{"id":"fa98aa56-bf0c-4e01-b592-dae615142bac","arxiv_id":"2411.17457","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"In passive PT-symmetric three-qubit systems, all-to-all coupling generates robust GHZ states and nearest-neighbour coupling generates W states, both sustained by strong driving.","lead":"This paper studies how tripartite entanglement behaves in three superconducting qubits with engineered loss, which form a passive PT-symmetric system. It finds that GHZ and W states can be generated and survive under non-uniform couplings, off-resonant driving, and strong Rabi drives.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The central practical claim depends on post-selected no-jump dynamics; because the no-jump success probability is never computed, the reported states may be exponentially rare and not representative of unconditional operation.","rationale":"The reader's verdict is CONDITIONAL, and I find the same weakest assumption. The core numerical results—GHZ/W generation in the renormalized non-Hermitian evolution—are internally consistent as a study of no-jump trajectories. However, every figure and headline statement uses the normalized conditional state, while the full Liouvillian dynamics, including quantum jumps, is never solved. The paper explicitly defers 'effects of quantum jumps' to future work (Sec. VII), confirming the gap. The missing success probability is not a minor technicality: for three lossy qubits evolved for several microseconds with γ=6 rad/µs, the no-jump probability is plausibly exponentially small, and if so the reported states are not something a user can reliably obtain. The strong-driving robustness claim in Sec. VI is also about the conditional state. Therefore the abstract's practical-usefulness statement overreaches. I would keep the CONDITIONAL verdict: the theoretical conditional-state results are worth publishing, but the success-probability and unconditional-dynamics checks should be added before the claims are framed as robust and useful.","tokens_in":15337,"tokens_out":4341,"duration_ms":51877,"concrete_test":"Fix the Fig. 2 parameters (Ω=1.576 rad/µs, γ=6 rad/µs, J=10^-3 rad/µs, ∆=0, initial state 2^{-3/2}(|f>-i|e>)⊗3). Compute P(3.23 µs)=||e^{-iHt}|ψ(0)>||^2. Then solve the full Lindblad master equation with the same drive and loss, including the quantum jumps implied by the γ terms, and evaluate the residual tangle or entanglement entropy of the unconditional three-qubit state at t=3.23 µs and at t=13 µs. If P is below ~10^-3 and/or the unconditional state has negligible genuine tripartite entanglement, the practical-robustness claims in the abstract and Sec. VII need to be downgraded.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The evolution in Eq. (2) uses e^{-iHt} with the non-Hermitian Hamiltonian of Eq. (1), and the paper states this is equivalent to post-selecting on no-jump trajectories (Sec. II and Sec. VII). All entanglement measures are then computed on the manually renormalized conditional state. The missing quantity is the success probability P(t)=||e^{-iHt}|ψ(0)>||^2 at the reported optimal times. For the parameters used in Figs. 1-2 (γ=6 rad/µs, t=3.23 µs, Ω≥1.5 rad/µs), a naive exponential estimate is extremely small, and the strong-driving 'sustained entanglement' claim in Sec. VI is made without any account of how often the required no-jump branch occurs. The abstract's statement that these states are 'useful for quantum technologies' therefore goes beyond what the conditional-state calculation supports. This does not invalidate the conditional-state entanglement results, but it makes the robustness/practicality claim load-bearing and unsupported.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript studies three-qubit entanglement generated by passive PT-symmetric non-Hermitian superconducting qubits with the Hamiltonian in Eq. (1). It uses the non-unitary evolution of Eq. (2) with manual renormalization, i.e., postselected no-jump dynamics, and computes pairwise concurrences, residual tangle, and von Neumann entropies. The main claims are that all-to-all coupling generates GHZ states, nearest-neighbour coupling generates W states, these states are robust to non-uniform couplings and off-resonant driving, hybrid Hermitian/non-Hermitian setups produce only biseparable states, and strong driving sustains entanglement in the PT-symmetric phase.","tokens_in":15527,"tokens_out":11954,"duration_ms":108006,"significance":"If the claims hold, the paper