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  • Open Access

Symmetry-resolved genuine multientropy: Random Haar and graph states

Norihiro Iizuka1,2,* and Simon Lin3,†

  • *Contact author: iizuka@phys.nthu.edu.tw
  • †Contact author: simonlin@nyu.edu
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Phys. Rev. D 113, 026016 – Published 21 January, 2026

DOI: https://doi.org/10.1103/yts4-fldf

Abstract

We study the symmetry-resolved genuine multientropy, a measure that captures genuine multipartite entanglement, in Haar random states and random graph states in the presence of a conserved quantity. For Haar random states, we derive explicit formulas for the genuine multientropy under a global U(1) symmetry in the thermodynamic limit, and find that its dependence on subsystem sizes closely resembles that of fully Haar random states without a conserved charge. We also perform numerical analyses, focusing on spin systems for both Haar random and graph states. For random graph states, our numerical analyses reveal distinctive features of their multipartite entanglement structure and we contrast them with the Haar random case.

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References (60)

  1. L. Bombelli, R. K. Koul, J. Lee, and R. D. Sorkin, A quantum source of entropy for black holes, Phys. Rev. D 34, 373 (1986).
  2. M. Srednicki, Entropy and area, Phys. Rev. Lett. 71, 666 (1993).
  3. C. G. Callan, Jr. and F. Wilczek, On geometric entropy, Phys. Lett. B 333, 55 (1994).
  4. H. Li and F. Haldane, Entanglement spectrum as a generalization of entanglement entropy: Identification of topological order in non-Abelian fractional quantum Hall effect states, Phys. Rev. Lett. 101, 010504 (2008).
  5. S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96, 181602 (2006).
  6. S. Ryu and T. Takayanagi, Aspects of holographic entanglement entropy, J. High Energy Phys. 08 (2006) 045.
  7. D. N. Page, Average entropy of a subsystem, Phys. Rev. Lett. 71, 1291 (1993).
  8. D. N. Page, Information in black hole radiation, Phys. Rev. Lett. 71, 3743 (1993).
  9. M. A. Nielsen and J. Kempe, Separable states are more disordered globally than locally, Phys. Rev. Lett. 86, 5184 (2001).
  10. A. Gadde, V. Krishna, and T. Sharma, New multipartite entanglement measure and its holographic dual, Phys. Rev. D 106, 126001 (2022).
  11. A. Gadde, V. Krishna, and T. Sharma, Towards a classification of holographic multi-partite entanglement measures, J. High Energy Phys. 08 (2023) 202.
  12. N. Iizuka and M. Nishida, Genuine multientropy and holography, Phys. Rev. D 112, 026011 (2025).
  13. N. Iizuka, S. Lin, and M. Nishida, More on genuine multientropy and holography, Phys. Rev. D 112, 066014 (2025).
  14. G. Penington, M. Walter, and F. Witteveen, Fun with replicas: Tripartitions in tensor networks and gravity, J. High Energy Phys. 05 (2023) 008.
  15. J. Harper, T. Takayanagi, and T. Tsuda, Multi-entropy at low Renyi index in 2d CFTs, SciPost Phys. 16, 125 (2024).
  16. B. Liu, J. Zhang, S. Ohyama, Y. Kusuki, and S. Ryu, Multi wavefunction overlap and multi entropy for topological ground states in (2+1) dimensions, Phys. Rev. B 112, 125160 (2025).
  17. N. Iizuka, S. Lin, and M. Nishida, Why many-partite entanglement is essential for holography, arXiv:2504.01625.
  18. C. Akers and P. Rath, Entanglement wedge cross sections require tripartite entanglement, J. High Energy Phys. 04 (2020) 208.
  19. C. Akers, T. Faulkner, S. Lin, and P. Rath, Reflected entropy in random tensor networks III: Triway cuts, J. High Energy Phys. 12 (2024) 209.
  20. P. Hayden, O. Parrikar, and J. Sorce, The Markov gap for geometric reflected entropy, J. High Energy Phys. 10 (2021) 047.
  21. Z. Li, T. Mori, and B. Yoshida, Tripartite Haar random state has no bipartite entanglement, arXiv:2502.04437.
  22. J. Harper, A. Mollabashi, T. Takayanagi, and K. Tasuki, Multi-entropy and the dihedral measures at quantum critical points, Phys. Rev. Res. 7, 043194 (2025).
  23. N. Iizuka, A. Miyata, and M. Nishida, Multipartite Markov gaps and entanglement wedge multiway cuts, J. High Energy Phys. 10 (2025) 148.
  24. C. Berthière and P. Gaudin, Genuine multi-entropy, dihedral invariants and Lifshitz theory, arXiv:2509.00593.
  25. V. Balasubramanian, M. J. Kang, C. Cummings, C. Murdia, and S. F. Ross, Purely GHZ-like entanglement is forbidden in holography, arXiv:2509.03621.
  26. N. Bao, K. Furuya, and J. Naskar, Tripartite entanglement signal from multipartite entanglement of purification, arXiv:2509.08209.
  27. S. Akella, Tripartite entanglement in the HaPPY code is not holographic, arXiv:2510.08520.
