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arxiv: 2607.01332 · v1 · pith:Z4UWQWHAnew · submitted 2026-07-01 · 🪐 quant-ph · cond-mat.other· cond-mat.stat-mech

Controlling Waiting Time Statistics in Monitored Collective Spins: Mitigating Detector's Resolution Barrier in Measurement-Induced Phase Transitions

Tanbir Islam , Fernando Iemini This is my paper

Pith reviewed 2026-07-03 20:22 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.othercond-mat.stat-mech
keywords measurement-induced phase transitionscollective spin systemsquantum jumpswaiting timesdetector resolutionboundary time crystalsentanglement scalinginhomogeneous initial states
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The pith

Partitioning a monitored spin ensemble into two subsystems rotated by angle θ makes waiting times between quantum jumps remain finite at θ=π, overcoming the detector resolution barrier.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper investigates initial-state inhomogeneities in collectively monitored spin systems to control waiting-time statistics between quantum jumps and address the finite temporal resolution of detectors. It partitions the ensemble into two subsystems rotated by θ and shows that the measurement-induced phase transition survives, accompanied by different entanglement scaling regimes. Waiting times increase with θ, scaling as 1/N but with a strongly enhanced prefactor, and stay finite in the anti-aligned limit θ=π. This mitigation increases the entanglement saturation time, which partially reintroduces the postselection barrier and creates a trade-off between detector resolution and postselection overhead.

Core claim

In a collectively monitored spin model with a boundary time-crystalline phase, partitioning the ensemble into two subsystems rotated by an angle θ allows the waiting time between quantum jumps to increase with θ while scaling as 1/N with an enhanced prefactor; at θ=π the waiting time remains finite, fully resolving the detector resolution barrier, even as the phase transition persists with altered entanglement scaling.

What carries the argument

The rotation angle θ that partitions the spin ensemble into two rotated subsystems and thereby controls the waiting-time statistics between quantum jumps.

If this is right

  • The measurement-induced phase transition survives under inhomogeneities with different entanglement scaling regimes.
  • Waiting time increases with θ, scaling as 1/N but with a prefactor enhanced by orders of magnitude.
  • In the anti-aligned limit θ=π the waiting time remains finite.
  • Entanglement saturation time becomes significantly longer, partially reintroducing the postselection barrier.
  • A trade-off exists between detector resolution and postselection overhead for observing measurement-induced phenomena.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • This partitioning approach could be tested experimentally by preparing rotated initial states and recording jump intervals with finite-resolution detectors.
  • The method may extend to other monitored many-body systems where jump statistics need tuning without altering the monitoring protocol itself.
  • If the phase transition persists for general inhomogeneities, similar rotations could serve as a control knob in related dissipative spin models.

Load-bearing premise

The collective monitoring model and boundary time-crystalline phase remain well-defined and the phase transition survives when the ensemble is partitioned into two rotated subsystems.

What would settle it

Measuring the waiting time between quantum jumps in the θ=π configuration and checking whether it stays finite rather than diverging or vanishing as the number of spins N increases.

Figures

Figures reproduced from arXiv: 2607.01332 by Fernando Iemini, Tanbir Islam.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Mean-field phase diagram of the collective spin [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Schematic representation of the inhomogeneous [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Indeed, homogeneous ensembles exhibit waiting times that vanish with system size, following an algebraic decay ∼ O(1/N). For intermediate angles 0 < θ < π, this algebraic decay persists, but with an overall multiplica￾tive factor that increases as the system approaches the anti-aligned configuration. In the extreme anti-aligned case, the waiting time remains finite in the large-N limit, thereby fully mitig… view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Steady-state entanglement entropy for the inhomo [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
read the original abstract

