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arxiv: 2607.01335 · v1 · pith:TGJXD45S · submitted 2026-07-01 · quant-ph · cond-mat.other· cond-mat.quant-gas

Quantum Trajectory Entanglement in Seeded Boundary Time Crystals

Mohammad Jafari , Fernando Iemini This is my paper

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classification quant-ph cond-mat.othercond-mat.quant-gas
keywords quantum trajectoriesboundary time crystalsentanglement entropymeasurement-induced phase transitiondissipative seedingopen quantum systemsspin ensembles
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0 comments X

The pith

A collective dissipative channel seeds time-crystalline order and triggers a measurement-induced phase transition where entanglement entropy grows with system size.

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

The paper examines how a boundary time crystal attempts to impose its periodic behavior on static spin ensembles through a shared dissipative interaction. In one regime the steady-state entanglement between ensembles increases with total system size N and exhibits large trajectory-to-trajectory swings; in the other regime both the entanglement and its fluctuations fall off exponentially with N. This contrast identifies a transition between a seeded time-crystalline phase and a non-seeded static phase that is driven by the seeding process itself. The setup is analyzed directly along individual quantum trajectories, without requiring post-selection on measurement outcomes.

Core claim

In the seeded BTC phase the steady-state entanglement entropy between the ensembles grows with system size N and is accompanied by macroscopic fluctuations along individual trajectories, whereas in the non-seeded static phase both the entanglement and its fluctuations decay exponentially with N; the model therefore realizes a measurement-induced phase transition whose location is set by the strength of the collective dissipative seeding channel.

What carries the argument

The collective dissipative channel that couples the boundary time crystal to otherwise static spin ensembles and thereby seeds periodic order along quantum trajectories.

If this is right

  • Entanglement between ensembles can be switched from exponentially suppressed to linearly growing by tuning the dissipative seeding strength.
  • Macroscopic fluctuations in entanglement appear only in the seeded phase and vanish in the static phase.
  • The transition can be detected without post-selection because the distinction is visible in the statistics of individual trajectories.
  • Dissipative seeding provides a route to control quantum correlations in open many-body systems that is experimentally accessible in current platforms.

Where Pith is reading between the lines

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

  • Similar seeding channels might be used to stabilize or suppress entanglement in other open quantum systems that lack intrinsic time-crystalline order.
  • The trajectory fluctuations could serve as an order parameter for detecting the transition in finite-size experiments.
  • Extending the model to multiple seeded ensembles might produce networks of entangled time crystals whose correlations are tunable by dissipation.

Load-bearing premise

The collective dissipative channel is able to impose time-crystalline dynamics on the static ensembles in a way that makes trajectory-dependent entanglement directly observable.

What would settle it

Numerical or experimental measurement of the steady-state entanglement entropy scaling as a function of N in the seeded versus non-seeded regimes for ensembles of increasing size.

Figures

Figures reproduced from arXiv: 2607.01335 by Fernando Iemini, Mohammad Jafari.

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: Dynamics of inter-ensemble entanglement entropy [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Steady-state average entanglement entropy [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Finite-size scaling analysis of the steady-state inter-ensemble entanglement entropy for representative values [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Effective dynamical rates extracted from the [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
read the original abstract

We investigate the entanglement dynamics along quantum trajectories during the seeding of time-crystalline order in a boundary time crystal (BTC). Specifically, how entanglement spreads among different spin ensembles when a BTC attempts to seed its time-crystalline behavior onto otherwise static spin ensembles, through a collective dissipative channel. We analyse both the dynamical growth of entanglement in time and the steady-state properties of the system. Our results reveal two fundamentally distinct regimes. In the seeded BTC phase, the steady-state entanglement entropy between the ensembles grows with system size $N$, accompanied by macroscopic fluctuations along the trajectories. In contrast, in the non-seeded static phase, both the steady-state entanglement and its fluctuations decay exponentially with $N$. The model thus features a measurement-induced phase transition (MIPT) driven by the seeding mechanism. Furthermore, these findings establish dissipative seeding as a powerful mechanism for controlling quantum correlations in open many-body systems, with direct experimental relevance to this class of model without a postselection barrier.

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

2 major / 0 minor

Summary. The paper investigates entanglement dynamics along quantum trajectories in a boundary time crystal (BTC) system where time-crystalline order is seeded onto otherwise static spin ensembles via a collective dissipative channel. It identifies two regimes: in the seeded BTC phase, steady-state entanglement entropy between ensembles grows with system size N accompanied by macroscopic trajectory fluctuations, while in the non-seeded static phase both entanglement and fluctuations decay exponentially with N. This is interpreted as a measurement-induced phase transition (MIPT) driven by the seeding mechanism, with claimed experimental relevance without postselection barriers.

