{"id":"0d7b9c18-03d4-4277-b74c-22fd65908efa","arxiv_id":"2412.01133","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"A postselected model of non-Hermitian superconducting qubits reaches GHZ and GHZ-class states of three and four qubits with fidelity above 0.99 under strong driving or strong all-to-all coupling.","lead":"This paper simulates three and four lossy superconducting qubits connected to each other and shows that GHZ-type entangled states can be produced with high fidelity when the qubits are driven or coupled strongly. If correct, it offers a one-step way to make multipartite entangled states in non-Hermitian qubit hardware without chaining many two-qubit gates.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The practical claim of high-fidelity GHZ creation is not supported because all quoted fidelities are conditional on the no-jump branch, whose success probability is never reported and may be exponentially small at the cited parameters.","rationale":"I read the paper as a numerical study of the postselected no-jump dynamics of a non-Hermitian qubit array, aiming to show that GHZ-class states can be produced at high fidelity. The internal calculations are likely correct as conditional-state computations: the equations are standard, the three-tangle and fidelity definitions are appropriate, and the authors honestly show their model and parameters. The decisive issue is that the physical meaning of 'creation' depends on the probability of remaining on the no-jump branch, and that probability is never given. For the strong-dissipation cases highlighted in the abstract (γ=6J), the naive exponential estimate suggests a tiny survival probability, so the headline fidelity may describe a state that is almost never produced without postselection. This is exactly the reader's weakest_assumption, and I find no basis to disagree. The concrete check is simple and fully within the paper's own framework: evaluate the norm of the unnormalized state at the quoted times and parameters, and optionally run a Monte Carlo wavefunction simulation. If the survival probability turns out to be small, the verdict should remain conditional or move toward reject for the practical claim; if it is large, the concern is resolved. I do not see a separate internal inconsistency worth elevating, so the reader's CONDITIONAL verdict is the right one pending this number.","tokens_in":7914,"tokens_out":4072,"duration_ms":37209,"concrete_test":"Compute P_succ(t)=⟨ψ(t)|ψ(t)⟩ for the exact parameters used for the headline numbers: (i) γ=0 and γ=6J, Ω=100J, initial |fff⟩, at Jt=π (Section III.A); (ii) the strong-coupling case of Fig. 3 with ϕ≈0.288π, γ=0.25J, at Jt=π/2; and (iii) the four-qubit case at Jt=π with Ω=100J, γ=0 and γ=6J. If P_succ is below a practical threshold (or if even the order of magnitude is below 10^{-2}), the 'creation' claim should be restated as a heralded-postselection protocol with the yield explicitly reported; if P_succ is order one, the concern is refuted.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central numbers (F≈0.999 in Section III.A, F≈0.998/0.99 in Section IV) are computed from the renormalized state in Eq. (1), which is the state conditioned on the absence of any quantum jump into the loss channel. The unnormalized evolution e^{-iHt} has norm squared P_succ(t)=⟨ψ(t)|ψ(t)⟩ equal to the probability of the no-jump branch, but P_succ is never reported or plotted anywhere. At the quoted operating points this probability can be extremely small: for γ=6J at Jt=π, γt≈18.8, and since the target GHZ state has half of the qubit population in the decaying |e⟩ state, the no-jump survival probability is plausibly of order e^{-O(γt)} or smaller. If P_succ is, say, 10^{-4} or lower, then the protocol creates a high-fidelity GHZ state only in a vanishing fraction of runs, and the abstract's claim that high-fidelity states 'can be created' is not supported as a practical generation scheme. The paper also never simulates unconditioned quantum trajectories, so it provides no evidence about the average output state including jump events. This is a missing support rather than an internal contradiction, but it is the load-bearing gap in the central claim.