  28. M.-K. Yuan, M. Li, and Y. Zhou, Multi-entropy from Linking in Chern-Simons Theory, arXiv:2510.18408.
  29. M. Goldstein and E. Sela, Symmetry-resolved entanglement in many-body systems, Phys. Rev. Lett. 120, 200602 (2018).
  30. J. C. Xavier, F. C. Alcaraz, and G. Sierra, Equipartition of the entanglement entropy, Phys. Rev. B 98, 041106 (2018).
  31. R. Bonsignori, P. Ruggiero, and P. Calabrese, Symmetry resolved entanglement in free fermionic systems, J. Phys. A 52, 475302 (2019).
  32. S. Fraenkel and M. Goldstein, Symmetry resolved entanglement: Exact results in 1D and beyond, J. Stat. Mech. (2020) P033106.
  33. S. Murciano, G. Di Giulio, and P. Calabrese, Symmetry resolved entanglement in gapped integrable systems: A corner transfer matrix approach, SciPost Phys. 8, 046 (2020).
  34. N. Feldman and M. Goldstein, Dynamics of charge-resolved entanglement after a local quench, Phys. Rev. B 100, 235146 (2019).
  35. S. Murciano, G. Di Giulio, and P. Calabrese, Entanglement and symmetry resolution in two dimensional free quantum field theories, J. High Energy Phys. 08 (2020) 073.
  36. L. Capizzi, P. Ruggiero, and P. Calabrese, Symmetry resolved entanglement entropy of excited states in a CFT, J. Stat. Mech. (2020) P073101.
  37. P. H. C. Lau, T. Noumi, Y. Takii, and K. Tamaoka, Page curve and symmetries, J. High Energy Phys. 10 (2022) 015.
  38. A. Neven et al., Symmetry-resolved entanglement detection using partial transpose moments, npj Quantum Inf. 7, 152 (2021).
  39. F. Ares, S. Murciano, and P. Calabrese, Entanglement asymmetry as a probe of symmetry breaking, Nat. Commun. 14, 2036 (2023).
  40. E. Bianchi and P. Dona, Typical entanglement entropy in the presence of a center: Page curve and its variance, Phys. Rev. D 100, 105010 (2019).
  41. S. Murciano, P. Calabrese, and L. Piroli, Symmetry-resolved Page curves, Phys. Rev. D 106, 046015 (2022).
  42. C. Berthiere and G. Parez, Reflected entropy and computable cross-norm negativity: Free theories and symmetry resolution, Phys. Rev. D 108, 054508 (2023).
  43. A. Jain, Symmetry resolved multipartite entanglement entropy, arXiv:2509.13410.
  44. D. A. Meyer and N. R. Wallach, Global entanglement in multiparticle systems, J. Math. Phys. (N.Y.) 43, 4273 (2002).
  45. N. Iizuka, S. Lin, and M. Nishida, Black hole multi-entropy curves—secret entanglement between Hawking particles, J. High Energy Phys. 03 (2025) 037.
  46. C. Nadal, S. N. Majumdar, and M. Vergassola, Statistical distribution of quantum entanglement for a random bipartite state, J. Stat. Phys. 142, 403 (2011).
  47. A. Gadde, S. Jain, and H. Kulkarni, Multi-partite entanglement monotones, arXiv:2406.17447.
  48. A. Gadde, S. Jain, V. Krishna, H. Kulkarni, and T. Sharma, Monotonicity conjecture for multi-party entanglement. Part I, J. High Energy Phys. 02 (2024) 025.
  49. V. Balasubramanian, P. Hayden, A. Maloney, D. Marolf, and S. F. Ross, Multiboundary wormholes and holographic entanglement, Classical Quantum Gravity 31, 185015 (2014).
  50. M. Hein, W. Dür, J. Eisert, R. Raussendorf, M. Van den Nest, and H. J. Briegel, Entanglement in graph states and its applications, arXiv:quant-ph/0602096.
  51. M. Hein, J. Eisert, and H. J. Briegel, Multiparty entanglement in graph states, Phys. Rev. A 69, 062311 (2004).
  52. D. Fattal, T. S. Cubitt, Y. Yamamoto, S. Bravyi, and I. L. Chuang, Entanglement in the stabilizer formalism, arXiv:quant-ph/0406168.
  53. V. F. Kolchin, Random Graphs, Encyclopedia of Mathematics and its Applications (Cambridge University Press, Cambridge, England, 1998).
  54. S. Bravyi, D. Fattal, and D. Gottesman, GHZ extraction yield for multipartite stabilizer states, J. Math. Phys. (N.Y.) 47, 062106 (2006).
  55. S. Nezami and M. Walter, Multipartite entanglement in stabilizer tensor networks, Phys. Rev. Lett. 125, 241602 (2020).
  56. M. Englbrecht, T. Kraft, and B. Kraus, Transformations of stabilizer states in quantum networks, Quantum 6, 846 (2022).
  57. J. Preskill, P. Schwarz, A. D. Shapere, S. Trivedi, and F. Wilczek, Limitations on the statistical description of black holes, Mod. Phys. Lett. A 06, 2353 (1991).
  58. J. M. Maldacena, J. Michelson, and A. Strominger, Anti-de Sitter fragmentation, J. High Energy Phys. 02 (1999) 011.
  59. D. N. Page, Thermodynamics of near extreme black holes, arXiv:hep-th/0012020.
  60. A. R. Brown, L. V. Iliesiu, G. Penington, and M. Usatyuk, The evaporation of charged black holes, arXiv:2411.03447.

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Phys. Rev. D 113, 026016– Published 21 January, 2026
  • Received 13 November 2025
  • Accepted 2 January 2026
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