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Initial-state inhomogeneities can make waiting times between quantum jumps finite and independent of system size, resolving detector limits while the measurement-induced phase transition survives, at the cost of longer entanglement saturati

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2026-07-12 08:53 UTC pith:Z4UWQWHA

load-bearing objection Clean angular-momentum control of waiting times that fully kills the 1/N detector problem at heta=π, with MIPT survival; the only real softness is the authors’ own caveat on saturation-time asymptotics. the 2 major comments →

arxiv 2607.01332 v2 pith:Z4UWQWHA submitted 2026-07-01 quant-ph cond-mat.othercond-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
classification quant-ph cond-mat.othercond-mat.stat-mech
keywords measurement-induced phase transitionsquantum trajectoriescollective spinswaiting timesdetector resolutionboundary time crystalpostselectionentanglement entropy
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

Collective monitored spin systems already ease the post-selection problem because entanglement saturates only logarithmically with size, yet their jump rate grows with N, so finite detector resolution eventually merges many jumps into one bin and spoils pure-state trajectories. This paper shows that a controllable initial-state twist—two equal sub-ensembles rotated by an angle θ—suppresses the collective decay rate and therefore lengthens the average waiting time between jumps. For intermediate θ the waiting time still falls as 1/N but with a prefactor that can be orders of magnitude larger; when the ensembles are fully anti-aligned the waiting time remains finite and size-independent, fully removing the detector-resolution barrier. The measurement-induced phase transition itself persists, with area-law and sub-logarithmic entanglement regimes still visible. The practical price is that entanglement now takes longer to saturate, partially reintroducing a post-selection overhead. The result is an experimentally tunable trade-off between detector resolution and the number of trajectories one must post-select.

Core claim

By partitioning a collectively monitored spin ensemble into two subsystems rotated by an angle θ, the average waiting time between quantum jumps can be controlled: it still scales as 1/N for intermediate θ but with a strongly enhanced prefactor, and becomes finite and independent of N when θ=π. The measurement-induced phase transition survives the inhomogeneity, showing area-law entanglement in the stationary phase and sub-logarithmic growth inside the boundary time-crystalline phase. Detector-resolution mitigation is therefore achieved, yet entanglement saturation times lengthen beyond the logarithmic scaling of the homogeneous case, partially restoring a post-selection cost.

What carries the argument

An angular-momentum bound on the jump rate: total spin is conserved on average over trajectories, so the waiting time satisfies W ≳ N/(2κ⟨J²⟩), where the initial relative orientation θ of the two sub-ensembles sets ⟨J²⟩ and can cancel the leading O(N²) term when the ensembles are anti-aligned.

Load-bearing premise

The claim that longer saturation times partially reintroduce the post-selection barrier rests on finite-size trends (up to N≈80) that the authors themselves describe as inconclusive for the largest sizes.

What would settle it

Prepare anti-aligned (θ=π) and intermediate-θ ensembles of several hundred spins, record waiting times and entanglement saturation times under continuous monitoring; if waiting time stays O(1) while saturation time grows only logarithmically (or slower than any power of N), the stated trade-off is weaker than claimed.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Detector temporal resolution no longer needs to improve with system size once the initial state is prepared anti-aligned.
  • The measurement-induced phase transition remains experimentally accessible with realistic finite-resolution detectors by tuning the initial-state angle.
  • Experiments must collect trajectories for longer times because entanglement saturates more slowly once inhomogeneity is present.
  • Intermediate angles give a continuous experimental dial between waiting-time gain and saturation-time cost.
  • Initial-state inhomogeneity itself becomes a route to highly entangled steady states without dark-state engineering.

