- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review A

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access
  • Access by Xinjiang University

Theory of the correlated quantum Zeno effect in a monitored qubit dimer

Severino Zeni1,2,*, Gobinda Chakraborty3, Alessandro Romito3, and Alberto Biella1,4,†

  • 1Pitaevskii BEC Center, CNR-INO and Dipartimento di Fisica, Università di Trento, I-38123 Trento, Italy
  • 2eXact Laboratory Srl–Janas Project, Via Francesco Crispi 56, 34126 Trieste, Italy
  • 3Department of Physics, Lancaster University, Lancaster LA1 4YB, England, United Kingdom
  • 4INFN-TIFPA, Trento Institute for Fundamental Physics and Applications, I-38123 Trento, Italy

  • *Contact author: severino.zeni@exact-lab.it
  • †Contact author: alberto.biella@cnr.it
PDF

Phys. Rev. A 113, 062424 – Published 8 June, 2026

DOI: https://doi.org/10.1103/x8n3-2fxt

Abstract

We theoretically investigate the stochastic dynamics of two qubits subject to one- and two-site correlated continuous weak measurements. When measurements dominate over the local unitary evolution, the system's dynamics is constrained and part of the physical Hilbert space becomes inaccessible: a typical signature of the quantum Zeno (QZ) effect. In this work, we show how the competition between these two measurement processes gives rise to two distinct QZ regimes, which we dubbed standard and correlated, characterized by a different topology of the allowed region of the physical Hilbert space, being a simply and nonsimply connected domain, respectively. We develop a theory based on a stochastic Gutzwiller ansatz for the wave function that is able to capture the structure of the phase diagram. Finally we show how the two QZ regimes are intimately connected to the topology of the flow of the underlying non-Hermitian Hamiltonian governing the no-click evolution.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (43)

