{"id":"1bbfb478-a3d1-48e2-959c-b328bc7fa14a","arxiv_id":"2607.28536","paper_version":1,"verdict":"ACCEPT","confidence":"HIGH","novelty_score":8.0,"correctness_risk":"low","formal_verification":"none","parameter_count":0,"one_line_summary":"Long-range Pauli Gibbs states lose entanglement, magic, and infinite-temperature analyticity at distinct constant inverse temperatures Θ(1/sk), Θ(log(1/ε)/sk), and Θ(1/s√k), with matching classical algorithms.","lead":"Quantum thermal states stay classical in several precise senses down to constant temperatures even with long-range interactions, and those senses fail at different temperature scales. The work gives tight bounds, classical poly-time algorithms colder than known quantum mixers, and settles open questions on entanglement death and correlation decay.","discovery_kind":"extension","skeptic_critique":{"model":"grok-4.5","headline":"No significant objection identified","rationale":"The paper's strongest claims are internal to the (s,k)-long-range Pauli class and are backed by matching entangled/zero examples (Appendix A) plus constructive pinning and cluster-expansion algorithms. The reader's weakest_assumption correctly identifies scope limits rather than cracks in the derivations. No concrete inconsistency (e.g., an unjustified interchange of limits, a missing factor that would collapse the √k gap, or a circular use of separability inside the zero-free argument) surfaced on a second pass through the load-bearing lemmas (9–15, 21–26, 30–34). An independent spot-check of the two combinatorial improvements (amortized on-site strength for long-range propagators; defect repair for polymers) is the highest-value verification still worth running, but it is a diligence step, not evidence of a present flaw. Verdict remains ACCEPT.","tokens_in":73743,"tokens_out":496,"duration_ms":9910,"concrete_test":"Independently re-derive the coefficient-mass bound in Lemma 9 (propagator expansion) and the defect-counting argument that yields the √k improvement in Lemma 24/26 for a small explicit (s,k) instance (e.g. k=2, all-to-all XX+YY+ZZ with uniform |c|); confirm the claimed (3ks)^t t! mass and the half-defect polymer growth, and check that the resulting β thresholds match Theorems 1 and 4 up to the stated constants.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The reader's ACCEPT verdict is well-supported. The central hierarchy (separability at Θ(1/sk), zero-free disk at Θ(1/(s√k)), classical preparation to the separability scale, and stabilizerness to Θ(log(1/ε)/sk) for nearly-commuting models) is stated with matching upper and lower bounds, explicit constants, and constructive algorithms. The domain restrictions the reader flags (Pauli ℓ1 strength, disk vs strip, pinned zeros failing at Θ(log k/sk)) are openly scoped rather than hidden assumptions that undermine the proofs inside that scope. Residual risk is ordinary lengthy-proof error in a human+AI-assisted stack without formal verification, not a load-bearing gap in the argument as written.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.5","summary":"The paper establishes a hierarchy of classical-to-quantum transitions for Gibbs states of (s,k)-long-range Pauli Hamiltonians (bounded per-site ℓ1 interaction strength, locality k). It proves separability for all β ≤ 1/(72 sk), tight to Θ(1/sk) even for commuting models, resolving an open question of Rouzé–França–Alhambra; a matching polynomial-time classical algorithm preparing the state as a mixture of pure product stabilizer states up to β ≤ 1/(4096 e sk); stabilizerness to β = Θ(log(1/ε)/sk) for ε-close-to-commuting Hamiltonians; and a zero-free disk of radius Θ(1/(s√k)) implying exponential correlation decay for geometrically local models (resolving Harrow–Mehraban–Soleimanifar) and poly-time classical estimation of log Z and local expectations. Matching upper bounds and explicit constructions are given in the appendices.","tokens_in":73969,"tokens_out":810,"duration_ms":29919,"significance":"If correct, this is a substantial advance in high-temperature quantum statistical mechanics and quantum algorithms. It tightens and extends Bakshi et al. (FOCS’24) from low-intersection to genuine long-range interactions, places classical preparation below known quantum Gibbs-sampler mixing temperatures, and separates the entanglement, magic, and thermodynamic transitions with matching upper and lower bounds. The defect-repair cluster expansion yielding the √k improvement, the interaction-picture pinning for magic, and the randomized polymer samplers giving polynomial (not quasipolynomial) runtime are technically novel and of independent interest. Open questions (zero-free strips, non-Pauli/fermionic models) are cleanly scoped.","major_comments":[],"minor_comments":[{"comment":"The constant gap between separability (1/72 sk) and classical preparability (1/(4096 e sk)) is large; a short remark in §2.3 or §6 on whether the algorithmic constant can be brought closer to the information-theoretic one would help readers.","section":"§2.3, Theorem 2"},{"comment":"Definition 2.6 (ε-close to commuting) is