Where Pith is reading between the lines

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

  • The same initial-state control of waiting times should transfer to other infinite-range monitored models whose jump operators scale with collective spin.
  • If larger-system data show that saturation time remains only polynomial, the residual post-selection overhead stays manageable for moderate experimental sizes.
  • Continuous drive or dissipation engineering might restore logarithmic saturation while preserving the waiting-time gain, eliminating the trade-off.
  • The logarithmic entanglement observed for all couplings when θ=π suggests anti-alignment effectively freezes the trajectory ensemble at a critical-like point.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 5 minor

Summary. The manuscript studies a collectively driven and monitored spin ensemble that supports a boundary time-crystalline (BTC) phase, and shows that a controllable initial-state inhomogeneity—implemented by bipartitioning the ensemble into two Dicke subsystems rotated by an angle θ—can systematically increase the average waiting time W between quantum jumps. An angular-momentum bound (Eqs. 16–22) demonstrates that W scales as 1/N with a θ-dependent prefactor that grows by orders of magnitude, remaining finite and N-independent for the anti-aligned case θ=π, thereby fully mitigating the detector-resolution barrier. Numerical quantum-trajectory simulations (MCWF, 250 trajectories) corroborate the bound (Fig. 4). The measurement-induced phase transition survives under inhomogeneity, with area-law and sub-logarithmic entanglement regimes whose critical point tracks the mean-field stationary-to-BTC boundary (Figs. 2 and 5). The authors also report that the entanglement saturation time t* lengthens with θ (Fig. 6c), partially reintroducing a post-selection cost and establishing an experimental trade-off between detector resolution and post-selection overhead.

Significance. The work addresses a concrete experimental bottleneck for measurement-induced phases in collective systems: finite detector temporal resolution that forces coarse-graining of trajectories when W∼1/N. The angular-momentum lower bound on W is model-derived, parameter-free once θ is fixed, and cleanly separates the waiting-time control from the more delicate saturation-time issue. Survival of the MIPT under inhomogeneity, together with the explicit trade-off between resolution and post-selection, supplies a practical design principle for cold-atom or cavity-QED platforms that already realize collective spin models. The finite-size caveat on t* is already acknowledged by the authors and does not undermine the central waiting-time claim.

major comments (2)
  1. Sec. IV B and Fig. 6c: the claim that inhomogeneity “partially reintroduces the postselection barrier” rests on a finite-size trend of t* that the authors themselves describe as inconclusive for the largest accessible sizes (N≤80). A polynomial fit t*∼N^α_θ is offered, yet the largest-N points for θ=π/2 and 2π/3 visibly flatten. Either additional system sizes, an asymptotic argument (e.g., spin-wave or large-N rate equations), or a more cautious statement that the thermodynamic scaling of t* remains open is needed before the quantitative severity of the re-introduced barrier can be asserted.
  2. Eqs. 16–22 and the surrounding text: the lower bound W≳N/(2κ⟨J^{2}⟩) is derived from the trajectory-averaged jump rate and angular-momentum conservation. While the numerics of Fig. 4 confirm that the bound captures the correct N and θ dependence, the manuscript never quantifies how tight the bound remains at intermediate times or deep in the BTC phase (where ⟨J_z⟩ and ⟨J_z^{2}⟩ fluctuate). A short comparison of the instantaneous ⟨J+J-⟩ against the initial ⟨J^{2}⟩ would strengthen the analytic claim.
minor comments (5)
  1. Fig. 2 caption and Sec. II A: the numerical threshold “standard deviation exceeds 0.05” used to locate the mean-field critical point is arbitrary; a brief sensitivity check or an alternative criterion (e.g., long-time Fourier peak) would improve reproducibility.
  2. Sec. IV, numerical methods: the first-order MCWF integrator with κdt=0.01/N is stated without a convergence test against smaller steps or higher-order schemes; a short remark would reassure readers that the waiting-time statistics are free of integrator bias.
  3. Eq. (8) and surrounding text: the long-time average window T_avg and the choice of t0 after the transient are not specified numerically; stating the values used for the data in Figs. 5–6 would aid reproduction.
  4. Typographical: “T rajectories” and “ST A TE PREP ARA TION” in section headings contain spurious spaces; “Schrödinger” is occasionally rendered with an incorrect umlaut encoding.
  5. References [54] and [55] are cited as arXiv preprints; if published versions now exist they should be updated.

