C. Hou, Additive maps on standard operator algebras preserving parts of the spectrum, J. Math. Anal. Appl., Vol.282(1), (2003), 266-278.

45. J.L. Cui, J.C. Hou, Linear maps preserving ideals of C*-algebras, Proceeding of Amer. Math. Soc., 131(11), (2003), 3441-3446.

46. J.C. Hou, J.L. Cui, Rank-1 preserving linear maps on nest algebras, Lin. Alg. Appl., Vol. 369 (2003), 263-277.

47. J.C. Hou, J.L. Cui, Additive maps on standard operator algebras preserving invertibilities or zero divisors, Lin. Alg. Appl., Vol. 359 (2003), 219-233.

48. J.L. Cui, J.C. Hou, Linear maps on von Neumann algebras preserving zero products or tr-rank, Bull. Austral. Math. Soc., Vol. 65 (2002), 79-91.

49. J.L. Cui, J.C. Hou, The spectrally bounded linear maps on operator algebras, Studia Math., Vol. 150 (3), (2002), 261-271.

50. J.L. Cui, J.C. Hou, Bingren Li, Linear preservers on upper triangular operator matrix algebras, Linear Algebra and its Applications, Vol. 336 (2001), 29-50.