{"id":"5999cdac-b027-4ad8-a224-266c97e1819e","arxiv_id":"2412.04168","paper_version":3,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"A feedback protocol that uses the quantum Fisher information as a cost function prepares GHZ-type entangled state manifolds, with numerical evidence of scalability to at least 22 qubits.","lead":"A new quantum control method repeatedly measures qubits weakly and applies feedback chosen to increase the quantum Fisher information, driving the system toward a genuinely entangled GHZ state. Simulations with up to 22 qubits indicate that the approach prepares such states with a step count that grows only slowly with system size.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The GHZ-manifold claim rests on average QFI and an N=5 phase histogram; per-trajectory fidelity and success probability are never reported, so 'efficiently reaches' and 'scalable' may overstate what the numerics establish.","rationale":"The reader's weakest_assumption names the same core issue: convergence to the GHZ manifold is supported only by numerical simulation to N=22, without direct state fidelity or analytic convergence guarantees. My stress-test sharpens this by emphasizing that the reported metric is the trajectory-averaged QFI, which can in principle be high even if many individual trajectories fail to approach the GHZ manifold. Since the paper's stated goal is to 'efficiently reach' a state manifold, the decisive evidence would be the per-trajectory distribution of overlap with Eq. (1), not just an entanglement witness. The protocol is nonetheless well posed, the numerics are reproducible, and the authors are appropriately cautious in their language. The conditional verdict is therefore not changed, but the proposed concrete test would either strengthen the central claim or expose a need to soften it.","tokens_in":14451,"tokens_out":8318,"duration_ms":96610,"concrete_test":"Run the deposited code/data for N = 5, 10, 16, 22 and, for each stored trajectory at nt = 500 (or at first crossing of FQ >= 0.9 N^2), compute F_GHZ = max_phi |<psi| (|0'...0'> + e^{i phi} |1'...1'>)/sqrt(2) |^2 in the rotated basis of Eq. (1), and record the distribution of F_GHZ together with the fraction of trajectories exceeding 0.9. If the median F_GHZ remains high and the success fraction does not decay with N, the concern is resolved; if the average QFI is carried by a minority of runs, the 'scalable efficiency' claim must be weakened.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim (abstract and Sec. III) is that the protocol reaches the one-parameter GHZ manifold of Eq. (1) and that the required number of steps scales as nt ~ A + B ln N (Fig. 5). The load-bearing evidence is the measurement-averaged QFI of Eq. (6), not a distance to the target manifold. For pure states, FQ/N^2 >= 0.9 does imply a large probability in the two-dimensional GHZ subspace, so large average QFI is suggestive; however, the paper only reports trajectory-averaged FQ and a phase histogram for N=5. It does not report the per-trajectory fidelity to the GHZ manifold or the fraction of trajectories that actually reach FQ >= 0.9 N^2 by nt=500. If the average is dominated by a subset of successful trajectories, then the protocol does not 'efficiently reach' the manifold in a scalable sense. Moreover, the greedy per-pair maximization of <dFQ>_ms in Sec. II has no convergence proof; the state space dimension is exponential, and local traps are plausible for N > 22. Together, these gaps make the scalability claim an extrapolation rather than a demonstrated property.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript proposes an active steering protocol for preparing multipartite entangled states. Each protocol step couples qubit pairs to detector qubits, evolves under a feedback Hamiltonian chosen to maximize the measurement-averaged change of the Quantum Fisher Information, and then performs weak Bell-pair measurements on the detectors. The protocol is applied to the one-parameter GHZ manifold of Eq. (1), with numerical simulations for N up to 22 showing that the average QFI approaches N^2 and that the number of steps to reach F_Q = 0.9 N^2 grows approximately logarithmically with N. The same cost-function framework is also used to target Dicke states for N up to 18. The paper claims that using the QFI as a cost function makes active steering scalable to larger system sizes, and it provides source code and data for the simulations.","tokens_in":14738,"tokens_out":4797,"duration_ms":51356,"significance":"If the central claims are correct, this is a genuinely useful step: replacing fidelity-based cost functions with the QFI avoids the exponential classical overhead of fidelity-based active steering and extends the reach of such protocols to larger N. The manuscript also provides reproducible code and data, and it demonstrates a concrete non-GHZ application to Dicke states. However, the convergence and scalability claims rest on trajectory-averaged QFI values and fits without error bars, rather than on direct per-trajectory fidelity to the target manifold or on success probabilities. Those gaps need to be closed