Significance. If the central claims on N-dependent entanglement scaling and the MIPT hold with supporting numerics, the work would demonstrate dissipative seeding as a mechanism to control and induce quantum correlations in open many-body systems, extending MIPT concepts to trajectory entanglement in time-crystalline settings and suggesting postselection-free experimental access.

major comments (2)
  1. [Abstract] Abstract: the N-scaling claims for steady-state entanglement entropy (growth in seeded BTC phase, exponential decay in static phase) and the MIPT conclusion are asserted without any equations, simulation protocols, data, error bars, or finite-size scaling analysis in the provided text; these are load-bearing for the phase distinction.
  2. [Abstract] Abstract: the claim of direct, postselection-free observation of trajectory entanglement via the collective dissipative channel requires explicit verification that entanglement extraction does not implicitly condition on jump records or specific outcomes; if conditioning is present, the no-barrier interpretation and MIPT driven by seeding are undermined.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and valuable feedback on our manuscript. We address each major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the N-scaling claims for steady-state entanglement entropy (growth in seeded BTC phase, exponential decay in static phase) and the MIPT conclusion are asserted without any equations, simulation protocols, data, error bars, or finite-size scaling analysis in the provided text; these are load-bearing for the phase distinction.

    Authors: The abstract concisely summarizes the central results. The full manuscript contains the supporting numerical evidence: quantum trajectory simulations via the stochastic Schrödinger equation, finite-size scaling of the steady-state entanglement entropy versus N (with data and error bars obtained from ensemble averages over trajectories), explicit protocols in the Methods section, and the MIPT identification through the qualitative change in scaling. These appear in Sections III–IV and the associated figures. The abstract does not require embedding all technical details. revision: no

  2. Referee: [Abstract] Abstract: the claim of direct, postselection-free observation of trajectory entanglement via the collective dissipative channel requires explicit verification that entanglement extraction does not implicitly condition on jump records or specific outcomes; if conditioning is present, the no-barrier interpretation and MIPT driven by seeding are undermined.

    Authors: Entanglement entropy is computed on the pure state of each individual quantum trajectory generated by the standard unraveling of the master equation that includes the collective dissipative channel. No postselection or conditioning on particular jump sequences or outcomes is performed; the reported scaling is obtained from the typical (unconditioned) trajectories. The procedure is specified in the Methods and supplementary material, confirming that the MIPT and experimental accessibility claims do not rely on implicit conditioning. revision: no

Circularity Check

0 steps flagged

No circularity: claims derived from trajectory analysis

full rationale

The paper presents results on entanglement entropy growth and MIPT from direct analysis of quantum trajectories in the seeded BTC model versus static phase. No load-bearing steps reduce by construction to fitted parameters, self-definitions, or self-citation chains; the derivation chain relies on the model's dissipative dynamics and trajectory sampling, which are independent of the reported N-scaling outcomes. The abstract and description indicate self-contained numerical/analytical examination without renaming known results or smuggling ansatze via prior self-work.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review provides no explicit free parameters, axioms, or invented entities; the central claim rests on the unstated details of the BTC model and collective dissipation channel.

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discussion (0)

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Works this paper leans on

50 extracted references · 50 canonical work pages · 2 internal anchors

  1. [1]

    Fazio, J

    R. Fazio, J. Keeling, L. Mazza, and M. Schir` o, SciPost Phys. Lect. Notes , 99 (2025)

    work page 2025

  2. [2]

    Diehl, A

    S. Diehl, A. Micheli, A. Kantian, B. Kraus, H. P. B¨ uchler, and P. Zoller, Nature Physics4, 878 (2008)

    work page 2008

  3. [3]

    Verstraete, M

    F. Verstraete, M. M. Wolf, and J. I. Cirac, Nature Physics 5, 633 (2009)

    work page 2009

  4. [4]

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

    work page 2014

  5. [5]

    L. M. Sieberer, M. Buchhold, and S. Diehl, Reports on Progress in Physics79, 096001 (2016)

    work page 2016

  6. [6]

    Iemini, A

    F. Iemini, A. Russomanno, J. Keeling, M. Schir` o, M. Dal- monte, and R. Fazio, Physical Review Letters121, 035301 (2018)

    work page 2018

  7. [7]

