{"id":"fadb64cc-d15f-45f6-84bc-2aff20393382","arxiv_id":"2509.10840","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"high","formal_verification":"none","parameter_count":2,"one_line_summary":"Precision of single-qubit dephasing thermometry is compared across Hermitian, PT-symmetric, and anti-PT-symmetric qubits, with anti-PT claimed best, but the central decoherence model is imported and inconsistent.","lead":"The paper compares how well a single qubit can measure the temperature of its environment when the qubit is Hermitian, PT-symmetric, or anti-PT-symmetric. It claims the anti-PT-symmetric qubit gives the most precise estimate, but the core calculation is borrowed from earlier work and not actually shown.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The paper's own QSNR results contradict the central APT-superior QFI claim: since QSNR = T²QFI, APT cannot have the highest QFI and the lowest QSNR in the same model.","rationale":"The reader's weakest-assumption analysis correctly identifies a real gap: the APT decoherence factor Γ_APT(T,t) is never derived or even stated, and the central QFI formula depends entirely on it. That omission alone justifies rejection because the paper's quantitative claim cannot be verified from the manuscript. However, I find an even more decisive problem: the paper's own reported results are internally contradictory. Section IV.B states that APT yields the highest QFI across all regimes, while Section V.B reports that APT yields the lowest QSNR and Hermitian the highest. Since QSNR is defined in Eq. (10) as T² times the QFI, and both quantities are evaluated at the same optimal interaction time, this ordering is mathematically impossible unless the QFI and QSNR curves were computed from different decoherence models or with different normalizations. The contradiction does not depend on the missing Γ_APT derivation: even if Γ_APT were correctly imported from the cited paper, the reported QFI and QSNR numbers cannot both be right. The manuscript also contains a second textual contradiction in Section V.B, where the high-T QSNR is first claimed to saturate to a universal value independent of symmetry and then assigned three different symmetry-dependent plateau values. These issues are load-bearing, not cosmetic: they undermine the central claim directly. I retain the reader's REJECT verdict, so no adjustment is needed, but I would rest the rejection primarily on the internal QFI-QSNR inconsistency rather than solely on the missing derivation.","tokens_in":15256,"tokens_out":9163,"duration_ms":82470,"concrete_test":"Regenerate H(T,t) for each symmetry from Eqs. (37)-(39) together with the Γ_APT(T,t) implied by Cen and Saxena (2022), or directly extract the data behind Figs. 4 and 8. At one representative temperature, say T=10 with ω_c=1, evaluate H(T,t_opt(T)) for Hermitian and APT and compute QSNR = T²H. If the Fig. 4/5 QFI curves give H_APT > H_Herm while the Fig. 8 plateaus give QSNR_APT < QSNR_Herm, the central claim is internally inconsistent. Also verify the reported high-T plateaus 0.25, 0.16, and 0.04 by recomputing QSNR from the same Γ used to produce the QFI surfaces; if they do not match, one of the two central numerical results is erroneous.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim in Sec. IV.B is that anti-PT symmetry yields the highest QFI across all regimes. Yet Sec. V.B reports the opposite ordering for the QSNR, which Eq. (10) defines as Q_T = T²H(T). The paper gives symmetry-dependent high-T saturation plateaus: Hermitian 0.25, PT 0.16, APT 0.04, evaluated at the optimal interaction time (Fig. 8). The QFI comparison in Sec. IV.C and Fig. 5 is also made at optimal times, so if H_APT(T,t_opt) > H_Herm(T,t_opt), then T²H_APT(T,t_opt) > T²H_Herm(T,t_opt). The two reported orderings are therefore logically incompatible; one of the two sets of curves cannot come from the same model. This is an internal inconsistency, not a matter of interpretation. It also connects to the gap the reader flagged: Eq. (37) shows H depends only on Γ(T,t), but Γ_APT(T,t) is never stated. The APT case is gestured at through Ω2−Ω1 in Eq. (24) with a reference to Ref. [62], and the main thermal formulas, Eqs. (38)-(39), are the standard Hermitian dephasing expressions. Without an explicit Γ_APT, the APT QFI curves cannot be reproduced, and the contradictory QSNR ranking cannot be debugged. Additionally, Sec. V.B describes the high-T QSNR first as 'universal' and 'independent of the symmetry,' then lists three different symmetry-dependent values—another direct self-contradiction.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript studies temperature estimation of an Ohmic thermal bath via dephasing of a single qubit, comparing Hermitian, PT-symmetric, and anti-PT-symmetric (APT) qubit Hamiltonians. It derives a QFI formula for the dephasing channel (Eq. 37), identifies the optimal initial state (θ=π/2), and reports numerical optimization of the QFI over interaction time and temperature for sub-Ohmic, Ohmic, and super-Ohmic environments. It also reports the QSNR, decoherence dynamics, von Neumann entropy, and exponential decay fits. The paper's central claim is that APT symmetry yields the highest QFI and the strongest decoherence resilience, with Hermitian dynamics giving the lowest QFI. However, the QSNR section reports the opposite ordering, which is logically incompatible with the QFI results.","tokens_in":15499,"tokens_out":4125,"duration_ms":33942,"significance":"If the APT-superiority claim were supported, the paper would offer a concrete and useful result for quantum thermometry: anti-PT-symmetric qubits would provide both higher precision and slower decoherence than Hermitian or PT-symmetric qubits in Ohmic environments. The manuscript also has positive features: it clearly formulates the QFI optimization, identifies the optimal state preparation, and reports explicit exponential decoherence fits with numerical parameters and uncertainties. The study builds on established single-qubit dephasing thermometry (Ref. [74]) and the APT-qubit decoherence model of Cen and Saxena [62], so the cross-symmetry comparison is a plausible extension. However, because the APT decoherence factor is never explicitly given and the QFI and QSNR orderings contradict each other, the central claim is not supported by the manuscript as written.","major_comments":[{"comment":"The central claim that APT symmetry yields the highest QFI across all regimes is logically incompatible with the QSNR results reported in Section V.B. Since Eq. (10) defines Q_T = T²H(T), and both Section IV.C (Fig. 5) and Section V.B (Fig. 8) evaluate quantities at the optimal interaction time t_opt, the ordering of the QSNR plateaus (Hermitian 0.25, PT 0.16, APT 0.04) must match the ordering of H at t_opt. The paper instead reports APT as the highest QFI and the lowest QSNR, which cannot both be true for the same H(T,t_opt). One of the two sets of curves must be erroneous, and this undermines the main conclusion.","section":"§IV.B and §V.B"},{"comment":"Equation (37) expresses the QFI solely in terms of the decoherence factor Γ(T,t), yet the manuscript never provides Γ(T,t) for the APT case. The APT case is introduced only through Ω2(t)−Ω1(t) in Eq. (24), with a reference to Cen and Saxena [62], and the thermal decoherence formulas in Eqs. (38)-(39) are the standard Hermitian dephasing expressions. Because no time-dependent Dyson map or resulting reduced density matrix is shown for the APT qubit, the APT QFI curves in Figs. 4-5 cannot be reproduced from the manuscript as written. The APT-superiority claim therefore rests on an unstated imported model, and the claimed derivation is not actually provided.","section":"§III (Eqs. 23-27) and §IV.A (Eq. 37)"},{"comment":"Section V.B contains a direct self-contradiction: it first states that the QSNR 'saturates to a universal value, independent of the symmetry and the nature of the spectral density,' and then immediately reports symmetry-dependent plateaus of 0.04 (APT), 0.16 (PT), and 0.25 (Hermitian). The Introduction similarly promises a universal high-temperature saturation. If the universal value is meant to be independent only of the spectral density s but not of the symmetry, this needs to be stated; as written, the two sentences are incompatible.","section":"§V.B"}],"minor_comments":[{"comment":"The word 'symmetrizes' is used where 'symmetries' is intended; this typo should be corrected.","section":"Abstract and §I"},{"comment":"The sentence 'whereas the anti-PT operator anticommutes with it, satisfying {H,PT}=0' appears twice in succession; one duplicate should be removed.","section":"§I"},{"comment":"The text says 'Inserting Γ(t,ω_c) as given in Eq. (6)'; Eq. (6) is the Cramér-Rao bound, not the decoherence factor. The cross-reference should point to the spectral density or decoherence equations.","section":"§IV.A"},{"comment":"The caption assigns 'sub-Ohmic (s=1.0)' and 'Ohmic (s=0.5)', which is inconsistent with the rest of the paper where s=0.5 is sub-Ohmic and s=1.0 is Ohmic; these labels should be corrected.","section":"Fig. 6 caption"},{"comment":"The exponential fit model D(t)=exp(−t/a) and the fitting region are described only in the caption; the fitting methodology should be stated in the main text for reproducibility.","section":"§V.A / Fig. 6 caption"}],"recommendation":"reject","confidential_remarks":"The paper's central comparison appears to reuse the single-qubit dephasing thermometry framework of Ref. [74] and the anti-PT decoherence model of Ref. [62] without deriving or stating the APT decoherence factor. The internal contradiction between the QFI ordering (APT highest) and the QSNR ordering (APT lowest) is a load-bearing error that cannot be fixed by minor edits; it requires identifying which set of numerical studies is incorrect and, for the APT case, supplying the missing model. Given the heaviness of the reliance on Refs. [62] and [74], the novelty claim should also be reconsidered once the technical issues are resolved."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The right thing to say up front: the paper has a reasonable research question, but the central claim doesn't hold together as written. The two things you need to know are (1) the claimed APT advantage in QFI depends entirely on an APT decoherence factor that is never derived or even stated, and (2) the QSNR results in Sec. V.B directly contradict the QFI results in Sec. IV.B, because QSNR = T²H. You cannot have APT with the highest H at the optimal time and the lowest QSNR at the optimal time in the same model.\n\nWhat is genuinely there: comparing Hermitian, PT-symmetric, and anti-PT-symmetric qubits for dephasing-based thermometry is a sensible extension of existing work. The paper correctly borrows the standard dephasing-thermometry machinery from Razavian et al. and the APT dynamics from Cen and Saxena, and it runs a fairly thorough numerical scan over Ohmicity parameter, interaction time, and temperature. If the APT model were correctly applied, the conclusion that APT qubits suppress decoherence and therefore improve thermometric precision would be a useful, if incremental, design rule for quantum sensing.\n\nThe soft spots are serious. Equation (37) shows QFI depends only on the decoherence factor Gamma, but Gamma for the APT case is never given; the paper gestures at Omega_2 − Omega_1 with a citation to Ref. [62] and moves on. A reader cannot reproduce the APT curves or check whether the comparison is fair. The QSNR contradiction is worse: Sec. V.B first says the high-T QSNR saturates to a universal value, then lists symmetry-dependent plateaus of 0.25, 0.16, and 0.04—and those plateaus, combined with QSNR = T²H, imply the opposite QFI ordering from what the figures show. This is an internal inconsistency in the paper's own equations, not a matter of interpretation. There are also smaller issues: the abstract promises identification of the optimal measurement, but none is specified, and the text has typos, swapped s-labels in figure captions, and duplicated sentences. Those would be minor on their own, but here they sit on top of a load-bearing gap.\n\nI would not send this to peer review in its current form. The missing APT decoherence factor and the QSNR contradiction are not fixable by tweaking language; the authors need to derive Gamma_APT explicitly, redo the QSNR calculation, and reconcile the ordering claims before the paper is coherent. The topic is fine, and a corrected version might be worth a look, but this version does not give a serious referee enough to work with.","headline":"The APT-superiority claim in this thermometry paper rests on a decoherence factor that is never derived, and the QSNR section contradicts the QFI section; this version should not go to referees.","tokens_in":16149,"tokens_out":2556,"would_cite":false,"duration_ms":24544,"reading_group":"no","serious_thinker":"no","would_accept_peer_review":false},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper claims that anti-PT-symmetric qubits are the most precise dephasing-based thermometers in Ohmic environments, retaining coherence longest and maximizing the quantum Fisher information for temperature.","keywords":["quantum thermometry","dephasing","quantum Fisher information","anti-PT symmetry","PT symmetry","Ohmic spectral density","qubit probe","quantum Cramér-Rao bound"],"falsifier":"Deriving $\\Gamma_{\\mathrm{APT}}(T,t)$ explicitly from the time-dependent Dyson map for Hamiltonian (18) and comparing it with $\\Omega_2(t)-\\Omega_1(t)$ would settle the calculation; a discrepancy at the optimal times changes $H(T,t)$ and the APT ranking. Experimentally, measuring the coherence decay of anti-PT, PT, and Hermitian qubits in one Ohmic bath and checking the fitted ordering $a\\approx 0.685<1.688<3.141$ (Hermitian, PT, APT) would settle the claim directly.","tokens_in":14963,"feed_emoji":"🌡️","tokens_out":11672,"duration_ms":97900,"temperature":0.7,"pith_summary":"This paper sets out to show that qubit dephasing can be used as a resource for thermometry and that the symmetry of the qubit determines how good the thermometer is. For a qubit coupled to a bosonic bath with an Ohmic spectral density, the paper claims that anti-PT-symmetric qubits—those whose Hamiltonian anticommutes with the combined parity-time operation—keep their coherence longest and yield the highest quantum Fisher information for the bath temperature, followed by PT-symmetric qubits, with Hermitian qubits last. The reason to care is that this turns decoherence, usually the enemy of quantum devices, into a precise probe of temperature without requiring the probe to reach thermal equilibrium with the sample, and it suggests that non-Hermitian engineering can protect quantum sensors in noisy low-temperature environments. The paper also identifies the optimal probe preparation and the optimal measurement, and shows that the best estimate happens at a finite interaction time rather than at the steady state.","feed_headline":"Anti-PT qubits beat Hermitian qubits as thermometers","feed_subtitle":"In Ohmic baths, anti-PT probes keep coherence longest and maximize quantum Fisher information.","key_machinery":"The central object is the dephasing dynamical map, whose off-diagonal entries decay as $e^{-\\Gamma(T,t)}$, and the quantum Fisher information it induces, $H(T,t)=\\sin^2\\theta\\,(\\partial_T\\Gamma)^2/(e^{2\\Gamma}-1)$. The bath is Ohmic with spectral density $J(\\omega,\\omega_c)=J_0(\\omega^s/\\omega_c^{s-1})e^{-\\omega/\\omega_c}$, and the symmetry enters through the phase function $\\Omega(\\tilde t)$ in Eq. (24): Hermitian uses $\\Omega(t)$, PT uses $-\\Omega(t)$, and anti-PT uses $\\Omega_2(t)-\\Omega_1(t)$, with the anti-PT reduced density matrix obtained through a time-dependent Dyson map to an equivalent Hermitian system. Optimizing $H$ over the preparation angle, the interaction time, and the temperature yields the paper's rankings and identifies the optimal measurement that saturates the quantum Cramér-Rao bound.","core_discovery":"The paper's central claim is a ranking: under pure dephasing in an Ohmic environment, an anti-PT-symmetric qubit has the slowest decoherence and gives the largest quantum Fisher information $H(T,t)$ for temperature, while a Hermitian qubit gives the smallest and a PT-symmetric qubit sits between them. Alongside this, the paper claims that the optimal initial state is the equatorial superposition $|+\\rangle=(|0\\rangle+|1\\rangle)/\\sqrt{2}$ for all temperatures, times, and Ohmicity parameters; that the maximum of $H(T,t)$ occurs at a finite interaction time, before the qubit reaches its stationary state or complete dephasing, except in the super-Ohmic low-temperature case where the optimum coincides with thermalization; and that the optimal measurement saturates the quantum Cramér-Rao bound. The paper further reports that the quantum signal-to-noise ratio is lowest for anti-PT symmetry and highest for Hermitian symmetry, saturating to a universal value at high temperature.","pith_inferences":["The paper's two metrics point in opposite directions—anti-PT maximizes QFI while Hermitian maximizes QSNR—so the practical winner depends on whether one is limited by the number of measurement repetitions (QFI) or by the dynamic range of normalized sensitivity (QSNR); the paper itself does not resolve that choice.","Equation (37) suggests a general design principle: a good dephasing thermometer should maximize the temperature derivative of the decoherence factor while keeping $\\Gamma$ near unity, so the denominator $e^{2\\Gamma}-1$ does not erase the signal; this principle could be applied to other non-Hermitian or multi-qubit probes.","The exponential decay constants reported from the fits ($a\\approx 0.685$ for Hermitian, $1.688$ for PT, $3.141$ for APT) give a concrete experimental signature: in existing anti-PT platforms (coupled atomic beams, electrical-circuit resonators, microcavities), measuring the pure-dephasing decay ordering in the same Ohmic bath would directly test the central ranking."],"forward_implications":["A thermometer using the anti-PT qubit needs fewer repetitions to reach a target variance, since the quantum Fisher information sets the per-measurement precision bound.","The optimal measurement is explicitly identified, so a protocol can be implemented that actually reaches the quantum Cramér-Rao bound rather than only quoting it.","Timing matters: the probe should be measured at the optimal interaction time rather than after it has equilibrated, except in super-Ohmic low-temperature environments where the optimum coincides with stationarity.","At high temperatures the environmental spectrum stops mattering: the quantum signal-to-noise ratio becomes