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  • Open Access

Non-Markovian noise limits for sustaining entanglement in multiparty quantum states

Suchetana Goswami1,2,* and Ujjwal Sen1,†

  • *Contact author: suchetana.goswami@gmail.com
  • †Contact author: ujjwalsen0601@gmail.com
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Phys. Rev. A 112, 052405 – Published 3 November, 2025

DOI: https://doi.org/10.1103/s963-rsm5

Abstract

The principal resource in several quantum information-processing tasks is entanglement. Building practically useful versions of such tasks, one often needs to consider multipartite systems. And in such scenarios, it is impossible to eliminate the effects of the environment while distributing the resources. We show how information backflow from the environment due to non-Markovianity in the system dynamics affects the resources in multipartite systems, specifically multiparty entanglement. In particular, we find that the entanglement of multiqubit Greenberger-Horne-Zeilinger cat states saturates with time to a nonzero value for a non-Markovian dephasing noise. The multiqubit W states saturate to a higher value. Such nonzero time-saturated values are washed out if the non-Markovianity in the channel is removed. The multiqubit W states provide a richer set of features, including a nonzero value for an asymptotic number of qubits and an even-odd dichotomy in the entanglement with the number of qubits. Moving to a non-Markovian depolarizing channel, we find that both cat and W states exhibit a revival of entanglement after the collapse.

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References (61)