  1. H. P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Oxford University, London, 2002).
  2. B. Misra and E. C. G. Sudarshan, The Zeno's paradox in quantum theory, J. Math. Phys. 18, 756 (1977).
  3. A. Peres, Zeno paradox in quantum theory, Am. J. Phys. 48, 931 (1980).
  4. W. M. Itano, D. J. Heinzen, J. J. Bollinger, and D. J. Wineland, Quantum Zeno effect, Phys. Rev. A 41, 2295 (1990).
  5. P. Facchi, H. Nakazato, and S. Pascazio, From the quantum Zeno to the inverse quantum Zeno effect, Phys. Rev. Lett. 86, 2699 (2001).
  6. P. Facchi and S. Pascazio, Quantum Zeno subspaces, Phys. Rev. Lett. 89, 080401 (2002).
  7. P. G. Kwiat, A. G. White, J. R. Mitchell, O. Nairz, G. Weihs, H. Weinfurter, and A. Zeilinger, High-efficiency quantum interrogation measurements via the quantum Zeno effect, Phys. Rev. Lett. 83, 4725 (1999).
  8. J. Wolters, M. Strauß, R. S. Schoenfeld, and O. Benson, Quantum Zeno phenomenon on a single solid-state spin, Phys. Rev. A 88, 020101(R) (2013).
  9. A. Signoles, A. Facon, D. Grosso, I. Dotsenko, S. Haroche, J.-M. Raimond, M. Brune, and S. Gleyzes, Confined quantum Zeno dynamics of a watched atomic arrow, Nat. Phys. 10, 715 (2014).
  10. P. Facchi and S. Pascazio, Quantum Zeno dynamics: Mathematical and physical aspects, J. Phys. A 41, 493001 (2008).
  11. P. Facchi and S. Pascazio, Chapter 3: Quantum Zeno and inverse quantum Zeno effects, in Progress in Optics, edited by E. Wolf, Progress in Optics (Elsevier, Amsterdam, 2001), Vol. 42, p. 147.
  12. P. Facchi, D. A. Lidar, and S. Pascazio, Unification of dynamical decoupling and the quantum Zeno effect, Phys. Rev. A 69, 032314 (2004).
  13. S. Greenfield, A. Kamal, J. Dressel, and E. Levenson-Falk, A unified picture for quantum Zeno and anti-Zeno effects – a review, arXiv:2506.12679.
  14. C. Guerlin, J. Bernu, S. Deléglise, C. Sayrin, S. Gleyzes, S. Kuhr, M. Brune, J.-M. Raimond, and S. Haroche, Progressive field-state collapse and quantum non-demolition photon counting, Nature (London) 448, 889 (2007).
  15. C. Sayrin, I. Dotsenko, X. Zhou, B. Peaudecerf, T. Rybarczyk, S. Gleyzes, P. Rouchon, M. Mirrahimi, H. Amini, M. Brune, J.-M. Raimond, and S. Haroche, Real-time quantum feedback prepares and stabilizes photon number states, Nature (London) 477, 73 (2011).
  16. K. W. Murch, S. J. Weber, K. M. Beck, E. Ginossar, and I. Siddiqi, Reduction of the radiative decay of atomic coherence in squeezed vacuum, Nature (London) 499, 62 (2013).
  17. K. W. Murch, S. J. Weber, C. Macklin, and I. Siddiqi, Observing single quantum trajectories of a superconducting quantum bit, Nature (London) 502, 211 (2013).
  18. S. J. Weber, A. Chantasri, J. Dressel, A. N. Jordan, K. W. Murch, and I. Siddiqi, Mapping the optimal route between two quantum states, Nature (London) 511, 570 (2014).
  19. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information: 10th Anniversary Edition, 10th ed. (Cambridge University, New York, 2011).
  20. F. Minganti and A. Biella, Open quantum systems – a brief introduction, Cahiers de l'Institut Pascal 2, 2 (2026).
  21. J. P. Garrahan, Aspects of non-equilibrium in classical and quantum systems: Slow relaxation and glasses, dynamical large deviations, quantum non-ergodicity, and open quantum dynamics, Physica A 504, 130 (2018).
  22. G. T. Landi, M. J. Kewming, M. T. Mitchison, and P. P. Potts, Current fluctuations in open quantum systems: Bridging the gap between quantum continuous measurements and full counting statistics, PRX Quantum 5, 020201 (2024).
  23. R. Fazio, J. Keeling, L. Mazza, and M. Schirò, Many-body open quantum systems SciPost Phys. Lect. Notes 99 (2025).
  24. K. Snizhko, P. Kumar, and A. Romito, Quantum Zeno effect appears in stages, Phys. Rev. Res. 2, 033512 (2020).
  25. H. Fröml, A. Chiocchetta, C. Kollath, and S. Diehl, Fluctuation-induced quantum Zeno effect, Phys. Rev. Lett. 122, 040402 (2019).
  26. H. Fröml, C. Muckel, C. Kollath, A. Chiocchetta, and S. Diehl, Ultracold quantum wires with localized losses: Many-body quantum Zeno effect, Phys. Rev. B 101, 144301 (2020).
  27. A. Biella and M. Schiró, Many-body quantum Zeno effect and measurement-induced subradiance transition, Quantum 5, 528 (2021).
  28. D. Rossini, A. Ghermaoui, M. B. Aguilera, R. Vatré, R. Bouganne, J. Beugnon, F. Gerbier, and L. Mazza, Strong correlations in lossy one-dimensional quantum gases: From the quantum Zeno effect to the generalized Gibbs ensemble, Phys. Rev. A 103, L060201 (2021).
  29. M. Seclì, M. Capone, and M. Schirò, Steady-state quantum Zeno effect of driven-dissipative bosons with dynamical mean-field theory, Phys. Rev. A 106, 013707 (2022).
  30. L. Rosso, L. Mazza, and A. Biella, Eightfold way to dark states in SU(3) cold gases with two-body losses, Phys. Rev. A 105, L051302 (2022).
  31. L. Rosso, A. Biella, J. De Nardis, and L. Mazza, Dynamical theory for one-dimensional fermions with strong two-body losses: Universal non-Hermitian Zeno physics and spin-charge separation, Phys. Rev. A 107, 013303 (2023).
  32. C. Y. Leung and A. Romito, Entanglement and operator correlation signatures of many-body quantum Zeno phases in inefficiently monitored noisy systems, Phys. Rev. A 111, 022427 (2025).
  33. M. M. Wauters, E. Ballini, A. Biella, and P. Hauke, Symmetry-protection Zeno phase transition in monitored lattice gauge theories, Phys. Rev. B 111, 094315 (2025).
  34. M. Ippoliti, M. J. Gullans, S. Gopalakrishnan, D. A. Huse, and V. Khemani, Entanglement phase transitions in measurement-only dynamics, Phys. Rev. X 11, 011030 (2021).
  35. G. Piccitto, A. Russomanno, and D. Rossini, Entanglement dynamics with string measurement operators, SciPost Phys. Core 6, 078 (2023).
  36. J. Jin, A. Biella, O. Viyuela, L. Mazza, J. Keeling, R. Fazio, and D. Rossini, Cluster mean-field approach to the steady-state phase diagram of dissipative spin systems, Phys. Rev. X 6, 031011 (2016).
  37. D. Huybrechts and M. Wouters, Dynamical hysteresis properties of the driven-dissipative Bose-Hubbard model with a Gutzwiller Monte Carlo approach, Phys. Rev. A 102, 053706 (2020).
  38. W. Verstraelen, D. Huybrechts, T. Roscilde, and M. Wouters, Quantum and classical correlations in open quantum spin lattices via truncated-cumulant trajectories, PRX Quantum 4, 030304 (2023).
  39. L. Ares, J. Pinske, B. Hinrichs, M. Kolb, and J. Sperling, Restricted Monte Carlo wave function method and Lindblad equation for identifying entangling open-quantum-system dynamics Phys. Rev. A 113, 012220 (2026).
  40. G. Villa, J. del Pino, V. Dumont, G. Rastelli, M. Michałek, A. Eichler, and O. Zilberberg, Topological classification of driven-dissipative nonlinear systems, Sci. Adv. 11, eadt9311 (2025).
  41. The flow represents the 2D velocity field of the variables (θL,θR) under the no-click dynamics of Eq. (9). The velocity (tangent to the streamlines) at any point (θL,θR) is given by (ΩL(θL,θR),ΩR(θL,θR)).
  42. Given that the full wave function is in general not factorizable one has to compute the on-site reduced density matrix for the L/R qubit and exploit the Bloch sphere representation which gives directly access to θL/R(i)(t) and thus compute the PDF.
  43. Z. Severino, G. Chakraborty, A. Romito, and A. Biella, Data for “Theory of the correlated quantum Zeno effect in a monitored qubit dimer” [Data set], Zenodo, 2025, http://doi.org/10.5281/zenodo.15260513.

Outline

Information

Phys. Rev. A 113, 062424– Published 8 June, 2026
  • Received 26 March 2026
  • Accepted 12 May 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation