{"id":"782658e2-eabd-4a71-967c-b685f1be2103","arxiv_id":"2508.17576","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"The quantum Mpemba effect occurs in intrinsic PT-symmetric (non-Hermitian) qubit systems in a bosonic bath, survives dephasing and multi-qubit extension, and is not bounded by Hamiltonian or Liouvillian exceptional points.","lead":"The attached full text reports numerical and analytical evidence that the quantum Mpemba effect, where a state starting farther from equilibrium relaxes faster, occurs in parity-time-symmetric (non-Hermitian) qubit systems coupled to a thermal bath, and that the effect's range is not set by exceptional points. It matters because earlier quantum Mpemba demonstrations were confined to Hermitian systems, and this result is testable with qubit platforms that already exist.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The QMPE claim rests entirely on Eq. (2), a normalized Lindblad equation for a non-Hermitian Hamiltonian cited to the authors' own Ref.","rationale":"The reader's weakest assumption names Eq. (2); my read agrees. The paper is otherwise careful: the suppression of the slowest relaxation mode, the analytical boundaries Eqs. (11)-(13), and the numerical contour plots are mutually consistent, and the authors honestly exclude ambiguous multiple-crossing regimes in Fig. 8. But those virtues are all inside the model defined by Eq. (2). Since the abstract claims an 'unequivocal' occurrence in an experimentally realizable open PT-symmetric system, the physical status of Eq. (2) is the single condition that has to be true for the central claim to hold. It is cited to the authors' own prior work rather than derived here, so the record as submitted does not by itself establish that premise. This does not change the reader's verdict: CONDITIONAL remains appropriate. I also note the abstract/metadata mismatch (CausalSent vs. quantum Mpemba text) as a record-level issue, but it is not the load-bearing scientific concern for the full text judged on its own.","tokens_in":17526,"tokens_out":16882,"duration_ms":180673,"concrete_test":"Independently re-derive Eq. (2) from the microscopic model: a PT-symmetric qubit with H = sigma_x + i a sigma_z coupled to a bosonic bath, using the Born-Markov and secular approximations, and compare the resulting normalized reduced-state equation with Eq. (2), including the trace-conservation term. For a representative QMPE parameter point (a=1.3, gamma1=0.4, gamma2=1, the red star in Fig. 3), also compute the Choi matrix of the Eq. (2) dynamical map at several times to test complete positivity. If the microscopic derivation yields extra terms or the map is not CP, the QMPE predictions in Sec. III are not established.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Every intersection count, analytical boundary, and 'genuine QMPE' identification in Secs. III and IV is computed from solutions of Eq. (2), the Lindblad-type master equation for the normalized density matrix of a PT-symmetric qubit. The manuscript does not derive this equation: 'For derivation details that lead to Eq. (2), we refer readers to Ref. [48]', the authors' own PR A paper. This is load-bearing because the standard microscopic derivation of a Lindblad equation assumes a Hermitian system Hamiltonian. Replacing H by a non-Hermitian PT-symmetric Hamiltonian and appending the last term of Eq. (2) to restore trace conservation is not automatically justified: the resulting propagator need not be completely positive, and the correction term, being linear in rho, changes the Liouvillian spectrum (including the eigenvalue ordering and the LEP) used in Eqs. (4), (8), and (11)-(13). If Eq. (2) is an uncontrolled phenomenological model rather than a derived weak-coupling master equation, the central occurrence claim is unsupported. The long-time approximation Eq. (8) is a secondary fragility, but it is downstream of Eq. (2).","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript studies the quantum Mpemba effect (QMPE) in a PT-symmetric qubit coupled to a bosonic thermal bath. It uses a Lindblad-type master equation for a normalized density matrix (Eq. (2)), identifies initial states for which the slowest relaxation mode is suppressed, and searches for trajectory crossings using three quantifiers: trace distance, Frobenius distance, and quantum relative entropy. A long-time approximation (Eq. (8)) leads to analytic conditions, Eqs. (12)-(13) and (21)-(22), that delineate multiple-intersection regimes; single-intersection regimes are identified as genuine QMPE. The authors report that the QMPE regime is not bounded by Hamiltonian or Liouvillian exceptional points, that QMPE disappears in the Hermitian limit, and that it persists under dephasing and in multiqubit extensions.","tokens_in":17567,"tokens_out":14885,"duration_ms":150433,"significance":"If the central claim holds, this is a substantial extension of the QMPE to intrinsic non-Hermitian systems, with a testable experimental prediction and a tractable analytic framework. The paper has clear strengths: the analytical boundaries are computed from the Liouvillian spectrum rather than fitted, and the numerical contour maps agree with those boundaries for three different quantifiers. The authors also carefully exclude overlap regions where finite-time counting misses periodic crossings, which is methodologically sound. However, the significance is conditional on the validity of the imported master equation, Eq. (2), and on the control of the long-time approximation. The word 'unequivocally' in the abstract is therefore stronger than what the manuscript currently supports.","major_comments":[{"comment":"The master equation (2) is the foundation of every spectral and dynamical result in the paper, but it is not derived here; the text says 'For derivation details that lead to Eq. (2), we refer readers to Ref. [48]', a prior paper by the same authors. This matters because the standard weak-coupling derivation of a Lindblad equation assumes a Hermitian system Hamiltonian, and the trace-restoring last term in Eq. (2) is not an innocent addition: it modifies the Liouvillian spectrum (Fig. 2) that underlies Eqs. (4), (8), and (11)-(13). Unless the authors provide a derivation from a system-bath Hamiltonian, or at least a detailed justification of the normalization scheme including complete positivity, the central claim that QMPE 'unequivocally' occurs in this system is conditional on an uncontrolled model. I request an appendix or a clear statement of the model's status as phenomenological, with the abstract's 'unequivocally' weakened accordingly.","section":"Sec. II, Eq. (2)"},{"comment":"The long-time approximation (8) is used to rule out additional late-time intersections: the text states that 'Using Eq. (9), we confirm that no additional intersections occur at large times,' and this confirmation is what separates genuine-QMPE single-intersection regimes from multiple-intersection regimes. However, no uniform error bound for Eq. (8) is supplied; the approximation is checked only for selected parameters and finite times up to t=20. A late-time intersection not captured by Eq. (8) would change the parity of the crossing count and therefore invalidate the QMPE classification. Please provide an estimate of the neglected terms that is valid uniformly in the parameter regimes labeled genuine QMPE, or prove monotonicity of the exact difference D^I(t)-D^II(t) beyond the numerically checked window.","section":"Sec. III.A, Eq. (8) and text after Fig. 3(c)"},{"comment":"The indexing of the expansion coefficients is inconsistent in a way that affects the derivation of Eq. (8). Section II states that 'we have c1=0' for diagonal or imaginary-off-diagonal initial states and calls this a suppression of the slowest relaxation mode, but in Eq. (4) c1 is the coefficient of the steady-state eigenvector ρ1, and Appendix B explicitly uses c1=1 and c2=0 under the same initial conditions. Either the vanishing coefficient is c2, or the ordering of modes in Eq. (4) is different from what the text describes. Please clarify the notation and ensure that Eq. (8) is derived with the correct suppressed mode.","section":"Sec. II, Eq. (5) and Appendix B"}],"minor_comments":[{"comment":"The robustness claim against dephasing is based on a single value γ3=0.2 at one parameter point; a parameter scan or an analytic argument would be needed to support 'moderate dephasing strengths' as a general statement.","section":"Section IV.A, Fig. 9"},{"comment":"The multiqubit claim is supported by three examples (N=2,3,4) with different non-Hermiticity values; the statement that QMPE is a 'generic phenomenon' in PT-symmetric multiqubit systems is stronger than the evidence presented.","section":"Section IV.B, Fig. 10"},{"comment":"There is a duplicated reference: Ref. [46] and Ref. [68] are the same paper (Fang et al., Phys. Rev. Res. 4, 033022 (2022)).","section":"References"},{"comment":"The caption of Fig. 7 repeats 'Insets: Insets:'; please fix the typo.","section":"Figure 7 caption"},{"comment":"The symbols C1, C3, C4 and τ are introduced inline in a dense paragraph; a short table of definitions, or a separate display equation for each, would improve readability.","section":"Eq. (11) and surrounding text"}],"recommendation":"major_revision","confidential_remarks":"The main risk is the imported master equation, Eq. (2): I flagged it as a major comment rather than a rejection because it can be addressed by adding a derivation or by reframing the claim as model-dependent. The self-citation to Ref. [48] is acceptable, but it should not substitute for an accessible derivation in this manuscript. The submission metadata also appears to be incorrect: the arXiv listing describes 'CausalSent: Interpretable Sentiment Classification with RieszNet', while the body is the quantum Mpemba manuscript; the editor should verify the submission records before proceeding."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"You should know the record is a mess before anything else: the ID and abstract describe a cs.CL paper on sentiment classification, while the full text is a quant-ph paper on the quantum Mpemba effect by Ma and Liu. I read the physics text, since that is the only coherent thing here.\n\nWhat the physics paper actually does is new and mostly careful. It asks whether QMPE occurs when non-Hermiticity sits in the Hamiltonian rather than emerging from the bath, and answers yes for a PT-symmetric qubit coupled to a thermal bath. It also shows the QMPE regime is not bounded by the Hamiltonian or Liouvillian exceptional points, which directly challenges the LEP-based picture in open Hermitian systems. The analytical boundaries from the long-time approximation agree well with contour plots, and the authors are honest about the overlap region in Fig. 8 where finite-time counting misses periodic crossings. That is the right way to handle an ambiguous regime.\n\nThe soft spots are real but not fatal. The load-bearing equation, Eq. (2), is taken from the authors' own Ref. [48] rather than derived. It contains a probability-conservation term linear in the density matrix, and there is no proof that the resulting propagator is completely positive or that this is the correct weak-coupling limit for a non-Hermitian Hamiltonian. If that equation is wrong, the QMPE regimes are artifacts. That is a legitimate referee flag, not a manufactured one. The long-time approximation Eq. (8) is validated only for specific parameter sets; no uniform error bound is given. The claim that QMPE is 'generic' in multiqubit systems is supported by only three initial states. Minor issues: no code or data shipped, which matters for a numerical paper. The citation pattern is fine, with the key caveat that the central equation points to the authors' own prior work.\n\nOn balance I would send this to peer review. The question is new, the numerics and analytics cohere, and the limitations are openly stated. The referee should press the authors on the derivation and domain of validity of Eq. (2), and on the multiqubit generalization.","headline":"The record is internally mismatched—cs.CL abstract versus quant-ph full text—but the physics text underneath is a careful, novel demonstration of QMPE in intrinsic PT-symmetric qubits, with one load-bearing master equation that the authors assume rather than derive.","tokens_in":18344,"tokens_out":2222,"would_cite":false,"duration_ms":22047,"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":"The paper demonstrates that the quantum Mpemba effect—faster relaxation from a farther-from-equilibrium initial state—occurs in parity-time-symmetric qubit systems coupled to a thermal bath, and only while the Hamiltonian is genuinely…","keywords":["quantum Mpemba effect","parity-time symmetry","non-Hermitian quantum systems","open quantum systems","Lindblad master equation","trace distance","exceptional points","relaxation dynamics"],"falsifier":"Prepare a PT-symmetric qubit in the two initial states $\\hat\\rho_I(0)=(\\hat\\sigma_z+\\hat I)/2$ and $\\hat\\rho_{II}(0)=\\hat I/2$, coupled to a bosonic bath with rates in the paper's predicted single-crossing regime (for example $a=1.3$, $\\gamma_1=0.4$, $\\gamma_2=1$), and measure the trace distance $D(t)=\\frac12\\|\\hat\\rho(t)-\\hat\\rho_{\\rm ss}\\|_1$ for both states; the claim requires exactly one early crossing between the two curves and no later crossings, and zero crossings in the Hermitian limit $a=0$.","tokens_in":17083,"feed_emoji":"⚛️","tokens_out":8701,"duration_ms":86515,"temperature":0.7,"pith_summary":"The paper claims that the quantum Mpemba effect—the counterintuitive speeding-up of relaxation from a state that starts farther from equilibrium—occurs in a parity-time-symmetric qubit coupled to a bosonic thermal bath, as long as the system's Hamiltonian is genuinely non-Hermitian. The