  1. R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Quantum entanglement, Rev. Mod. Phys. 81, 865 (2009).
  2. S. Das, T. Chanda, M. Lewenstein, A. Sanpera, A. S. De, and U. Sen, The separability versus entanglement problem, arXiv:1701.02187.
  3. T. Eggeling and R. F. Werner, Hiding classical data in multipartite quantum states, Phys. Rev. Lett. 89, 097905 (2002).
  4. R. Rahaman and M. G. Parker, Quantum scheme for secret sharing based on local distinguishability, Phys. Rev. A 91, 022330 (2015).
  5. Z.-C. Zhang and X. Zhang, Strong quantum nonlocality in multipartite quantum systems, Phys. Rev. A 99, 062108 (2019).
  6. S. Goswami and S. Halder, Information locking and its resource-efficient extraction, Phys. Rev. A 108, 012405 (2023).
  7. A. Karlsson, M. Koashi, and N. Imoto, Quantum entanglement for secret sharing and secret splitting, Phys. Rev. A 59, 162 (1999).
  8. D. Markham and B. C. Sanders, Graph states for quantum secret sharing, Phys. Rev. A 78, 042309 (2008).
  9. M. B. Plenio, V. Vedral, and P. L. Knight, Quantum error correction in the presence of spontaneous emission, Phys. Rev. A 55, 67 (1997).
  10. M. Koashi and M. Ueda, Reversing measurement and probabilistic quantum error correction, Phys. Rev. Lett. 82, 2598 (1999).
  11. D. A. Lidar and K. Birgitta Whaley, Decoherence-free subspaces and subsystems, in Irreversible Quantum Dynamics (Springer, Berlin, 2003), Vol. 622, pp. 83–120.
  12. A. Shabani and D. A. Lidar, Theory of initialization-free decoherence-free subspaces and subsystems, Phys. Rev. A 72, 042303 (2005).
  13. A. N. Korotkov and A. N. Jordan, Undoing a weak quantum measurement of a solid-state qubit, Phys. Rev. Lett. 97, 166805 (2006).
  14. S. Braungardt, A. Sen(De), U. Sen, and M. Lewenstein, Error-resistant distributed quantum computation in a trapped ion chain, Phys. Rev. A 76, 042307 (2007).
  15. R. Blume-Kohout, H. K. Ng, D. Poulin, and L. Viola, Characterizing the structure of preserved information in quantum processes, Phys. Rev. Lett. 100, 030501 (2008).
  16. C. Nayak, S. H. Simon, A. Stern, M. Freedman, and S. Das Sarma, Non-Abelian anyons and topological quantum computation, Rev. Mod. Phys. 80, 1083 (2008).
  17. Y.-S. Kim, J.-C. Lee, O. Kwon, and Y.-H. Kim, Protecting entanglement from decoherence using weak measurement and quantum measurement reversal, Nat. Phys. 8, 117 (2012).
  18. S. Datta, S. Goswami, T. Pramanik, and A. Majumdar, Preservation of a lower bound of quantum secret key rate in the presence of decoherence, Phys. Lett. A 381, 897 (2017).
  19. S. Goswami, S. Ghosh, and A. Majumdar, Protecting quantum correlations in presence of generalised amplitude damping channel: The two-qubit case, J. Phys. A 54, 045302 (2021).
  20. V. Gorini, A. Kossakowski, and E. C. G. Sudarshan, Completely positive dynamical semigroups of N-level systems, J. Math. Phys. 17, 821 (1976).
  21. G. Lindblad, On the generators of quantum dynamical semigroups, Commun. Math. Phys. 48, 119 (1976).
  22. H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, New York, 2002).
  23. A. Shabani and D. A. Lidar, Vanishing quantum discord is necessary and sufficient for completely positive maps, Phys. Rev. Lett. 102, 100402 (2009).
  24. A. Brodutch, A. Datta, K. Modi, A. Rivas, and C. A. Rodríguez-Rosario, Vanishing quantum discord is not necessary for completely positive maps, Phys. Rev. A 87, 042301 (2013).
  25. L. Liu and D. M. Tong, Completely positive maps within the framework of direct-sum decomposition of state space, Phys. Rev. A 90, 012305 (2014).
  26. F. Buscemi, Complete positivity, Markovianity, and the quantum data-processing inequality, in the presence of initial system-environment correlations, Phys. Rev. Lett. 113, 140502 (2014).
  27. A. Shabani and D. A. Lidar, Erratum: Vanishing quantum discord is necessary and sufficient for completely positive maps [Phys. Rev. Lett. 102, 100402 (2009)], Phys. Rev. Lett. 116, 049901(E) (2016).
  28. D. Schmid, K. Ried, and R. W. Spekkens, Why initial system-environment correlations do not imply the failure of complete positivity: A causal perspective, Phys. Rev. A 100, 022112 (2019).
  29. A. Colla, N. Neubrand, and H.-P. Breuer, Initial correlations in open quantum systems: Constructing linear dynamical maps and master equations, New J. Phys. 24, 123005 (2022).
  30. H.-P. Breuer, E.-M. Laine, and J. Piilo, Measure for the degree of non-markovian behavior of quantum processes in open systems, Phys. Rev. Lett. 103, 210401 (2009).
  31. A. Rivas, S. F. Huelga, and M. B. Plenio, Entanglement and non-markovianity of quantum evolutions, Phys. Rev. Lett. 105, 050403 (2010).
  32. D. S. França and R. Garcia-Patron, Limitations of optimization algorithms on noisy quantum devices, Nat. Phys. 17, 1221 (2021).