provides a concrete resource for accelerated multipartite entanglement generation in superconducting circuits using higher-order exceptional points, with explicit parameter regimes and quantitative comparisons to Hermitian qubits. The numerics are straightforward and appear internally consistent; the use of multiple entanglement monotones is appropriate. The main caveat is that all entanglement statements concern the conditional no-jump state, and the manuscript does not quantify the corresponding success probability or fidelity, so the practical/robustness claims extend beyond the presented evidence. With those quantities added, the work would be a useful contribution to the non-Hermitian quantum information literature.","major_comments":[{"comment":"The manuscript acknowledges that manual normalization is equivalent to postselecting no-jump trajectories, but it never reports the success probability P(t)=||e^{-iHt}|ψ(0)>||^2 at the optimal times used in Figs. 1-4. For the initial state with equal weights on |e> and |f>, P(t) may not be exponentially small (in the noninteracting limit it is roughly (1/2 + e^{-γt}/2)^3 ~ 1/8 for t=3.23 µs), but the paper should verify this for the coupled dynamics. Without P(t), the abstract's statements that the states are 'useful for quantum technologies' and that strong driving 'sustains' entanglement are not supported for unconditional operation. Please add P(t) curves or clearly restrict all practical claims to the conditional postselected state.","section":"Sec. II (Eq. (2)) and Sec. VII"},{"comment":"The identification of the nearest-neighbour state as a W state rests on the three reduced entropies approximately reaching ln3 - (2/3)ln2 and the tangle vanishing. These are necessary signatures, but they are indirect; the same entropy triple could in principle occur for a state in the W class that is not locally equivalent to the symmetric |W> state. To make the classification rigorous, report the fidelity of the generated state with |W> (or with the W class after optimization over local unitaries), and give the state amplitudes at t=3.23 µs.","section":"Sec. III, Fig. 1(b)"},{"comment":"The text states that entanglement remains robust for Δ ≲ J_opt with J_opt = 10^-3 rad/µs, but the figure shows detunings up to 10^-1 rad/µs. This leaves the quantitative robustness window ambiguous: is Δ=10^-2 rad/µs inside or outside the claimed regime? Please specify the threshold Δ_max for a chosen entanglement tolerance and reconcile the statement with the plotted curves, since the abstract's 'resilient to off-resonant driving' depends on this window.","section":"Sec. IV, Fig. 2(b)"},{"comment":"The claim that strong Rabi driving 'counteracts losses' and sustains entanglement is made in the renormalized conditional-state picture; in the unconditional Lindblad evolution the norm still decays and the no-jump branch occurs with probability that is not reported. Please either present the unconditional (jump-included) dynamics for the strong-driving regime or explicitly state that the sustained entanglement is a property of the conditional trajectory only.","section":"Sec. VI, Fig. 4"}],"minor_comments":[{"comment":"The formula for Wootters concurrence has a typesetting corruption ('q p ... p ...'); please replace it with the standard expression using the Hermitian matrix sqrt(sqrt(ρ) \tilde{ρ} sqrt(ρ)).","section":"Eq. (5)"},{"comment":"The relation t_opt^NHQ ∝ J_jk × t_opt^HQ has incompatible units (J is a rate, t a time); please rewrite it in dimensionless form or clarify the intended scaling.","section":"Sec. III"},{"comment":"The axes labels are partially garbled in the figure caption and image; please ensure the axes for J12/J23 and the color scale for τ are legible.","section":"Fig. 2(a)"},{"comment":"The text says 'tripartite entanglement entanglement' (duplicate word); please fix this typo.","section":"Sec. V"},{"comment":"Please define 'optimal coupling' J_opt in the text before using it in the robustness criterion; currently it is introduced parenthetically in a way that is easy to miss.","section":"Sec. IV"}],"recommendation":"major_revision","confidential_remarks":"The paper relies substantially on Ref. [33] (same group, unpublished preprint) for the underlying GHZ-generation mechanism; the current manuscript reproduces some of the numerics, but the dependence should be made explicit and the relevant fidelity/success quantities should be computed here. The topic fits a quantum-information or non-Hermitian physics venue; the main revision needed is to quantify the postselection cost and strengthen state classification."