used heavily; a one-line example computation for TFIM and perturbed toric code next to the definition would make the parameter immediately concrete.","section":"§2.1, Definition 2.6"},{"comment":"Figure 1 and Figure 2 are conceptually clear but the axis labels and the precise placement of β_sep vs β_phase could be annotated with the explicit Θ expressions from the theorems.","section":"Figures 1–2"},{"comment":"In §5.2 the transcript sampler (repair/birth) is intricate; a short pseudocode block parallel to Algorithm 1 would aid verification.","section":"§5.2, Lemma 24"},{"comment":"Typos/notation: occasional switches between λ_a and c_a for coefficients; “na ¨ıve” spacing; and “Tr” vs “tr” conventions could be restated once in §2.1 for the whole paper.","section":"Throughout"}],"recommendation":"accept","confidential_remarks":"The manuscript acknowledges substantial AI assistance on Appendices A–B and on improving k-dependence; the main-line arguments appear human-led and the authors take responsibility. For a journal that values reproducibility, the absence of formal verification or reference code for the polymer samplers is a mild residual risk typical of long analytic papers, not a reason to delay acceptance. Scope fit for a top theory/physics venue is excellent."},"author_rebuttal":null,"desk_editor":{"model":"grok-4.5","letter":"The headline result is clean: for (s,k)-long-range Pauli Hamiltonians they pin down distinct constant-temperature scales—separability at Θ(1/sk), a zero-free disk at Θ(1/(s√k)), classical preparation all the way to the separability edge, and stabilizerness out to Θ(log(1/ε)/sk) when the Hamiltonian is ε-close to commuting. Matching upper bounds and constructive algorithms make this more than a restatement of BLMT24/HMS20.\n\nWhat is actually new is the technical stack that gets them there. They amortize the propagator by on-site ℓ1 strength instead of degree, so all-to-all tails with bounded strength still work; adaptive pinning removes the extra k factor and tightens the low-intersection case to Θ(1/d); the interaction-picture argument for magic is genuinely different from the product-stabilizer route; and the defect-repair polymer counting is what buys the √k improvement in the cluster expansion. That package resolves the RFA25 question on constant-temperature entanglement death for long-range systems and the HMS20 correlation-decay conjecture beyond 1D, and it gives poly-time classical estimation and preparation colder than the known quantum Glauber regimes.\n\nSoft spots are mostly scope, not broken math. Everything is Pauli with bounded per-site strength; non-Pauli and fermionic models with unbounded ℓ1 are left open. They get a disk, not the strip one would want for the full classical hardness threshold at 1/s. Pinned zero-freeness, which the preparation algorithm needs, fails earlier (Θ(log k/sk)), and they prove that. The proof stack is long and partly AI-assisted without machine checks—ordinary residual risk for a paper of this length, not a load-bearing gap. Citations look appropriate; upper-bound examples are independent constructions.\n\nThis is for people working on high-temperature quantum Gibbs states, classical simulation, and quantum advantage thresholds. I would bring it to reading group, cite it, and send it to referees. Engage.","headline":"Tight hierarchy of classical-to-quantum transitions for long-range Pauli Gibbs states, with real open-question resolutions and algorithms that beat known quantum mixers on temperature.","tokens_in":74547,"tokens_out":529,"would_cite":true,"duration_ms":15965,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["82B10","81P40","68Q12"],"pacs":["05.30.-d","03.65.Ud","05.70.Fh"],"model":"grok-4.5","headline":"Quantum Gibbs states of long-range Pauli systems keep classical features down to finite, size-independent temperatures that fail in a sharp hierarchy.","keywords":["quantum Gibbs states","separability","magic","cluster expansion","long-range interactions","zero-freeness","thermal algorithms","correlation decay"],"falsifier":"Find an (s,k)-long-range Pauli Hamiltonian whose Gibbs state is entangled, or whose partition function has a zero, at an inverse temperature asymptotically colder than the claimed thresholds, or show that the classical preparation routine fails inside the claimed separable window.","tokens_in":74631,"feed_emoji":"🌡️","tokens_out":1048,"duration_ms":37182,"temperature":0.7,"pith_summary":"This paper shows that high-temperature quantum thermal states keep several classical traits of the infinite-temperature mixed state, and that those traits fail at different inverse-temperature scales that do not grow with system size. For Pauli Hamiltonians with bounded total interaction strength on every site—including long-range and all-to-all couplings—entanglement disappears below a constant temperature of order 1/(sk), magic can persist longer when the Hamiltonian is nearly commuting, and the thermodynamic infinite-temperature phase (a zero-free disk for the partition function) extends still colder, to order 1/(s√k). The authors give polynomial-time classical algorithms that prepare the Gibbs state as a mixture of pure product stabilizer states up to the separability threshold, and that estimate the log partition function and local thermal expectations throughout the infinite-temperature phase. The bounds are tight up to constants, settle open questions on long-range entanglement death and correlation decay, and place classical algorithms at colder temperatures than known quantum Gibbs samplers for the same models.","feed_headline":"Quantum heat stays classical down to sharp thresholds","feed_subtitle":"Long-range Pauli Gibbs states lose entanglement, magic, and hardness at distinct scales","key_machinery":"Convergent cluster expansions of the ordinary partition function, of pinned post-selected partition functions after measuring qubits, and of interaction-picture propagators, paired with an adaptive pinning procedure that iteratively removes terms while preserving a separable or stabilizer decomposition; the expansions become polynomial-time algorithms by randomized sampling of polymers.","core_discovery":"For (s,k)-long-range Pauli Hamiltonians, every Gibbs state is fully separable for β ≤ 1/(72 sk), a threshold that is tight Θ(1/sk) even for commuting examples; when the Hamiltonian is ε-close to commuting it remains a mixture of stabilizer states down to β = Θ(log(1/ε)/sk); and the partition function is zero-free in a disk of radius Θ(1/(s√k)). That disk yields exponential correlation decay for geometrically local systems and polynomial-time classical algorithms for log Z and local expectations, while a separate classical algorithm prepares the state as a mixture of pure product stabilizer states up to β = O(1/sk).","pith_inferences":["A zero-free strip of real width ~1/s (instead of a disk of radius ~1/(s√k)) would likely extend classical estimation all the way to known hardness thresholds for classical spins.","Pinned zeros appearing already at scale ~log k/(sk) suggest that quantum mixing arguments based on computational-basis conditioning may stop short of the full infinite-temperature phase.","The window between separability (~1/sk) and the zero-free radius (~1/s√k) is a concrete regime where entanglement and magic can exist while thermodynamic classicality and classical estimation still hold.","Whether the same hierarchy survives for non-Pauli local terms or fermionic models with unbounded ℓ1 strength remains the natural next stress test."],"forward_implications":["Death of entanglement occurs at constant temperature even for all-to-all Pauli interactions with bounded per-site strength.","Classical polynomial-time preparation of these Gibbs states reaches colder temperatures than known quantum Gibbs samplers.","Any pair of observables on a geometrically local Pauli system has exponentially decaying correlations throughout the infinite-temperature phase.","Proposed superpolynomial quantum advantage for estimating thermal expectations in long-range Pauli systems is ruled out inside the zero-free regime.","Nearly commuting Hamiltonians keep stabilizer Gibbs states at parametrically colder temperatures than the separability scale."],"fun_headline_variants":["Quantum Gibbs states stay classical to sharp finite-temperature thresholds","Entanglement dies at constant β for long-range Pauli Hamiltonians","Classical-to-quantum transitions form a hierarchy in thermal states","Gibbs states remain separable down to β = Θ(1/sk), tight bound","Partition function zero-free disk yields classical thermal algorithms"],"cache_read_input_tokens":65664,"weakest_assumption_plain":"The Hamiltonian must be a sum of Pauli strings whose total absolute strength on every single qubit stays bounded, independent of how large the system is.","fun_headline_variants_meta":{"raw":{"variants":["Quantum Gibbs states stay classical to sharp finite-temperature thresholds","Entanglement dies at constant β for long-range Pauli Hamiltonians","Classical-to-quantum transitions form a hierarchy in thermal states","Gibbs states remain separable down to β = Θ(1/sk), tight bound","Partition function zero-free disk yields classical thermal algorithms"]},"model":"grok-4.5","effort":"low","cost_usd":0.004932,"raw_usage":{"total_tokens":1427,"prompt_tokens":853,"num_sources_used":0,"completion_tokens":90,"cost_in_usd_ticks":49324000,"prompt_tokens_details":{"text_tokens":853,"audio_tokens":0,"image_tokens":0,"cached_tokens":128},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":484,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":853,"tokens_out":90,"duration_ms":9392,"temperature":1.0,"reasoning_tokens":484,"cache_read_input_tokens":128,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-31T04:19:12.857414+00:00","model_set":{"reader":"grok-4.5"},"falsifier":"Find an (s,k)-long-range Pauli Hamiltonian whose Gibbs state is entangled, or whose partition function has a zero, at an inverse temperature asymptotically colder than the claimed thresholds, or show that the classical preparation routine fails inside the claimed separable window.","supporting_citations":[],"review_version":1}