  33. M. Cerezo, A. Arrasmith, R. Babbush, S. C. Benjamin, S. Endo, K. Fujii, J. R. McClean, K. Mitarai, X. Yuan, L. Cincio et al., Variational quantum algorithms, Nat. Rev. Phys. 3, 625 (2021).
  34. S. Wang, E. Fontana, M. Cerezo, K. Sharma, A. Sone, L. Cincio, and P. J. Coles, Noise-induced barren plateaus in variational quantum algorithms, Nat. Commun. 12, 6961 (2021).
  35. D. Hangleiter and J. Eisert, Computational advantage of quantum random sampling, Rev. Mod. Phys. 95, 035001 (2023).
  36. D. M. Greenberger, M. A. Horne, and A. Zeilinger, Going beyond Bell's theorem, in Bell's Theorem, Quantum Theory and Conceptions of the Universe, edited by M. Kafatos (Kluwer, Dordrecht, 1989), pp. 69–72.
  37. N. D. Mermin, Quantum mysteries revisited, Am. J. Phys. 58, 731 (1990).
  38. A. Zeilinger, M. A. Horne, and D. M. Greenberger, Higher-order quantum entanglement, in Proceedings of Squeezed States and Quantum Uncertainty, edited by D. Han, Y. S. Kim, and W. W. Zachary (NASA Conference Publication, 1992), p. 73.
  39. W. Dür, G. Vidal, and J. I. Cirac, Three qubits can be entangled in two inequivalent ways, Phys. Rev. A 62, 062314 (2000).
  40. A. Sen(De), U. Sen, M. Wie śniak, D. Kaszlikowski, and M. Żukowski, Multiqubit W states lead to stronger nonclassicality than Greenberger-Horne-Zeilinger states, Phys. Rev. A 68, 062306 (2003).
  41. C. Simon and J. Kempe, Robustness of multiparty entanglement, Phys. Rev. A 65, 052327 (2002).
  42. A. R. R. Carvalho, F. Mintert, and A. Buchleitner, Decoherence and multipartite entanglement, Phys. Rev. Lett. 93, 230501 (2004).
  43. M. Hein, W. Dür, and H.-J. Briegel, Entanglement properties of multipartite entangled states under the influence of decoherence, Phys. Rev. A 71, 032350 (2005).
  44. O. Gühne, F. Bodoky, and M. Blaauboer, Multiparticle entanglement under the influence of decoherence, Phys. Rev. A 78, 060301(R) (2008).
  45. T. Yu and J. Eberly, Sudden death of entanglement, Science 323, 598 (2009).
  46. N. Killoran, M. Cramer, and M. B. Plenio, Extracting entanglement from identical particles, Phys. Rev. Lett. 112, 150501 (2014).
  47. M. Mansour and S. Haddadi, Bipartite entanglement of decohered mixed states generated from maximally entangled cluster states, Mod. Phys. Lett. A 36, 2150010 (2021).
  48. Z.-Y. Peng, F.-L. Wu, J. Li, H.-N. Xue, S.-Y. Liu, and Z.-Y. Wang, Analytical method of multiqubit entanglement robustness in correlated quantum channels, Phys. Rev. A 107, 022405 (2023).
  49. Z.-P. Xu, S. Imai, and O. Gühne, Fate of multiparticle entanglement when one particle becomes classical, Phys. Rev. A 107, L040401 (2023).
  50. J. M. Martinis, K. B. Cooper, R. McDermott, M. Steffen, M. Ansmann, K. D. Osborn, K. Cicak, S. Oh, D. P. Pappas, R. W. Simmonds, and C. C. Yu, Decoherence in Josephson qubits from dielectric loss, Phys. Rev. Lett. 95, 210503 (2005).
  51. J. Bylander, S. Gustavsson, F. Yan, F. Yoshihara, K. Harrabi, G. Fitch, D. G. Cory, Y. Nakamura, J.-S. Tsai, and W. D. Oliver, Noise spectroscopy through dynamical decoupling with a superconducting flux qubit, Nat. Phys. 7, 565 (2011).
  52. C. Langer, R. Ozeri, J. D. Jost, J. Chiaverini, B. DeMarco, A. Ben-Kish, R. B. Blakestad, J. Britton, D. B. Hume, W. M. Itano, D. Leibfried, R. Reichle, T. Rosenband, T. Schaetz, P. O. Schmidt, and D. J. Wineland, Long-lived qubit memory using atomic ions, Phys. Rev. Lett. 95, 060502 (2005).
  53. C. J. Ballance, T. P. Harty, N. M. Linke, M. A. Sepiol, and D. M. Lucas, High-fidelity quantum logic gates using trapped-ion hyperfine qubits, Phys. Rev. Lett. 117, 060504 (2016).
  54. G. Vidal and R. F. Werner, Computable measure of entanglement, Phys. Rev. A 65, 032314 (2002).
  55. K. Życzkowski, P. Horodecki, A. Sanpera, and M. Lewenstein, Volume of the set of separable states, Phys. Rev. A 58, 883 (1998).
  56. J. Lee, M. Kim, Y. Park, and S. Lee, Partial teleportation of entanglement in a noisy environment, J. Mod. Opt. 47, 2151 (2000).
  57. M. B. Plenio, Logarithmic negativity: A full entanglement monotone that is not convex, Phys. Rev. Lett. 95, 090503 (2005).
  58. P. Haikka, T. H. Johnson, and S. Maniscalco, Non-Markovianity of local dephasing channels and time-invariant discord, Phys. Rev. A 87, 010103(R) (2013).
  59. D. Chruściński and F. A. Wudarski, Non-Markovian random unitary qubit dynamics, Phys. Lett. A 377, 1425 (2013).
  60. D. Chruściński and S. Maniscalco, Degree of non-Markovianity of quantum evolution, Phys. Rev. Lett. 112, 120404 (2014).
  61. https://github.com/suchetana92/Non-Markovian-noise-limits-for-sustaining-entanglement-in-multiparty-quantum-states.git.

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Phys. Rev. A 112, 052405– Published 3 November, 2025
  • Received 24 January 2025
  • Accepted 26 September 2025
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