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Read this if you care about non-Hermitian superconducting qubits: the paper extends the same group's earlier EP-based GHZ/W generation (Ref. [33]) with systematic robustness scans, hybrid Hermitian/non-Hermitian setups, and a strong-driving analysis. The numerics are internally consistent and the entanglement measures support the stated claims. The big caveat is that all results live on the post-selected no-jump trajectory; the success probability is never computed, so the abstract's \"useful for quantum technologies\" is an overreach.\n\nWhat is actually new and worth credit: the robustness maps in Fig. 2 show GHZ persists over a broad range of non-uniform couplings and degrades gracefully with detuning up to J_opt. The hybrid results are a clean negative: replacing one qubit by a Hermitian one gives biseparable states, which is a useful boundary on where EPs matter. The strong-driving section shows a PT-symmetric phase transition and faster entanglement than Hermitian—on the conditional state, again. The paper is also explicit in Sec. II that manual normalization amounts to post-selection, and the conclusion flags quantum jumps as future work. That honesty is good, but it makes the abstract's practical claim harder to defend.\n\nThree soft spots, in order of size. First, the missing no-jump success probability. P(t) = ||e^{-iHt}|ψ(0)>||^2 at t = 3.23 µs with γ = 6 rad/µs is likely exponentially small; the paper neither computes it nor discusses what happens when jumps occur. That is load-bearing for any practical claim. The Sec. VI \"sustain entanglement over time\" statement is especially vulnerable, because the no-jump branch becomes rarer as time grows. Second, W-state identification is indirect: entropy values matching ln3 - (2/3)ln2 and zero tangle are consistent with W, but a direct fidelity to the W state would close the loop. That is minor. Third, the off-resonant robustness window is narrow (detuning up to J_opt ≈ 10^-3 rad/µs), so \"robust\" should be read as \"robust over a small absolute range.\" That is a wording issue, not a flaw. No code is provided, but parameters are specified.\n\nOverall: this is a competent numerical study, not a breakthrough. The conditional-state entanglement results hold up; the hole is the missing success probability. A serious referee should see it—the post-selection gap is fixable in revision by computing P(t) and adding a short unconditional/Liouvillian discussion. I would accept it for peer review, and I would not cite it in my own work until that gap is closed. Bring it to reading group only if someone is working on post-selected non-Hermitian circuits.","headline":"A competent numerical extension of the same group's earlier EP-based GHZ/W generation; the conditional-state results hold together, but the abstract overclaims practicality without quantifying the post-selected no-jump success probability.","tokens_in":16093,"tokens_out":2673,"would_cite":false,"duration_ms":44646,"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":"Three dissipative qubits operated at an exceptional point can generate genuine tripartite GHZ and W states faster than Hermitian qubits, and these states survive non-uniform couplings and detuned driving.","keywords":["non-Hermitian quantum systems","exceptional points","PT symmetry","tripartite entanglement","GHZ states","W states","superconducting qubits","post-selection"],"falsifier":"A direct test would be a full Liouvillian master-equation simulation of the same three-qubit system including quantum jumps, evaluated at $t \\approx 3.23\\,\\mu\\text{s}$ without post-selection. If the unconditional density matrix shows vanishing three-tangle and entanglement entropies far from the GHZ/W values, the central claim, as stated, would be falsified. An experimental alternative is to measure the success probability of the post-selected protocol on a superconducting transmon platform and check whether genuine tripartite entanglement survives when trajectories are averaged.","tokens_in":15147,"feed_emoji":"⚛️","tokens_out":6817,"duration_ms":57469,"temperature":0.7,"pith_summary":"This paper tries to establish that non-Hermitian (lossy) superconducting qubits, tuned near a higher-order exceptional point, are not just a mathematical curiosity but a practical resource for fast multipartite entanglement. The central