Circularity Check

0 steps flagged

No significant circularity: waiting-time bound and MIPT survival are derived from the model operators and direct numerics, not forced by definition or self-citation.

full rationale

The central analytical result is the lower bound on average waiting time W(t) ≳ N/(2κ ⟨J^{2}⟩_{t=0}) obtained from the angular-momentum identity ⟨J_{+}J_{-}⟩ ≤ ⟨J^{2}⟩ + ⟨J_z⟩ together with conservation of total spin sectors under the Lindbladian (Eqs. 16–22). Expanding ⟨J^{2}⟩ for the bipartition initial state of Eq. (15) immediately yields the explicit θ dependence, including the O(1) finite value at θ=π; this is a direct algebraic consequence of the jump operator and the prepared state, not a fit or a renamed input. The survival of the MIPT and the entanglement scalings are measured from quantum-trajectory averages (Figs. 5–6), not assumed. Self-citations to earlier BTC/MIPT works supply background phase-diagram context and the homogeneous-limit logarithmic saturation time, but none of them is invoked as a uniqueness theorem or load-bearing premise that forces the new θ-dependent waiting-time or trade-off claims. No parameters are fitted to one data subset and then “predicted” on a related subset; no ansatz is smuggled via citation. The only softness (finite-size saturation-time trend) is already flagged by the authors themselves and does not circularize the waiting-time result. The derivation chain is therefore self-contained against the paper’s own equations and numerics.

Axiom & Free-Parameter Ledger

4 free parameters · 4 axioms · 0 invented entities

The paper rests on standard open-quantum-system axioms (Lindblad master equation, quantum-jump unraveling, angular-momentum conservation) plus one modeling choice (bipartite rotation of two equal Dicke ensembles). No new particles or forces are introduced. Free parameters are ordinary control knobs ( heta, ω_{0}/κ) and two fitted scaling exponents that are reported but not load-bearing for the waiting-time claim.

free parameters (4)
  • inhomogeneity angle heta
    Continuous experimental control parameter that sets the initial relative orientation of the two sub-ensembles; not fitted to data.
  • drive-to-dissipation ratio ω_{0}/κ
    Standard control parameter of the model; scanned to map the phase diagram.
  • entanglement scaling exponent eta_ heta
    Fitted from steady-state S_{N/2} vs N curves in the BTC phase; used only for characterization, not for the waiting-time bound.
  • saturation-time exponent α_ heta
    Polynomial fit t* ~ N^{α_ heta} to finite-size data; authors note the fit is inconclusive at largest N.
axioms (4)
  • domain assumption Lindblad master equation with collective jump operator L = √(2κ/N) J_- generates the ensemble-averaged dynamics
    Standard quantum-optics description of a driven, collectively decaying atomic ensemble (Sec. II A).
  • standard math Total angular momentum J^{2} is conserved on average over trajectories, so the weight of each total-spin sector is fixed by the initial state
    Follows from [J^{2}, H] = [J^{2}, L] = 0; used to bound the jump rate (Sec. IV A).
  • domain assumption Quantum-jump (MCWF) unraveling correctly samples the pure-state trajectories whose entanglement is the MIPT diagnostic
    Standard unraveling of the Lindblad equation (Sec. II B).
  • ad hoc to paper Initial state is a product of two fully polarized Dicke states rotated by heta about x
    Modeling choice that introduces controllable inhomogeneity while preserving intra-subsystem permutation symmetry (Eq. 15, Sec. III).

pith-pipeline@v1.1.0-grok45 · 17263 in / 2849 out tokens · 29135 ms · 2026-07-12T08:53:21.902411+00:00 · methodology

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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.

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 ↗

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