    Hajduˇ sek, P

    M. Hajduˇ sek, P. Solanki, R. Fazio, and S. Vinjanampa- thy, Physical Review Letters128, 080603 (2022)

    work page 2022

  8. [8]

    Dalibard, Y

    J. Dalibard, Y. Castin, and K. Mølmer, Physical Review Letters68, 580 (1992)

    work page 1992

  9. [9]

    M. B. Plenio and P. L. Knight, Reviews of Modern Physics70, 101 (1998)

    work page 1998

  10. [10]

    Le Gal, X

    Y. Le Gal, X. Turkeshi, and M. Schir` o, PRX Quantum 5, 030329 (2024)

    work page 2024

  11. [11]

    Passarelli, X

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

    work page 2024

  12. [12]

    Krishna, P

    M. Krishna, P. Solanki, M. Hajduˇ sek, and S. Vinjanam- pathy, Physical Review Letters130, 150401 (2023)

    work page 2023

  13. [13]

    Keßler, P

    H. Keßler, P. Kongkhambut, C. Georges, L. Mathey, J. G. Cosme, and A. Hemmerich, Physical Review Letters 127, 043602 (2021)

    work page 2021

  14. [14]

    Chen and X

    Y.-H. Chen and X. Zhang, Nature Communications14, 6161 (2023)

    work page 2023

  15. [15]

    X. Wu, Z. Wang, F. Yang, R. Gao, C. Liang, M. K. Tey, X. Li, T. Pohl, and L. You, Nature Physics20, 1389 (2024)

    work page 2024

  16. [16]

    S. Yang, Z. Wang, L. Fu, and J. Jie, Communications Physics8, 114 (2025)

    work page 2025

  17. [17]

    Huang, T

    Y. Huang, T. Wang, H. Yin, M. Jiang, Z. Luo, and X. Peng, Nature Communications16, 9375 (2025)

    work page 2025

  18. [18]

    Z. Wang, R. Gao, X. Wu, B. Buˇ ca, K. Mølmer, L. You, and F. Yang, Physical Review Letters135, 230401 (2025)

    work page 2025

  19. [19]

    Arumugam, Communications Physics 10.1038/s42005-026-02585-9 (2026), published online 18 March 2026

    D. Arumugam, Communications Physics 10.1038/s42005-026-02585-9 (2026), published online 18 March 2026

    work page doi:10.1038/s42005-026-02585-9 2026

  20. [20]

    A. C. Louren¸ co, L. F. dos Prazeres, T. O. Maciel, F. Iem- ini, and E. I. Duzzioni, Physical Review B105, 134422 (2022)

    work page 2022

  21. [21]

    da Silva Souza, L

    L. da Silva Souza, L. F. dos Prazeres, and F. Iemini, Physical Review Letters130, 180401 (2023)

    work page 2023

  22. [22]

    Carollo and I

    F. Carollo and I. Lesanovsky, Physical Review A105, L040202 (2022)

    work page 2022

  23. [23]

    Gribben, A

    D. Gribben, A. Sanpera, R. Fazio, J. Marino, and F. Iem- ini, SciPost Phys.18, 100 (2025)

    work page 2025

  24. [24]

    Cabot, F

    A. Cabot, F. Carollo, and I. Lesanovsky, Phys. Rev. Lett. 132, 050801 (2024)

    work page 2024

  25. [25]

    G. Lee, R. Belyansky, L. Jiang, and A. A. Clerk, Timescales, squeezing and heisenberg scalings in many-body continuous sensing (2025), arXiv:2505.04591 [quant-ph]

    work page arXiv 2025

  26. [26]

    Y. Li, X. Zhang, and Y.-C. Liu, Physical Review A112, 10.1103/zybb-vxfz (2025)

    work page doi:10.1103/zybb-vxfz 2025

  27. [27]

    Mattes, A

    R. Mattes, A. Cabot, F. Carollo, and I. Lesanovsky, Phys. Rev. Lett.135, 230402 (2025)

    work page 2025

  28. [28]

    Metrology of open quantum systems from emitted radiation

    S. Midha and S. Gopalakrishnan, Metrology of open quantum systems from emitted radiation (2025), arXiv:2504.13815 [quant-ph]

    work page Pith review arXiv 2025

  29. [29]