universal, which simplifies calibration of hot-sample thermometers.","Non-Markovian memory effects do not improve the estimate, so a memoryless treatment is sufficient for optimizing the protocol."],"supporting_citations":[{"why":"Supplies the anti-PT qubit decoherence factor through the functions $\\Omega_1(t)$ and $\\Omega_2(t)$, the input on which the APT superiority claim rests.","marker":"[62]"},{"why":"Establishes that PT-symmetric qubits slow decoherence in weakly coupled Hermitian environments, the baseline the paper extends to anti-PT symmetry.","marker":"[34]"},{"why":"Provides the single-qubit dephasing thermometry protocol with QFI that this paper generalizes to non-Hermitian symmetries.","marker":"[74]"},{"why":"Gives the qubit-probe thermometry results for Ohmic environments that set the comparison benchmarks for QFI and QSNR.","marker":"[75]"},{"why":"Provides the time-dependent Dyson map method used to obtain the APT qubit's reduced density matrix.","marker":"[38]"},{"why":"Underlies the open-system dephasing formalism and thermal-bath averaging that produce the decoherence factor $\\Gamma(T,t)$.","marker":"[30]"},{"why":"Defines the quantum Fisher information and the quantum Cramér-Rao bound that set the precision limits optimized throughout the paper.","marker":"[6]"}],"fun_headline_variants":["Anti-PT qubits sharpen thermometry in Ohmic baths","Non-Hermitian qubits top Hermitian for temperature sensing","Optimal qubit thermometry occurs before steady state","Anti-PT symmetry maximizes qubit Fisher information","Qubit dephasing thermometry: anti-PT beats Hermitian"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The anti-PT advantage rests entirely on a decoherence factor $\\Gamma_{\\mathrm{APT}}(T,t)$ that the paper imports from reference [62] rather than deriving from its own Dyson-map construction; if that imported factor is wrong or misapplied to this setup, the central ranking collapses.","fun_headline_variants_meta":{"raw":{"variants":["Anti-PT qubits sharpen thermometry in Ohmic baths","Non-Hermitian qubits top Hermitian for temperature sensing","Optimal qubit thermometry occurs before steady state","Anti-PT symmetry maximizes qubit Fisher information","Qubit dephasing thermometry: anti-PT beats Hermitian"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00037,"raw_usage":{"total_tokens":1978,"prompt_tokens":934,"completion_tokens":1044,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":550,"completion_tokens_details":{"reasoning_tokens":960}},"tokens_in":550,"tokens_out":1044,"duration_ms":8466,"temperature":1.0,"reasoning_tokens":960,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T15:52:17.005857+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Deriving $\\Gamma_{\\mathrm{APT}}(T,t)$ explicitly from the time-dependent Dyson map for Hamiltonian (18) and comparing it with $\\Omega_2(t)-\\Omega_1(t)$ would settle the calculation; a discrepancy at the optimal times changes $H(T,t)$ and the APT ranking. Experimentally, measuring the coherence decay of anti-PT, PT, and Hermitian qubits in one Ohmic bath and checking the fitted ordering $a\\approx 0.685<1.688<3.141$ (Hermitian, PT, APT) would settle the claim directly.","supporting_citations":[{"cited_title":"Monras, Optimal phase measurements with pure Gaussian states,Phys","cited_arxiv_id":null,"evidence_quote":"Supplies the anti-PT qubit decoherence factor through the functions $\\Omega_1(t)$ and $\\Omega_2(t)$, the input on which the APT superiority claim rests."},{"cited_title":"Piilo and S","cited_arxiv_id":null,"evidence_quote":"Establishes that PT-symmetric qubits slow decoherence in weakly coupled Hermitian environments, the baseline the paper extends to anti-PT symmetry."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the single-qubit dephasing thermometry protocol with QFI that this paper generalizes to non-Hermitian symmetries."},{"cited_title":"Giazotto, T","cited_arxiv_id":null,"evidence_quote":"Gives the qubit-probe thermometry results for Ohmic environments that set the comparison benchmarks for QFI and QSNR."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the time-dependent Dyson map method used to obtain the APT qubit's reduced density matrix."},{"cited_title":"El Makouri, A","cited_arxiv_id":null,"evidence_quote":"Underlies the open-system dephasing formalism and thermal-bath averaging that produce the decoherence factor $\\Gamma(T,t)$."},{"cited_title":"Darmois, Sur les limites de la dispersion de certaines esti- mations,Rev","cited_arxiv_id":null,"evidence_quote":"Defines the quantum Fisher information and the quantum Cramér-Rao bound that set the precision limits optimized throughout the paper."}],"review_version":2}