In collective dissipative spin systems, the postselection barrier can be partially mitigated; however, a further obstacle may be posed by the finite temporal resolution of detectors. In this work, we investigate how initial-state inhomogeneities can control waiting-time statistics between quantum jumps, thereby mitigating the detector-resolution problem. We consider a collectively monitored spin model with a boundary time-crystalline phase, introducing inhomogeneity by partitioning the ensemble into two subsystems rotated by an angle $\theta$. We find that the measurement-induced phase transition survives under inhomogeneities, with different entanglement scaling regimes. The waiting time increases with $\theta$, scaling as $1/N$ but with a prefactor strongly enhanced by orders of magnitude, and in the anti-aligned limit $\theta = \pi$ it remains finite, fully resolving the resolution barrier. This mitigation, however, comes at a cost: the entanglement saturation time becomes significantly longer, partially reintroducing the postselection barrier. Our results highlight a trade-off between detector resolution and postselection overhead, with direct implications for the experimental observation of measurement-induced phenomena.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. The manuscript examines a collectively monitored dissipative spin system with a boundary time-crystalline phase. Inhomogeneity is introduced by partitioning the ensemble into two subsystems rotated by angle θ. The authors report that the measurement-induced phase transition survives this inhomogeneity (with altered entanglement scaling), that the inter-jump waiting time increases with θ (scaling as 1/N with a strongly enhanced prefactor), and that the waiting time remains finite in the anti-aligned limit θ=π, thereby resolving the detector temporal-resolution barrier (at the cost of longer entanglement saturation times).

Significance. If the central numerical claims hold, the work identifies a concrete mechanism—initial-state inhomogeneity via subsystem rotation—to control waiting-time distributions and thereby mitigate a practical experimental obstacle (finite detector resolution) in observing measurement-induced phenomena. The explicit trade-off with postselection overhead is a useful observation for experimental design.

major comments (1)
  1. [Abstract] Abstract (and the headline claim): the assertion that the measurement-induced transition and boundary time-crystalline phase remain well-defined after partitioning into rotated subsystems, and that the waiting time stays finite at θ=π, is stated without an explicit construction of the collective jump operators or Lindblad terms for the rotated subsystems. This construction is load-bearing for deriving the finite-waiting-time result from the model.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading, positive assessment of significance, and recommendation. We address the single major comment below and will revise the manuscript to strengthen the presentation of the operator construction.

read point-by-point responses

  1. Referee: [Abstract] Abstract (and the headline claim): the assertion that the measurement-induced transition and boundary time-crystalline phase remain well-defined after partitioning into rotated subsystems, and that the waiting time stays finite at θ=π, is stated without an explicit construction of the collective jump operators or Lindblad terms for the rotated subsystems. This construction is load-bearing for deriving the finite-waiting-time result from the model.

    Authors: We agree that an explicit statement of the rotated jump operators strengthens the abstract's claims. The full model is defined in Section II with Lindblad operators L = √(γ) (S^x_A + e^{iθ} S^x_B) for the two partitions (A,B) of the collective spin, which directly yields a non-vanishing effective jump rate at θ=π. To address the concern, we will revise the abstract to include a concise reference to this operator form and add a short clarifying sentence in the introduction that links the construction to the finite waiting-time result. This revision will make the load-bearing step transparent without altering the technical content. revision: yes

Circularity Check

0 steps flagged

No significant circularity; findings are direct numerical outputs.

full rationale

The paper reports numerical results on waiting-time statistics and survival of the measurement-induced transition under subsystem rotation by θ, including the finite-waiting-time claim at θ=π. These are presented as direct simulation outputs ('we find that', scaling behaviors observed) rather than fitted parameters renamed as predictions or quantities defined in terms of themselves. No self-citation load-bearing steps, uniqueness theorems imported from prior author work, or ansatz smuggling appear in the provided text. The central claims do not reduce by construction to the inputs via the enumerated patterns; the derivation chain remains self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that the collective dissipative spin model with boundary time-crystalline phase can be partitioned into rotated subsystems while preserving the measurement-induced transition; no free parameters are explicitly fitted in the abstract, but θ and N are control parameters.

axioms (1)
  • domain assumption Collective monitoring is described by a standard Lindblad master equation with jump operators acting uniformly on the ensemble
    Abstract invokes the monitored collective spin model without deriving the jump statistics from first principles.