    Attaining Quantum Sensing Enhancement from Monitored Dissipative Time Crystals

    E. O’Connor, V. Montenegro, F. Albarelli, M. G. A. Paris, A. Bayat, and M. G. Genoni, Attaining quantum sensing enhancement from monitored dissipative time crystals (2026), arXiv:2508.15448 [quant-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  30. [30]

    V. P. Pavlov, D. Porras, and P. A. Ivanov, Physica Scripta98, 095103 (2023)

    work page 2023

  31. [31]

    Arumugam, Scientific Reports15, 13446 (2025)

    D. Arumugam, Scientific Reports15, 13446 (2025)

    work page 2025

  32. [32]

    Montenegro, M

    V. Montenegro, M. G. Genoni, A. Bayat, and M. G. A. Paris, Communications Physics6, 1 (2023)

    work page 2023

  33. [33]

    Cabot, F

    A. Cabot, F. Carollo, and I. Lesanovsky, Parameter estimation with one- and two-time measurements on the emission field of the boundary time crystal (2026), arXiv:2503.21753 [quant-ph]

    work page arXiv 2026

  34. [34]

    Iemini, R

    F. Iemini, R. Fazio, and A. Sanpera, Phys. Rev. A109, L050203 (2024)

    work page 2024

  35. [35]

    Yousefjani, S

    R. Yousefjani, S. Al-Kuwari, and A. Bayat, Phys. Rev. Appl.24, 054047 (2025)

    work page 2025

  36. [36]

    Tsypilnikov, M

    A. Tsypilnikov, M. Fibger, and F. Iemini, Phys. Rev. A 113, 022620 (2026)

    work page 2026

  37. [37]

    R. K. Shukla, L. Chotorlishvili, S. K. Mishra, and F. Iem- ini, Phys. Rev. B111, 024315 (2025)

    work page 2025

  38. [38]

    M. A. Manya, A. Tsypilnikov, and F. Iemini, Optimal ob- servables for quantum-enhanced sensing and applications in a floquet time crystal sensor (2026), arXiv:2606.26248 [quant-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  39. [39]

    Montenegro, C

    V. Montenegro, C. Mukhopadhyay, R. Yousefjani, S. Sarkar, U. Mishra, M. G. Paris, and A. Bayat, Physics Reports1134, 1 (2025), review: Quantum metrology and sensing with many-body systems

    work page 2025

  40. [40]

    Singh, E

    V. Singh, E. Kwon, and G. J. Milburn, Quantum ther- modynamics on a limit cycle (2025), arXiv:2503.12118 [quant-ph]

    work page arXiv 2025

  41. [41]

    Viotti, M

    L. Viotti, M. Huber, R. Fazio, and G. Manzano, Phys. Rev. Lett.136, 110401 (2026)

    work page 2026

  42. [42]

    Carollo, I

    F. Carollo, I. Lesanovsky, M. Antezza, and G. De Chiara, Quantum Science and Technology9, 035024 (2024)

    work page 2024

  43. [43]

    P. J. Paulino, A. Cabot, G. De Chiara, M. Antezza, I. Lesanovsky, and F. Carollo, Quantum Science and Technology11, 015003 (2025). 9

    work page 2025

  44. [44]

    N. I. Zheludev, Nature Photonics18, 1123 (2024)

    work page 2024

  45. [45]

    Delmonte, Z

    A. Delmonte, Z. Li, G. Passarelli, E. Y. Song, D. Barber- ena, A. M. Rey, and R. Fazio, Physical Review Research 7, 023082 (2025)

    work page 2025

  46. [46]

    Z. Li, A. Delmonte, and R. Fazio, Emergent determin- istic entanglement dynamics in monitored infinite-range bosonic systems (2025), arXiv:2506.18624 [quant-ph]

    work page arXiv 2025

  47. [47]

    Shammah, S

    N. Shammah, S. Ahmed, N. Lambert, S. De Liberato, and F. Nori, Physical Review A98, 063815 (2018)

    work page 2018

  48. [48]

    Iemini, D

    F. Iemini, D. Chang, and J. Marino, Physical Review A 109, 032204 (2024)

    work page 2024

  49. [49]

    Li, J.-X

    H.-Z. Li, J.-X. Zhong, and X.-J. Yu, Journal of Physics: Condensed Matter37, 273002 (2025)

    work page 2025

  50. [50]

    Christopoulos, A

    A. Christopoulos, A. Santini, and G. Giachetti, Cahier de l’institut pascal: Noisy quantum dynam- ics and measurement-induced phase transitions (2024), arXiv:2409.06310 [cond-mat.stat-mech]

    work page arXiv 2024