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript studies a symmetric all-to-all coupled model of non-Hermitian superconducting qubits, with the Hamiltonian introduced in Sec. II, and analyzes the postselected no-jump evolution of pure states. For three qubits it computes the three-tangle dynamics and GHZ fidelity in the strong-driving (Ω ≫ J, γ) and strong-coupling (J ≫ Ω, γ) regimes; for four qubits it plots single-qubit entanglement entropy and reports GHZ fidelity at one operating time. The main quantitative claims are F ≈ 0.9999 and 0.999 for the three-qubit GHZ state at γ = 0 and γ = 6J with Ω = 100J at Jt = π (Sec. III.A), and F ≈ 0.998 and 0.99 for the four-qubit GHZ state at γ = 0 and γ = 6J with Ω = 100J at Jt = π (Sec. IV), up to a single-qubit phase gate. All of these fidelities are evaluated on the renormalized state defined in Eq. (1), i.e. on the no-jump branch of the non-Hermitian evolution.","tokens_in":8151,"tokens_out":8341,"duration_ms":76863,"significance":"If the no-jump branch occurs with non-negligible probability, the paper would demonstrate a simple one-step protocol producing high-fidelity GHZ and GHZ-class states in a dissipative circuit-QED platform, with no parameter fitting: the Hamiltonian is explicit, the target-state fidelity is computed directly, and the claimed robustness to γ is checkable from the displayed dynamics. However, because the central output is conditional, the practical significance hinges on a quantity the paper never reports: the success probability of the postselected branch. The manuscript therefore currently establishes a conditional entanglement-generation claim, not a practical generation scheme. The strength of the paper is that the numerics are transparent and the measures (three-tangle, entropy, fidelity) are standard; the weakness is the unquantified role of postselection and the absence of trajectory-averaged or unconditional results.","major_comments":[{"comment":"All fidelity values quoted in the abstract and in Sections III and IV are computed from the postselected, renormalized state ρ(t)=|ψ(t)⟩⟨ψ(t)|/|⟨ψ(t)|ψ(t)⟩| defined in Eq. (1). This state conditions on the absence of any quantum jump into the loss channel, yet the paper never reports the no-jump survival probability P_succ(t)=⟨ψ(t)|ψ(t)⟩, nor does it simulate unconditioned quantum trajectories or the Lindblad master equation. At the operating point γ=6J, Jt=π (Sec. III.A), the integrated loss γt is about 18.8, so P_succ could be exponentially small; if so, the high conditional fidelity does not imply that a high-fidelity GHZ state is created in a useful fraction of runs. The central practical claim in the abstract therefore lacks load-bearing support. The authors should report P_succ at the quoted operating points, show its time dependence, and provide either the unconditioned average-state fidelity or an explicit heralding model for the no-jump branch.","section":"II, Eq. (1); III.A; IV"},{"comment":"The strong-coupling protocol is presented as one of the two central routes, but the manuscript reports no fidelity number in this regime and no quantitative check of the stated insensitivity to the initial phase φ. The initial spin-coherent state is chosen with φ ≈ 0.288π, and the text asserts that different φ values show similar dynamics, but no scan or supporting data is shown. If the high-fidelity GHZ-class generation depends sensitively on φ, then φ is effectively a tuned parameter rather than an arbitrary phase. Please provide a φ-dependence plot for τ and for the target-state fidelity, and report the fidelity achieved at the operating point of Fig. 3.","section":"III.B, Fig. 3"}],"minor_comments":[{"comment":"The section title 'FOUR QUBTIS' should be corrected to 'FOUR QUBITS'.","section":"IV (title)"},{"comment":"The sentence 'The system generates a particular GHZ class state during the period when S reaches around log 2' is too strong: a single-qubit entanglement entropy of log 2 is necessary but not sufficient for a four-qubit GHZ-class state. The fidelity F reported at Jt=π is the appropriate witness and should be presented as the primary evidence; the entropy plateaus should be described as an indicator only.","section":"IV, Fig. 4"},{"comment":"The statement that the strong-coupling regime 'corresponds to the PT symmetric phase as it yields real eigenvalues' is not supported by any spectral calculation in the manuscript; please add a brief derivation or soften the claim.","section":"III.B"},{"comment":"The four-qubit fidelity is quoted only in the text after applying Z(3π/4) to one qubit; please state