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One Application of Duistermaat-Heckman Measure in Quantum Information Theory Cover

One Application of Duistermaat-Heckman Measure in Quantum Information Theory

By: Lin Zhang,  Xiaohan Jiang and  Bing Xie  
Open Access
|Mar 2026

References

  1. K. Życzkowski, P. Horodecki, A. Sanpera and M. Lewenstein (1998). Volume of the set of separable states. Phys. Rev. A, 58, 883.
  2. K. Życzkowski (1999). Volume of the set of separable states. II, Phys. Rev. A, 60, 3496.
  3. K. Życzkowski and H-J. Sommers (2003). Hilbert-Schmidt volume of the set of mixed quantum states. J. Phys. A : Math. Gen., 36, 10115.
  4. P.B. Slater (2007). Dyson indices and Hilbert-Schmidt separability functions and probabilities. J. Phys. A : Math. Theor., 40, 14279.
  5. P.B. Slater and C.F. Dunkl (2012). Moment-based evidence for simple rational-valued Hilbert-Schmidt generic 2 × 2 separability probabilities. J. Phys. A : Math. Theor., 45, 095305.
  6. P.B. Slater (2013). A concise formula for generalized two-qubit Hilbert-Schmidt separability probabilities. J. Phys. A : Math. Theor., 46, 445302.
  7. H.T. Huong and V.T. Khoi (2024). Separability probability of two-qubit states. J. Phys. A : Math. Theor., 57, 445304.
  8. A. Lovas and A. Andai (2017). Invariance of separability probability over reduced states in 4 × 4 bipartite systems. J. Phys. A : Math. Theor., 50, 295303.
  9. A. Andai (2006). Volume of the quantum mechanical state space. J. Phys. A : Math. Gen., 39, 13641.
  10. J.J. Duistermaat and G.J. Heckman (1982). On the variation in the cohomology of the symplectic form of the reduced phase space. Invent. Math., 69, 259-268.
  11. P. Crooks and J. Weitsman (2023). Abelianization and the Duistermaat-Heckman theorem. Bulletin of the London Mathematical Society 55, 2732-2742.
  12. P. Crooks and J. Weitsman (2024). Gelfand-Cetlin abelianizations of symplectic quotients. Pacific J. Math., 333, 253-271.
  13. A. Boysal and M Vergne (2009). Paradan’s wall crossing formula for partition functions and Khovanski-Pukhlikov differential operator. Annales de l’Institut Fourier, Tome, 59, 1715-1752.
  14. M. Christandl, B. Doran, S. Kousidis and M. Walter (2014). Eigenvalue distributions of reduced density matrices. Comm. Math. Phys., 332, 1-5.
  15. L. Zhang. Volumes of orthogonal groups and unitary groups, arXiv:1509.00537
  16. P. Deift and D. Gioev (2019). Random Matrix Theory: Invariant Ensembles and Universality, American Mathematical Society.
  17. L. Zhang and S. Hong (2018). Volume of the set of locally diagonalizable bipartite states, J. Phys. A : Math. Theor., 51,385302.
  18. G. Olshanski (2013). Projections of orbital measures, Gelfand-Tsetlin polytopes, and splines. Journal of Lie Theory, 23, 1011-1022.
  19. B. Collins and C. McSwiggen (2023). Projections of orbital measures and quantum marginal problems. Trans. Amer. Math. Soc., 376, 5601-5640.
  20. A.C. Silva (2008). Lectures on Symplectic Geometry, Springer-Verlag.
  21. N. Berline, E. Getzler and M. Vergne (1992). Heat Kernels and Dirac Operators, Springer-Verlag.
  22. Harish-Chandra (1975). Harmonic analysis on real reductive groups I: the theory of the constant term. J. Funct. Anal., 19, 104-204.
  23. A.A. Bytsenko, M. Libine and F.L. Williams (2005). Localization of equivariant cohomology for compact and noncompact group actions, 3, 171-195.
  24. L. Zhang, Y. Jiang and J. Wu (2019). Duistermaat-Heckman measure and the mixture of quantum states. J. Phys. A : Math. Theor., 52, 495203.
  25. M. Walter. Multipartite quantum states and their marginals, PhD Thesis arXiv:1410.6820
  26. S. Bravyi (2004). Requirements for compatibility between local and multipartite quantum states. Quantum Information & Computation, 4, 12-26.
  27. S. Milz and W.T. Strunz (2015). Volumes of conditioned bipartite state spaces. J. Phys. A: Math. Theor., 48, 035306.
DOI: https://doi.org/10.2478/qic-2025-0033 | Journal eISSN: 3106-0544 | Journal ISSN: 1533-7146
Language: English
Page range: 598 - 632
Submitted on: Jul 7, 2025
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Accepted on: Sep 10, 2025
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Published on: Mar 9, 2026
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year

© 2026 Lin Zhang, Xiaohan Jiang, Bing Xie, published by Cerebration Science Publishing Co., Limited
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.