before the abstract-level claims are fully supported.","major_comments":[{"comment":"The assertion that the protocol 'efficiently reaches' the GHZ manifold is supported only by the trajectory-averaged QFI and by an N=5 phase histogram. For a pure state, F_Q/N^2 >= 0.9 does imply a large overlap with the GHZ subspace, but the average over trajectories could be dominated by a subset of successful runs. Please report the full distribution of F_Q at the final time (or at first-passage time), the fraction of trajectories satisfying F_Q >= 0.9 N^2, and the per-trajectory fidelity to the manifold of Eq. (1). Without these data, the convergence claim is not established at the level stated in the abstract.","section":"Sec. III, Figs. 2 and 3"},{"comment":"The scalability conclusion n_t ~ A + B ln N is based on fits to data points without error bars, and the text reports fit parameters for only one curve (A ≈ 104.7, B ≈ 123.9 for nearest-neighbor couplings with J δt = 0.1). Please provide statistical uncertainties for A and B, fit residuals, and the number of trajectories used for each N; also clarify whether n_t is the average first-passage time per trajectory or the time at which the averaged QFI first crosses 0.9 N^2. With only about 100 trajectories for the largest N and visible scatter in Fig. 5, the logarithmic scaling is not yet compelling against other slowly growing scalings.","section":"Sec. III, Fig. 5"},{"comment":"The protocol chooses (K_n, K_{n+1}) by greedy local maximization of the measurement-averaged QFI change, and global convergence to the GHZ manifold is demonstrated only numerically for N ≤ 22. Because the state space grows exponentially, the possibility of local traps for larger N is not addressed. Since the scalability claim extrapolates beyond the simulated range, please either provide a convergence argument or report additional diagnostics, such as dependence on the initial state and long-time saturation behavior for intermediate N. This is load-bearing for the central claim.","section":"Sec. II, Eq. (6) and Table I"}],"minor_comments":[{"comment":"The paper refers to 'Green-Hornberger-Zeilinger (GHZ) states'; the standard name is 'Greenberger-Horne-Zeilinger' and should be corrected.","section":"Introduction"},{"comment":"The entanglement-depth criterion is stated imprecisely: F_Q > m N implies that at least m+1 parties are entangled, so m is not itself 'the size of the biggest entangled block' as written.","section":"Sec. II"},{"comment":"The quantity Γ_m in Eq. (9) is not defined in the main text; please define it or state explicitly that it follows Ref. [6].","section":"Sec. II, Eq. (9)"},{"comment":"The phrase 'efficiently reaches' should be qualified as referring to numerical simulations of the ideal, noiseless model, since the paper explicitly leaves error channels and non-ideal measurements for future work.","section":"Abstract and Sec. III"},{"comment":"The dataset and code titles contain the typo 'manifods'; this should be corrected in the Zenodo records as well as in the reference list.","section":"Data availability"},{"comment":"The three individual measurement trajectories shown in the inset are not labeled; please clarify whether they are representative, best, or worst cases.","section":"Sec. III, Fig. 2 inset"}],"recommendation":"major_revision","confidential_remarks":"The paper is within scope and the idea of using the QFI as a steering cost function is interesting. The main issue is evidentiary: the convergence and scalability claims are supported by averaged QFI and unadorned fits. If the authors add direct fidelity or success-probability data and quantify the fit uncertainties, the paper would be substantially strengthened. I do not see concerns about the citation pattern or novelty disclosure."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Read the paper. The genuinely new thing is using the Quantum Fisher Information as the cost function in an active steering loop. That is a smart move: fidelity-based costs scale exponentially with N, while the QFI of a pure state depends only on one- and two-body correlations, so the classical optimization per step is polynomial. They also show the same idea works for Dicke manifolds by minimizing |FQ − FQ*|. Those are real contributions.\n\nWhat the paper does well: the protocol is described clearly, the numerics are reproducible (data and code on Zenodo), the authors are careful about the distinction from passive steering, and they freely admit that direct projective measurement circuits are more efficient for GHZ preparation. They also flag the state-tracking requirement as a limitation and sketch a measurement-based variant.\n\nMy concerns: the central claim is that the protocol efficiently reaches the GHZ manifold. The evidence is measurement-averaged QFI (Fig. 2) and, for N=5, a flat phase histogram and purity. They never report the probability that an individual trajectory ends up with FQ/N^2 ≥ 0.9, nor the fidelity to the manifold. The inset in Fig. 2 shows three individual trajectories, which look fine, but that is anecdotal. For a scalable preparation claim, you want the success fraction, not just the mean. Also, the logarithmic scaling in Fig. 5 is a fit to data up to N=22 with no error bars; the fitted B parameter is large (124 for Jδt=0.1), and the even-odd scatter is significant. I would call the scalability claim plausible but not demonstrated.