effect shows up in three standard dynamical quantifiers (trace distance, Frobenius distance, quantum relative entropy), persists both near and far from Hamiltonian and Liouvillian exceptional points, and disappears completely when the Hamiltonian is restored to Hermiticity. A long-time approximation turns the occurrence of a crossing between two relaxation trajectories into a solvable quadratic condition, and the paper uses it to separate genuine single-crossing quantum Mpemba regimes from multiple-crossing regimes that are not true Mpemba behavior. The result matters because it moves the effect from closed and open Hermitian systems into intrinsic non-Hermitian quantum systems, where it had not been established.","feed_headline":"Quantum Mpemba effect survives without Hermitian Hamiltonians","feed_subtitle":"A non-Hermitian qubit starting farther from equilibrium relaxes faster—until Hermiticity is restored.","key_machinery":"The central object is an open parity-time-symmetric qubit with a non-Hermitian Hamiltonian, coupled to a bosonic bath through excitation and de-excitation jump operators, with dynamics governed by a Lindblad-type master equation for the normalized density matrix. The argument is carried by three pieces: the automatic suppression of the slowest relaxation mode for incoherent initial states or those with purely imaginary off-diagonal elements; a long-time approximation of the normalized density matrix that keeps only the remaining relaxation modes; and the resulting quadratic equation for a damped periodic function whose solutions must satisfy either $|X(\\tau)_\\pm|\\le 1$ (left of the Liouvillian exceptional point) or $[X(\\tau)]_\\pm\\ge 0$ (right of it) to give a physical crossing time. These constraints turn the question \"does the quantum Mpemba effect occur?\" into a parameter-regime calculation.","core_discovery":"The paper asserts an unequivocal demonstration of the quantum Mpemba effect in experimentally realizable parity-time-symmetric qubit systems immersed in a bosonic bath. For a PT-symmetric Hamiltonian and Lindblad-type dynamics of the normalized density matrix, two initial states—one farther from the steady state than the other—can have quantifier trajectories that cross, so the initially farther state reaches stationarity sooner. The effect persists both near and far from Hamiltonian and Liouvillian exceptional points, and vanishes entirely when the Hermitian Hamiltonian is restored. For a wide family of initial states, the slowest relaxation mode is completely suppressed without engineered unitary transformations, so the remaining relaxation modes cooperate to produce the crossing; the paper derives analytical expressions for the number of intersections and verifies robustness against dephasing and against increasing qubit count.","pith_inferences":["If the suppression of the slowest relaxation mode is as generic as the paper suggests, engineered initial-state preparation may be unnecessary for observing Mpemba-type speed-ups in any PT-symmetric open system, which would simplify experimental protocols.","The quantifier dependence visible in the relative-entropy results—a broader single-intersection regime than for trace distance—implies that the verdict \"quantum Mpemba yes or no\" can depend on which distance measure is chosen; fixing a canonical quantifier would tighten the definition.","The analytical constraints could be turned into a predictive diagnostic: scan the Liouvillian spectrum of a candidate non-Hermitian system and check the $|X_\\pm|\\le 1$ or $X_\\pm\\ge 0$ conditions before simulating relaxation, identifying new platforms for the effect.","Extending the tensor-product multiqubit result to genuinely interacting or disordered non-Hermitian chains would test whether the effect survives when the slowest mode is no longer automatically suppressed."],"forward_implications":["The quantum Mpemba effect is a real feature of intrinsic non-Hermitian dynamics, not an artifact of Hermitian open-system descriptions.","Exceptional points should not be used as a universal predictor for the quantum Mpemba effect: in this model the effect's regime is bounded by neither Hamiltonian nor Liouvillian exceptional points.","The Hermitian limit is a sharp diagnostic: restoring Hermiticity to the Hamiltonian eliminates the effect, so non-Hermiticity is the operative ingredient.","The analytical long-time conditions provide parameter regimes with exactly one crossing, so experiments can choose parameters guaranteed to show genuine quantum Mpemba behavior rather than multiple crossings.","The effect survives dephasing noise and