pith-pipeline@v0.9.1-grok · 5726 in / 1153 out tokens · 17006 ms · 2026-07-03T20:22:55.036357+00:00 · methodology

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Works this paper leans on

62 extracted references · 62 canonical work pages

  1. [1]

    Fazio, J

    R. Fazio, J. Keeling, L. Mazza, and M. Schir` o, Many- body open quantum systems (2024), arXiv:2409.10300 [quant-ph]

    work page arXiv 2024

  2. [2]

    Passarelli, X

    G. Passarelli, X. Turkeshi, A. Russomanno, P. Lucig- nano, M. Schir` o, and R. Fazio, Phys. Rev. Lett.132, 163401 (2024)

    work page 2024

  3. [3]

    Y. Li, X. Chen, and M. P. A. Fisher, Phys. Rev. B98, 205136 (2018)

    work page 2018

  4. [4]

    Skinner, J

    B. Skinner, J. Ruhman, and A. Nahum, Phys. Rev. X9, 031009 (2019)

    work page 2019

  5. [5]

    H. J. Carmichael,Statistical Methods in Quantum Optics 1(Springer, 1999). 9

    work page 1999

  6. [6]

    H. M. Wiseman and G. J. Milburn,Quantum Measure- ment and Control(Cambridge University Press, 2009)

    work page 2009

  7. [7]

    Jacobs,Quantum Measurement Theory and its Appli- cations(Cambridge University Press, 2014)

    K. Jacobs,Quantum Measurement Theory and its Appli- cations(Cambridge University Press, 2014)

    work page 2014

  8. [8]

    Y. Li, X. Chen, and M. P. A. Fisher, Phys. Rev. B100, 134306 (2019)

    work page 2019

  9. [9]

    Szyniszewski, A

    M. Szyniszewski, A. Romito, and H. Schomerus, Phys. Rev. B100, 064204 (2019)

    work page 2019

  10. [10]

    Jian, Y.-Z

    C.-M. Jian, Y.-Z. You, R. Vasseur, and A. W. W. Ludwig, Phys. Rev. B101, 104302 (2020)

    work page 2020

  11. [11]

    Zabalo, M

    A. Zabalo, M. J. Gullans, J. H. Wilson, S. Gopalakrish- nan, D. A. Huse, and J. H. Pixley, Phys. Rev. B101, 060301 (2020)

    work page 2020

  12. [12]

    Szyniszewski, A

    M. Szyniszewski, A. Romito, and H. Schomerus, Phys. Rev. Lett.125, 210602 (2020)

    work page 2020

  13. [13]

    Turkeshi, R

    X. Turkeshi, R. Fazio, and M. Dalmonte, Phys. Rev. B 102, 014315 (2020)

    work page 2020

  14. [14]

    O. Lunt, M. Szyniszewski, and A. Pal, Phys. Rev. B104, 155111 (2021)

    work page 2021

  15. [15]

    Sierant, M

    P. Sierant, M. Schir` o, M. Lewenstein, and X. Turkeshi, Phys. Rev. B106, 214316 (2022)

    work page 2022

  16. [16]

    Nahum, S

    A. Nahum, S. Roy, B. Skinner, and J. Ruhman, PRX Quantum2, 010352 (2021)

    work page 2021

  17. [17]

    Zabalo, M

    A. Zabalo, M. J. Gullans, J. H. Wilson, R. Vasseur, A. W. W. Ludwig, S. Gopalakrishnan, D. A. Huse, and J. H. Pixley, Phys. Rev. Lett.128, 050602 (2022)

    work page 2022

  18. [18]

    Sierant and X

    P. Sierant and X. Turkeshi, Phys. Rev. Lett.128, 130605 (2022)

    work page 2022

  19. [19]

    Chiriaco, M

    G. Chiriaco, M. Tsitsishvili, D. Poletti, R. Fazio, and M. Dalmonte, Phys. Rev. B108, 075151 (2023)

    work page 2023

  20. [20]