explicitly that this is a local unitary and give the unrotated state coefficients or a distance measure so the result is reproducible.","section":"IV"}],"recommendation":"major_revision","confidential_remarks":"To the editor: The main fix is straightforward and within the manuscript's scope: report the no-jump probabilities and, if possible, trajectory-averaged fidelities. If those probabilities turn out to be exponentially small at the quoted parameters, the authors should reframe the contribution as the preparation of conditional states, which would substantially lower the practical significance claimed in the abstract. There is no indication of an internal inconsistency in the conditional evolution; the gap is missing support rather than a demonstrated error."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nYou should know two things about arXiv:2412.01133. First, it is a straightforward numerical extension of the authors' earlier work on non-Hermitian qubits: same Hamiltonian, same entanglement measures, now run for three and four qubits in the strong-driving and strong all-to-all coupling regimes. Second, all quoted fidelities (F ≈ 0.999, etc.) are conditional on the no-jump branch of the quantum trajectory, but the probability of that branch is never reported. That is the paper's real soft spot.\n\nWhat the paper does well: the numerics are simple and almost certainly correct for the stated postselected evolution. The three-tangle plots in Figs. 2 and 3 show robust maxima near unity, and the authors are transparent about using the renormalized state of Eq. (1). The observation that strong driving sustains GHZ-class fidelity over a wide range of decay rates is a genuine, if modest, addition. The same holds for the strong-coupling regime with spin-coherent initial states, though the choice of phase phi needs a scan to be fully convincing.\n\nThe main problem is the missing no-jump probability. The paper computes everything from e^{-iHt}|psi0>, normalized, and calls that the generated state. But that state is conditioned on zero jumps into the loss channel. The actual probability of that branch, P_succ(t) = <psi(t)|psi(t)>, is never plotted or tabulated. At gamma = 6J and Jt = pi, gamma t ≈ 18.8, and with half the population in the decaying |e> state, P_succ is likely exponentially small. If so, the abstract's claim that high-fidelity states 'can be created' is not supported as a practical protocol. The paper also never simulates unconditioned trajectories, so it gives no evidence about the average output state. This is missing support, not an internal contradiction, and it can be fixed by reporting P_succ and, ideally, the unconditioned dynamics.\n\nA secondary issue: for four qubits, the paper relies on single-qubit entanglement entropy S ≈ log 2 as evidence of GHZ-class entanglement. That is not a multipartite witness; many non-GHZ states share this entropy. They also mention one local Z-rotation to match the GHZ state, but a fixed phase gate at one time point does not replace a parameter scan.\n\nWho is this for? People working on non-Hermitian quantum engineering who care about postselected entanglement generation. The paper deserves a serious referee: the main numbers are checkable, the omission is addressable, and the model sits in a growing literature. My recommendation: send it to review with a request to report P_succ and to either add a multipartite witness for four qubits or soften the strength of the claims.","headline":"A clean numerical extension of prior non-Hermitian qubit work whose fidelity claims are hostage to an unreported no-jump survival probability; worth refereeing but not as-is.","tokens_in":8704,"tokens_out":3437,"would_cite":false,"duration_ms":28435,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["81P40","81P68"],"pacs":[],"model":"deepseek-v4-flash","headline":"A symmetric non-Hermitian qubit model can prepare three- and four-qubit GHZ states with near-unit fidelity in a single step.","keywords":["non-Hermitian qubits","GHZ states","multipartite entanglement","three tangle","entanglement entropy","superconducting qubits","postselection","all-to-all coupling"],"falsifier":"At the claimed operating point ($\\Omega = 100J$, $\\gamma = 6J$, $Jt = \\pi$), compute the no-jump survival probability $|\\langle\\psi(t)|\\psi(t)\\rangle|$ for the three- and four-qubit protocols; if it is negligible, or if an unconditioned