claim is that three such qubits evolve into a GHZ state when coupled all-to-all and into a W state when coupled only between neighbours, reaching these states at the same early time of about 3.23 microseconds, well before a comparable Hermitian system would. The paper further argues that this entanglement is robust: it survives a broad range of non-uniform coupling strengths and detunings up to the optimal coupling strength, and strong Rabi driving can sustain it by shifting the system into the PT-symmetric phase. Hybrid systems containing one or two Hermitian qubits, by contrast, produce only biseparable entanglement because the Hermitian and non-Hermitian parts evolve on incompatible timescales. If correct, the result matters because fast, robust multipartite entanglement is a scarce resource for quantum communication and computation within coherence times.","feed_headline":"Lossy qubits near exceptional points create fast GHZ and W states","feed_subtitle":"Exceptional-point dynamics entangle three qubits quickly, even with imperfect couplings or detuned drives.","key_machinery":"The engine of the effect is the eighth-order exceptional point of the non-Hermitian Hamiltonian in Eq. (1), the point where all eigenvalues and eigenvectors coalesce. Operating near this EP makes the qubits highly sensitive to even tiny inter-qubit couplings, which redistributes population and phase among the three qubits, producing entanglement on a timescale set by the EP structure rather than by the coupling strength. The evolution is computed with the non-Hermitian Hamiltonian and manual renormalization, equivalent to post-selection of the no-jump trajectory. The diagnostics used to identify the states are the pairwise concurrences, the residual three-tangle, and the von Neumann entropies of the reduced single-qubit states, whose values distinguish GHZ states ($S_j=\\ln2$, $\\tau=1$) from W states ($S_j\\approx0.637$, $\\tau=0$).","core_discovery":"Under the passive PT-symmetric Hamiltonian for three coupled transmons, with manual normalization that corresponds to post-selecting no-jump trajectories, the authors find that all-to-all coupled qubits generate a state whose pairwise concurrences vanish while entanglement entropies reach $\\ln 2$ and the residual three-tangle reaches unity—the signatures of a GHZ state. Nearest-neighbour coupled qubits instead reach entanglement entropies $S_j = \\ln 3 - (2/3)\\ln 2$ with vanishing three-tangle, signalling a W state; both appear at $t \\approx 3.23\\,\\mu\\text{s}$, independent of the coupling topology. The same entangled states persist when the couplings are made non-uniform and when the driving field is detuned, as long as the detuning stays below the optimal inter-qubit coupling. Adding one or two Hermitian qubits destroys genuine tripartite entanglement: the mismatched evolution times produce only biseparable states. Finally, increasing the Rabi frequency drives the system from the PT-broken to the PT-symmetric phase and sustains the tripartite entanglement, whereas increasing the coupling strength alone helps only in the low-dissipation regime.","pith_inferences":["A natural extension the authors do not carry out is to compute the post-selection success probability and the unconditional (jump-included) fidelity; if the success probability decays with qubit number, the practical speed-up may not survive full Liouvillian dynamics.","The same EP mechanism might be used to engineer specific target states by choosing the coupling graph, since the all-to-all versus nearest-neighbour distinction selects GHZ versus W classes.","One could test the robustness predictions directly by sweeping a single coupling asymmetry in a three-transmon experiment and measuring the three-tangle at the predicted time.","The claim that strong driving sustains entanglement suggests a possible connection to Floquet engineering of non-Hermitian phases, a direction the paper does not explore."],"forward_implications":["Three-qubit GHZ and W states can be generated in roughly $3\\,\\mu\\text{s}$, much faster than Hermitian qubits with the same couplings, making the scheme viable within coherence times.","The entanglement survives detunings up to the optimal coupling and moderate coupling disorder, so the protocol does not require fine-tuned fabrication.","Strong Rabi driving sustains tripartite entanglement by moving the system into the PT-symmetric phase and counteracting losses.","Hybrid Hermitian/non-Hermitian arrays can rapidly produce