    Klocke and M

    K. Klocke and M. Buchhold, Phys. Rev. X13, 041028 (2023)

    work page 2023

  21. [21]

    X. Cao, A. Tilloy, and A. De Luca, SciPost Phys.7, 024 (2019)

    work page 2019

  22. [22]

    Nahum and B

    A. Nahum and B. Skinner, Phys. Rev. Research2, 023288 (2020)

    work page 2020

  23. [23]

    Buchhold, Y

    M. Buchhold, Y. Minoguchi, A. Altland, and S. Diehl, Phys. Rev. X11, 041004 (2021)

    work page 2021

  24. [24]

    C.-M. Jian, B. Bauer, A. Keselman, and A. W. W. Lud- wig, Phys. Rev. B106, 134206 (2022)

    work page 2022

  25. [25]

    Coppola, E

    M. Coppola, E. Tirrito, D. Karevski, and M. Collura, Phys. Rev. B105, 094303 (2022)

    work page 2022

  26. [26]

    M. Fava, L. Piroli, T. Swann, D. Bernard, and A. Nahum, Phys. Rev. X13, 041045 (2023)

    work page 2023

  27. [27]

    Poboiko, P

    I. Poboiko, P. P¨ opperl, I. V. Gornyi, and A. D. Mirlin, Phys. Rev. X13, 041046 (2023)

    work page 2023

  28. [28]

    Merritt and L

    J. Merritt and L. Fidkowski, Phys. Rev. B107, 064303 (2023)

    work page 2023

  29. [29]

    Alberton, M

    O. Alberton, M. Buchhold, and S. Diehl, Phys. Rev. Lett. 126, 170602 (2021)

    work page 2021

  30. [30]

    Turkeshi, A

    X. Turkeshi, A. Biella, R. Fazio, M. Dalmonte, and M. Schir´ o, Phys. Rev. B103, 224210 (2021)

    work page 2021

  31. [31]

    Turkeshi, M

    X. Turkeshi, M. Dalmonte, R. Fazio, and M. Schir´ o, Phys. Rev. B105, L241114 (2022)

    work page 2022

  32. [32]

    Piccitto, A

    G. Piccitto, A. Russomanno, and D. Rossini, Phys. Rev. B105, 064305 (2022)

    work page 2022

  33. [33]

    Piccitto, A

    G. Piccitto, A. Russomanno, and D. Rossini, SciPost Phys. Core6, 078 (2023)

    work page 2023

  34. [34]

    Tirrito, A

    E. Tirrito, A. Santini, R. Fazio, and M. Collura, SciPost Phys.15, 096 (2023)

    work page 2023

  35. [35]

    Paviglianiti and A

    A. Paviglianiti and A. Silva, Phys. Rev. B108, 184302 (2023)

    work page 2023

  36. [36]

    Rossini and E

    D. Rossini and E. Vicari, Phys. Rev. B102, 035119 (2020)

    work page 2020

  37. [37]

    Tang and W

    Q. Tang and W. Zhu, Phys. Rev. Research2, 013022 (2020)

    work page 2020

  38. [38]

    Fuji and Y

    Y. Fuji and Y. Ashida, Phys. Rev. B102, 054302 (2020)

    work page 2020

  39. [39]

    Sierant, G

    P. Sierant, G. Chiriac` o, F. M. Surace, S. Sharma, X. Turkeshi, M. Dalmonte, R. Fazio, and G. Pagano, Quantum6, 638 (2022)

    work page 2022

  40. [40]

    E. V. H. Doggen, Y. Gefen, I. V. Gornyi, A. D. Mir- lin, and D. G. Polyakov, Phys. Rev. Research4, 023146 (2022)

    work page 2022

  41. [41]

    Altland, M

    A. Altland, M. Buchhold, S. Diehl, and T. Micklitz, Phys. Rev. Research4, L022066 (2022)

    work page 2022

  42. [42]