\n\nThere is also no analytic argument for convergence. The greedy per-pair maximization can in principle get stuck in local traps. That is acceptable for a numerical paper, but the abstract's 'suggests' should be read strictly—it does suggest, not prove.\n\nWho gets value: people working on measurement-based state preparation and quantum control; the QFI cost idea is worth borrowing. The paper deserves a serious referee. Revisions should report per-trajectory success statistics, error bars on the scaling plots, and a direct fidelity check for small N. I would send it to review. The work is honest and the idea is useful.","headline":"Useful new QFI-based steering protocol with real numerical evidence; the scalability claim is softer than the abstract suggests because the metric is always measurement-averaged QFI, never per-trajectory fidelity.","tokens_in":15228,"tokens_out":2171,"would_cite":true,"duration_ms":19831,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A greedy measurement-feedback rule built on the Quantum Fisher Information steers N-qubit states into the genuinely entangled GHZ manifold, with numerical evidence for up to 22 qubits and a step count growing only logarithmically with N.","keywords":["active steering","quantum feedback","Quantum Fisher Information","multipartite entanglement","GHZ states","weak measurements","Bell measurements","Dicke states"],"falsifier":"Run the same protocol for, say, $N=30$ or $N=40$ and record both the step count needed to reach $F_Q=0.9N^2$ and the direct overlap with the GHZ manifold; the scalability claim fails if the step count departs from the $A+B\\ln N$ fit, if the QFI saturates below $N^2$, or if the state's fidelity to the manifold is low.","tokens_in":14253,"feed_emoji":"🎯","tokens_out":12598,"duration_ms":112628,"temperature":0.7,"pith_summary":"This paper introduces an active steering protocol that uses the Quantum Fisher Information (QFI) as the cost function to guide a chain of qubits into a genuinely entangled GHZ manifold. Instead of optimizing fidelity, which becomes exponentially costly, the protocol greedily chooses, for each qubit pair at each step, the weak measurement coupling that maximizes the expected QFI increase. Numerical simulations for up to 22 qubits show the QFI approaching its maximum $N^2$ after roughly two hundred steps, with the required step count growing only logarithmically with $N$. The same protocol, using a fixed target QFI as the cost, also prepares Dicke-state manifolds. If the numerics hold, it offers a measurement-and-feedback route to scalable multipartite entanglement that avoids exponential overhead in the control algorithm.","feed_headline":"QFI cost steers qubits into GHZ states in ~log N steps","feed_subtitle":"A QFI-based feedback rule prepares 22-qubit entangled states; the step count rises only logarithmically.","key_machinery":"The central machinery is the measurement-averaged QFI increment $\\langle dF_Q\\rangle_{\\mathrm{ms}}$. For every allowed steering coupling $K=(K_n,K_{n+1})$, chosen from Pauli system operators $\\sigma_x,\\sigma_y,\\sigma_z$ and detector operators $\\tau_x,\\tau_z$, the protocol computes how much the QFI is expected to change after one weak coupling step followed by a Bell-basis measurement of the detector pair, then applies the coupling with the largest $\\langle dF_Q\\rangle_{\\mathrm{ms}}$ and repeats. The evaluation is done in a Bloch tensor representation, and the formula for $\\langle dF_Q\\rangle_{\\mathrm{ms}}$ depends only on single-qubit Bloch vectors and two-qubit correlators, so the classical control computation costs polynomially in $N$ rather than exponentially.","core_discovery":"The paper's central claim is that a purely local, greedy optimization of the measurement-averaged QFI—choosing the system-detector coupling $(K_n,K_{n+1})$ for each qubit pair independently at every timestep—drives the $N$-qubit state into the one-parameter family of GHZ states $|\\Psi\\rangle = (|0\\cdots0\\rangle + e^{i\\phi}|1\\cdots1\\rangle)/\\sqrt{2}$ that saturates the QFI bound $F_Q = N^2$. The evidence is numerical: for $N$ up to 22, the averaged QFI reaches $0.9N^2$ in a number of steps that fits $A + B\\ln N$, and for $N=5$ the phase $\\phi$ is sampled uniformly across the manifold, indicating that trajectories keep cycling through the manifold rather than settling into a dark state. The paper further claims that the same QFI-based cost, applied to a fixed target value $F_Q^*$, prepares Dicke-state manifolds.","pith_inferences":["If the log-step scaling extends beyond $N=22$, this is a practical preparation route for GHZ states in platforms with fast weak measurement and feedback, because the per-step classical control cost is only polynomial in $N$.","Since $\\langle dF_Q\\rangle_{\\mathrm{ms}}$ depends only on one- and two-body correlators, the algorithm could in principle run without storing the full