biseparable states, which may serve as resources that retain entanglement when some qubits are lost.","Optimal GHZ and W generation occurs for uniform couplings; large coupling asymmetries suppress the entanglement."],"supporting_citations":[{"why":"Establishes that proximity to higher-order exceptional points speeds up Bell-state generation in two non-Hermitian qubits; the present work generalizes this to three-qubit tripartite states.","marker":"[32]"},{"why":"Previous paper by the same group reports accelerated multipartite entanglement in non-Hermitian superconducting qubits; this work takes the robustness analysis further.","marker":"[33]"},{"why":"Demonstrates quantum jumps in a non-Hermitian superconducting qubit and supports the manual-normalization/post-selection description used here.","marker":"[4]"},{"why":"Provides the hybrid-Liouvillian formalism that justifies connecting non-Hermitian exceptional points to post-selected quantum trajectories.","marker":"[16]"},{"why":"Defines the two inequivalent classes of three-qubit entanglement (GHZ and W) and the residual three-tangle used to distinguish them.","marker":"[42]"},{"why":"Introduces the three-tangle as a measure of genuine tripartite entanglement, used throughout as a state diagnostic.","marker":"[47]"},{"why":"Provides the concurrence formula used to compute pairwise entanglement and identify GHZ states by vanishing pairwise concurrences.","marker":"[46]"}],"fun_headline_variants":["Non-Hermitian qubits yield GHZ or W states at exceptional points","PT-symmetric qubits robustly spin out GHZ and W states","Exceptional points in lossy qubits forge GHZ and W states","Passive PT-symmetric qubits: robust tripartite entanglement"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The entire analysis relies on the non-Hermitian Hamiltonian with manual normalization, which is equivalent to keeping only the no-jump quantum trajectory; if that post-selection cannot be performed with a realistically high success probability in an experiment, the fast and robust entangled states described here will not appear in the unconditioned dynamics.","fun_headline_variants_meta":{"raw":{"variants":["Non-Hermitian qubits yield GHZ or W states at exceptional points","PT-symmetric qubits robustly spin out GHZ and W states","Exceptional points in lossy qubits forge GHZ and W states","Passive PT-symmetric qubits: robust tripartite entanglement"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000673,"raw_usage":{"total_tokens":3120,"prompt_tokens":1053,"completion_tokens":2067,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":669,"completion_tokens_details":{"reasoning_tokens":1988}},"tokens_in":669,"tokens_out":2067,"duration_ms":13813,"temperature":1.0,"reasoning_tokens":1988,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T12:05:30.749223+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A direct test would be a full Liouvillian master-equation simulation of the same three-qubit system including quantum jumps, evaluated at $t \\approx 3.23\\,\\mu\\text{s}$ without post-selection. If the unconditional density matrix shows vanishing three-tangle and entanglement entropies far from the GHZ/W values, the central claim, as stated, would be falsified. An experimental alternative is to measure the success probability of the post-selected protocol on a superconducting transmon platform and check whether genuine tripartite entanglement survives when trajectories are averaged.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Establishes that proximity to higher-order exceptional points speeds up Bell-state generation in two non-Hermitian qubits; the present work generalizes this to three-qubit tripartite states."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Demonstrates quantum jumps in a non-Hermitian superconducting qubit and supports the manual-normalization/post-selection description used here."},{"cited_title":"Minganti, A","cited_arxiv_id":null,"evidence_quote":"Provides the hybrid-Liouvillian formalism that justifies connecting non-Hermitian exceptional points to post-selected quantum trajectories."},{"cited_title":"Coffman, J","cited_arxiv_id":null,"evidence_quote":"Introduces the three-tangle as a measure of genuine tripartite entanglement, used throughout as a state diagnostic."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the concurrence formula used to compute pairwise entanglement and identify GHZ states by vanishing pairwise concurrences."}],"review_version":1}