tensor-product multi-qubit extensions, so currently available PT-symmetric qubit platforms should be able to observe it."],"supporting_citations":[{"why":"Supplies the Lindblad-type master equation for the normalized density matrix that governs all of the paper's dynamics.","marker":"[48]"},{"why":"Provides the normalized-density-matrix evolution formalism and the probability-conservation correction term used in the master equation.","marker":"[65]"},{"why":"Introduces the exponentially accelerated approach to stationarity and the slowest-mode suppression strategy that the paper extends.","marker":"[2]"},{"why":"Reports the experiment linking the quantum Mpemba effect to a Liouvillian exceptional point, the contrast case for the paper's claim that exceptional points do not bound the effect.","marker":"[23]"},{"why":"Review that defines the established dynamical quantifiers (trace distance, Frobenius distance, relative entropy) used to identify the effect.","marker":"[28]"},{"why":"Prior theoretical work on multiple quantum Mpemba crossings and exceptional points that supplies the odd-versus-even intersection convention.","marker":"[57]"},{"why":"Reports an experimental realization of PT-symmetric quantum coherence, supporting the paper's experimental-feasibility claim.","marker":"[44]"},{"why":"Reports a superconducting-qubit implementation of non-Hermitian PT-symmetric dynamics, one of the platforms the authors say can test the effect.","marker":"[63]"}],"fun_headline_variants":["RieszNet headcount: 2 heads, 3x better causal effects","CausalSent: 'love' lifts positive sentiment by 2.9%","Interpretable NLP: RieszNet cuts effect MAE 2-3x","Two-headed RieszNet deciphers causal sentiment","Causal effects from reviews: 'love' wins by 2.9%"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The whole analysis rests on the unproven (here) master equation for the normalized density matrix of an open PT-symmetric qubit, taken from the authors' earlier paper; if that equation misdescribes the bath coupling, the predicted quantum-Mpemba regimes are model artifacts.","fun_headline_variants_meta":{"raw":{"variants":["RieszNet headcount: 2 heads, 3x better causal effects","CausalSent: 'love' lifts positive sentiment by 2.9%","Interpretable NLP: RieszNet cuts effect MAE 2-3x","Two-headed RieszNet deciphers causal sentiment","Causal effects from reviews: 'love' wins by 2.9%"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000233,"raw_usage":{"total_tokens":1464,"prompt_tokens":886,"completion_tokens":578,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":502,"completion_tokens_details":{"reasoning_tokens":478}},"tokens_in":502,"tokens_out":578,"duration_ms":5751,"temperature":1.0,"reasoning_tokens":478,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T17:05:48.209466+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Prepare a PT-symmetric qubit in the two initial states $\\hat\\rho_I(0)=(\\hat\\sigma_z+\\hat I)/2$ and $\\hat\\rho_{II}(0)=\\hat I/2$, coupled to a bosonic bath with rates in the paper's predicted single-crossing regime (for example $a=1.3$, $\\gamma_1=0.4$, $\\gamma_2=1$), and measure the trace distance $D(t)=\\frac12\\|\\hat\\rho(t)-\\hat\\rho_{\\rm ss}\\|_1$ for both states; the claim requires exactly one early crossing between the two curves and no later crossings, and zero crossings in the Hermitian limit $a=0$.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the Lindblad-type master equation for the normalized density matrix that governs all of the paper's dynamics."},{"cited_title":"Brody and E.-M","cited_arxiv_id":null,"evidence_quote":"Provides the normalized-density-matrix evolution formalism and the probability-conservation correction term used in the master equation."},{"cited_title":"Carollo, A","cited_arxiv_id":null,"evidence_quote":"Introduces the exponentially accelerated approach to stationarity and the slowest-mode suppression strategy that the paper extends."},{"cited_title":"Zhang, G","cited_arxiv_id":null,"evidence_quote":"Reports the experiment linking the quantum Mpemba effect to a Liouvillian exceptional point, the contrast case for the paper's claim that exceptional points do not bound the effect."},{"cited_title":"Chatterjee, S","cited_arxiv_id":null,"evidence_quote":"Prior theoretical work on multiple quantum Mpemba crossings and exceptional points that supplies the odd-versus-even intersection convention."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Reports a superconducting-qubit implementation of non-Hermitian PT-symmetric dynamics, one of the platforms the authors say can test the effect."}],"review_version":1}