simulation that includes quantum jumps yields a GHZ fidelity far below the reported $0.99$ values, the central claim is contradicted.","tokens_in":7709,"feed_emoji":"⚛️","tokens_out":12435,"duration_ms":96547,"temperature":0.7,"pith_summary":"This paper claims that a single global step of evolution under a symmetric non-Hermitian Hamiltonian can create three- and four-qubit GHZ states, or GHZ-class states, of superconducting qubits with fidelity approaching unity. In the strong-driving regime ($\\Omega=100J$), the three-qubit fidelity reaches $0.9999$ at zero decay and $0.999$ at $\\gamma=6J$, while the four-qubit protocol reaches $0.998$ and $0.99$ after a local phase correction. The entanglement is certified by the three tangle for three qubits and by entanglement entropy for four qubits. If the claim is correct, this offers a one-step entangling gate that avoids sequential two-qubit gates and remains effective under modest loss rates.","feed_headline":"One step makes GHZ states at 0.999 fidelity in non-Hermitian qubits","feed_subtitle":"Strong driving plus symmetric coupling turns no-jump decay dynamics into a fast, single-shot multipartite entangler.","key_machinery":"The load-bearing object is the renormalized postselected state $\\rho(t) = |\\psi(t)\\rangle\\langle\\psi(t)| / |\\langle\\psi(t)|\\psi(t)\\rangle|$ with $|\\psi(t)\\rangle = e^{-i\\hat H t}|\\psi(0)\\rangle$, where $\\hat H$ is the symmetric all-to-all non-Hermitian qubit Hamiltonian with driving $\\Omega$, coupling $J$, and decay $\\gamma$. This renormalization conditions on the no-jump trajectory and is what turns non-unitary evolution into a candidate GHZ state; it is also the quantity on which all reported fidelities are computed. The entanglement witnesses are the three tangle $\\tau$ for three qubits and the entanglement entropy $S$ for four qubits, which identify the GHZ class and the maximally entangled plateau $S \\approx \\log 2$.","core_discovery":"The central discovery is that the interplay of strong driving, symmetric all-to-all couplings, and a tunable loss rate in a non-Hermitian transmon-qubit model drives the postselected no-jump state into the GHZ class. Starting from $(|f\\rangle)^{\\otimes 3}$ and evolving to $Jt = \\pi$ with $\\Omega \\gg J, \\gamma$, the three tangle $\\tau$ approaches unity and the fidelity to the GHZ state exceeds $0.999$, even at $\\gamma = 6J$. For four qubits, the same evolution produces a state that, up to a single-qubit $Z(3\\pi/4)$ rotation, has fidelity $\\approx 0.998$ at $\\gamma = 0$ and $\\approx 0.99$ at $\\gamma = 6J$. In the strong-coupling regime ($J \\gg \\Omega, \\gamma$) with spin-coherent initial states, GHZ-class states appear at odd multiples of $Jt = \\pi/2$ and remain robust for small $\\gamma$. The paper concludes that non-Hermitian qubit systems can host genuine maximal multipartite entanglement in a one-step protocol.","pith_inferences":["The missing success probability is the key practical quantity to add: because all quoted fidelities are conditional on no jump, one should report $|\\langle\\psi(t)|\\psi(t)\\rangle|$ and simulate the unconditioned master equation before claiming a usable source of GHZ states.","A natural extension is to $N > 4$ qubits: the symmetric all-to-all dynamics likely generalizes, but the no-jump probability will typically fall exponentially with $N$ and with $\\gamma t$, so the fidelity-versus-success-rate trade-off should be quantified.","The revival of $\\tau$ at moderate $\\Omega$ suggests an optimization landscape in which one can choose $(\\Omega, \\gamma, J)$ to balance fidelity, speed, and resource cost, a direction the authors mention but do not fully map.","Because the model assumes the decay from $|f\\rangle$ is negligible relative to that from $|e\\rangle$, including a finite $|f\\rangle$ loss channel could shift the optimal times and fidelities; testing this would constrain the validity of the two-level reduction."],"forward_implications":["In the strong-driving limit, a single global evolution step prepares a three-qubit GHZ-class state with fidelity $0.9999$ at $\\gamma = 0$ and $0.999$ at $\\gamma = 6J$ when $Jt = \\pi$.","The same protocol prepares a four-qubit GHZ state up to a local $Z(3\\pi/4)$ rotation, with fidelity $0.998$ at $\\gamma = 0$ and $0.99$ at $\\gamma = 6J$.","GHZ-class generation stays robust for decay rates up to $\\gamma = 6J$ when the drive is strong, and