quantum state, using weak measurements of those correlators; that version would remove the exponential simulation bottleneck and make noisy-system tests feasible.","The uniform cycling over $\\phi$ under active steering, in contrast to passive steering's convergence to a dark state, suggests that the phase could be exploited as an effectively random but steerable parameter, for example for random-access phase encoding in quantum sensing.","By changing the collective operator $O$ in the QFI definition, the same greedy protocol should target other maximal-QFI manifolds, such as spin-squeezed states, not just GHZ and Dicke states."],"forward_implications":["For $N$ up to 22, the averaged QFI approaches its maximum $N^2$ after roughly 200 steps, essentially independent of $N$, so repeated weak measurements plus feedback can create genuine multipartite entanglement without deep circuits.","The number of steps needed to reach $F_Q = 0.9N^2$ fits $A + B\\ln N$, which is the basis of the paper's scalability claim for larger systems.","Because the phase $\\phi$ of the GHZ state keeps cycling uniformly over the manifold under continued steering, adding a termination rule lets the experimenter select a GHZ state with a predetermined phase.","Replacing the cost function by $|F_Q - F_Q^*|$ targets other highly entangled manifolds such as symmetric Dicke states, which converge in roughly 70 steps for the cases shown.","Allowing Bell measurements between arbitrary detector-qubit pairs speeds up convergence compared with nearest-neighbor-only pairings."],"supporting_citations":[{"why":"Supplies the active-steering feedback scheme this work extends, including the explicit single- and two-qubit correlator update formulas (its Eq. (27)) reused for the QFI cost.","marker":"[6]"},{"why":"Introduces the Quantum Fisher Information as an estimation-theoretic quantity, the cost function the protocol is built on.","marker":"[12]"},{"why":"Shows that values of the QFI above $mN$ witness multipartite entanglement, making saturation at $N^2$ a legitimate genuine-multipartite-entanglement target.","marker":"[13–15]"},{"why":"Provides the standard QFI definition and the Heisenberg-limit metrology context for collective observables.","marker":"[16–20]"},{"why":"Supplies the QFI value for Dicke states used as the target $F_Q^*$ when steering to non-GHZ manifolds.","marker":"[19]"},{"why":"Defines the GHZ states and the Bell basis used for detector measurements, fixing the target manifold and the measurement scheme.","marker":"[21]"},{"why":"Supplies the quantum-feedback and stochastic-Schrödinger-equation formalism used to propagate the state and compute measurement-averaged changes.","marker":"[30]"},{"why":"Provides the continuous weak-measurement formalism underlying the jump-type update equation.","marker":"[34]"}],"fun_headline_variants":["QFI feedback steers 22 qubits into GHZ states in log N steps","Logarithmic scaling for QFI-driven entanglement preparation","Greedy QFI optimization yields scalable GHZ state manifolds","Active steering to GHZ states: only log N measurements","QFI-bound steering preps 22-qubit GHZ manifolds in log steps"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"Everything rests on the numerical finding that greedily choosing, for each qubit pair, the couplings that maximize the expected QFI increase steers the whole $N$-qubit state into the GHZ manifold; there is no analytic convergence proof, and the simulations stop at $N=22$.","fun_headline_variants_meta":{"raw":{"variants":["QFI feedback steers 22 qubits into GHZ states in log N steps","Logarithmic scaling for QFI-driven entanglement preparation","Greedy QFI optimization yields scalable GHZ state manifolds","Active steering to GHZ states: only log N measurements","QFI-bound steering preps 22-qubit GHZ manifolds in log steps"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000709,"raw_usage":{"total_tokens":3131,"prompt_tokens":821,"completion_tokens":2310,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":437,"completion_tokens_details":{"reasoning_tokens":2216}},"tokens_in":437,"tokens_out":2310,"duration_ms":15902,"temperature":1.0,"reasoning_tokens":2216,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T21:40:46.733231+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the same protocol for, say, $N=30$ or $N=40$ and record both the step count needed to reach $F_Q=0.9N^2$ and the direct overlap with the GHZ manifold; the scalability claim fails if the step count departs from the $A+B\\ln N$ fit, if the QFI saturates below $N^2$, or if the state's fidelity to the manifold is low.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Introduces the Quantum Fisher Information as an estimation-theoretic quantity, the cost function the protocol is built on."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the quantum-feedback and stochastic-Schrödinger-equation formalism used to propagate the state and compute measurement-averaged changes."},{"cited_title":"Kim, D.-G","cited_arxiv_id":null,"evidence_quote":"Provides the continuous weak-measurement formalism underlying the jump-type update equation."}],"review_version":1}