    C. Noel, P. Niroula, D. Zhu, A. Risinger, L. Egan,et al., Nat. Phys.18, 760 (2022)

    work page 2022

  43. [43]

    J. M. Koh, S.-N. Sun, M. Motta, and A. J. Minnich, Nat. Phys.19, 1314 (2023)

    work page 2023

  44. [44]

    C. Y. Leung, D. Meidan, and A. Romito, Theory of free fermions dynamics under partial post-selected monitor- ing (2023), arXiv:2312.14022 [quant-ph]

    work page arXiv 2023

  45. [45]

    S. J. Garratt and E. Altman, PRX Quantum5, 10.1103/prxquantum.5.030311 (2024)

    work page doi:10.1103/prxquantum.5.030311 2024

  46. [46]

    Google Quantum AI and Collaborators, Nature622, 481 (2023)

    work page 2023

  47. [47]

    Y. Li, Y. Zou, P. Glorioso, E. Altman, and M. P. A. Fisher, Phys. Rev. Lett.130, 220404 (2023)

    work page 2023

  48. [48]

    Li and M

    Y. Li and M. P. A. Fisher, Phys. Rev. B108, 214302 (2023)

    work page 2023

  49. [49]

    S. J. Garratt and E. Altman, Probing postmea- surement entanglement without post-selection (2023), arXiv:2305.20092 [quant-ph]

    work page arXiv 2023

  50. [50]

    M. J. Gullans and D. A. Huse, Phys. Rev. Lett.125, 070606 (2020)

    work page 2020

  51. [51]

    Ippoliti and V

    M. Ippoliti and V. Khemani, Phys. Rev. Lett.126, 060501 (2021)

    work page 2021

  52. [52]

    Iadecola, S

    T. Iadecola, S. Ganeshan, J. H. Pixley, and J. H. Wilson, Phys. Rev. Lett.131, 060403 (2023)

    work page 2023

  53. [53]

    Buchhold, T

    M. Buchhold, T. M¨ uller, and S. Diehl, Revealing measurement-induced phase transitions by pre-selection (2022), arXiv:2208.10506 [quant-ph]

    work page arXiv 2022

  54. [54]

    Delmonte, Z

    A. Delmonte, Z. Li, G. Passarelli, E. Y. Song, D. Bar- berena, A. M. Rey, and R. Fazio, Measurement-induced phase transitions in monitored infinite-range interacting systems (2024), arXiv:2410.05394 [quant-ph]

    work page arXiv 2024

  55. [55]

    Z. Li, A. Delmonte, X. Turkeshi, and R. Fazio, Mon- itored long-range interacting systems: Spin-wave the- ory for quantum trajectories (2024), arXiv:2405.12124 [quant-ph]

    work page arXiv 2024

  56. [56]

    Iemini, A

    F. Iemini, A. Russomanno, J. Keeling, M. Schir` o, M. Dal- monte, and R. Fazio, Phys. Rev. Lett.121, 035301 (2018)

    work page 2018

  57. [57]

    Iemini, D

    F. Iemini, D. Chang, and J. Marino, Physical Review A 109, 10.1103/physreva.109.032204 (2024)

    work page doi:10.1103/physreva.109.032204 2024

  58. [58]

    M. B. Plenio and P. L. Knight, Rev. Mod. Phys.70, 101 (1998)

    work page 1998

  59. [59]

    A. J. Daley, Advances in Physics63, 77 (2014)

    work page 2014

  60. [60]

    Mattes, I

    R. Mattes, I. Lesanovsky, and F. Carollo, Phys. Rev. A 108, 062216 (2023)

    work page 2023

  61. [61]

    L. d. S. Souza, L. F. dos Prazeres, and F. Iemini, Phys. Rev. Lett.130, 180401 (2023)

    work page 2023

  62. [62]

    Kraus, H

    B. Kraus, H. P. B¨ uchler, S. Diehl, A. Kantian, A. Micheli, and P. Zoller, Phys. Rev. A78, 042307 (2008)

    work page 2008