moderate drives still show revivals of the three tangle at larger $\\gamma$.","These one-step schemes avoid sequences of two-qubit entangling gates, reducing the time and circuit complexity needed for multipartite entanglement creation.","The strong-coupling regime with spin-coherent initial states offers an alternative route, producing GHZ-class states at odd multiples of $Jt = \\pi/2$."],"supporting_citations":[{"why":"Supplies the non-Hermitian qubit Hamiltonian and the exceptional-point framework for entanglement generation that this paper extends to strong driving and strong coupling.","marker":"[28]"},{"why":"Uses the same non-Hermitian transmon-qubit model to accelerate multipartite entanglement near exceptional points, providing the baseline that the present one-step high-fidelity scheme contrasts with.","marker":"[29]"},{"why":"Provides the single-dissipative-qubit postselection protocol that justifies the normalized no-jump state used for all fidelities in Eq. (1).","marker":"[41]"},{"why":"Defines the three tangle, the residual-entanglement measure used to certify genuine GHZ-class tripartite entanglement.","marker":"[40]"},{"why":"Establishes the GHZ class as inequivalent to W states under LOCC, supporting identification of the generated states as GHZ-class.","marker":"[44]"},{"why":"Provides the LOCC and local-unitary equivalence framework used to claim that the generated state, after a single-qubit phase correction, belongs to the GHZ class.","marker":"[46]"},{"why":"Demonstrates the one-step three-qubit entangling gate in a superconducting circuit, the experimental benchmark against which this protocol's one-step GHZ preparation is framed.","marker":"[33]"}],"fun_headline_variants":["Non-Hermitian qubits yield GHZ states with 0.999 fidelity","One-step protocol creates maximal multipartite entanglement in non-Hermitian qubits","GHZ states at 0.999 fidelity from non-Hermitian qubits","Lossy qubits make high-fidelity GHZ via one-step","One-step to 0.999-fidelity GHZ states in non-Hermitian qubits"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The near-unit fidelities are computed on the branch of the dynamics where no loss event happens, and the paper never reports the probability of actually staying on that branch, so the state may not be produced with a useful probability in practice.","fun_headline_variants_meta":{"raw":{"variants":["Non-Hermitian qubits yield GHZ states with 0.999 fidelity","One-step protocol creates maximal multipartite entanglement in non-Hermitian qubits","GHZ states at 0.999 fidelity from non-Hermitian qubits","Lossy qubits make high-fidelity GHZ via one-step","One-step to 0.999-fidelity GHZ states in non-Hermitian qubits"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000626,"raw_usage":{"total_tokens":2907,"prompt_tokens":965,"completion_tokens":1942,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":581,"completion_tokens_details":{"reasoning_tokens":1836}},"tokens_in":581,"tokens_out":1942,"duration_ms":12908,"temperature":1.0,"reasoning_tokens":1836,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T04:39:31.638113+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"At the claimed operating point ($\\Omega = 100J$, $\\gamma = 6J$, $Jt = \\pi$), compute the no-jump survival probability $|\\langle\\psi(t)|\\psi(t)\\rangle|$ for the three- and four-qubit protocols; if it is negligible, or if an unconditioned simulation that includes quantum jumps yields a GHZ fidelity far below the reported $0.99$ values, the central claim is contradicted.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Uses the same non-Hermitian transmon-qubit model to accelerate multipartite entanglement near exceptional points, providing the baseline that the present one-step high-fidelity scheme contrasts with."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines the three tangle, the residual-entanglement measure used to certify genuine GHZ-class tripartite entanglement."},{"cited_title":"Islam, R","cited_arxiv_id":null,"evidence_quote":"Establishes the GHZ class as inequivalent to W states under LOCC, supporting identification of the generated states as GHZ-class."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Demonstrates the one-step three-qubit entangling gate in a superconducting circuit, the experimental benchmark against which this protocol's one-step GHZ preparation is framed."}],"review_version":1}