{"id":"f8f8e098-455f-41c6-afd4-4c21c983cddc","arxiv_id":"2505.18393","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"Frustrated local Hamiltonians can sometimes be steered into their ground-state manifold via discrete local measurement steps, and when they cannot, local steering is bounded by a 'glass floor' set by the smallest eigenvalue of local reduced density matrices.","lead":"This paper shows that ground states of certain frustrated many-body Hamiltonians, including commuting Pauli spin models, can be prepared by sequences of local measurements or 'steering', something previously thought impossible. For Hamiltonians where this fails, it derives a 'glass floor', a quantitative limit on how close local steering can bring a system to the true ground state.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eq. (17) assumes without derivation that the asymptotic steering state is a Gibbs state of the target Hamiltonian; the temperature-based 'glass floor' is therefore unsupported even though the fidelity and energy bounds stand.","rationale":"The reader's verdict was CONDITIONAL, with the temperature-bound/Gibbs-ansatz assumption listed among the fragile premises. My stress-test independently converged on that same step as the most load-bearing issue: it is the only place where a physical interpretation (temperature) is attached to a quantity that the derivation does not constrain. I checked the other central claims in good faith: Theorem 4's construction is plausible and the apparent locality obstacle is resolved by the fact that the valid energy configurations are spanned by local single-qubit characters; Theorem 1's proof is standard. The incorrect Heisenberg-picture equation in Sec. VI is a typo-like error that does not propagate to Appendix C. Thus I do not believe the reader's verdict should change; it should remain CONDITIONAL because the temperature floor, as stated, is an unproven ansatz. If a numerical simulation shows the asymptotic state is approximately thermal, then the concern would be mitigated and the paper could be upgraded; if not, the temperature claim should be softened to a statement about ground-state population only.","tokens_in":59041,"tokens_out":33518,"duration_ms":301979,"concrete_test":"Numerically simulate a concrete steering protocol for the 1D antiferromagnetic Heisenberg ring with N=4 or 6 spin-1/2 sites and periodic boundary conditions, using local two-site superoperators that project each neighboring pair onto its local spin-singlet (ground) subspace, consistent with the two-body steering operators discussed in Sec. VIII A. From many random initial states, obtain the asymptotic state ρ_∞. Verify: (i) the fidelity satisfies F ≤ 1 - p(Π_GS) and the energy obeys the bound of Eq. (15); (ii) compute the effective temperature T* from the ratio of populations of the ground and first excited states, then check whether the full population distribution of ρ_∞ matches Boltzmann weights e^{-β E_n}/Z at β=1/T*. If the excited-state ratios deviate from those weights while the ground-state population matches, then Eq. (17) has no physical meaning as a temperature bound.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central positive claims are Theorem 1 (steady steerability iff a frustration-free parent Hamiltonian exists) and Theorem 4 (ground-state manifolds of commuting Pauli Hamiltonians are steerable). I found no fatal flaw in these arguments: Appendix C's proof of Theorem 4 is internally consistent, and the locality of the superoperators can be justified because the kernel of the relation matrix is spanned by single-qubit characters of bounded support. One presentational error appears in Sec. VI: the claimed Heisenberg-picture identity P(i)†(H_{i-1}) = -1 is false; the correct identity is P(i)†(H_{i-1}) = -H_{i-1}H_i. This does not affect the Appendix-C proof. The load-bearing concern concerns the second headline result, the 'glass floor.' In Sec. VII D, Eq. (17) replaces the asymptotic surrogate state with a thermal (Gibbs) state of the target Hamiltonian H, writing Tr(ρ_surr Π_GS) ≈ deg(H)e^{-βE_GS}/Z(β). But H is not part of the steering dynamics; the local superoperators are chosen only from the target manifold and need not thermalize the system. Nothing in the derivation rules out an asymptotic state with the same ground-state population but an arbitrary, non-Boltzmann distribution over excited states. In that case, the lower bound on T_eff derived from Eq. (17) is not the temperature of any physical Gibbs state; it is only a re-parameterization of the ground-state population. The fidelity bound (Eq. 13) and the energy bound (Eq. 15) do not rely on the Gibbs ansatz and remain rigorous, as the authors themselves acknowledge by calling the thermal replacement a 'working approximation.' Since the temperature bound is a central advertised result, this is the weakest load-bearing step.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies passive ('blind') steering of many-body quantum states by sequences of local non-unitary superoperators, with the target being the ground-state manifold of a local Hamiltonian. It proposes a four-way classification: frustration-free steerable (FFS), non-frustration-free steadily steerable (NFFSS), non-frustration-free jittery steerable (NFFJS), and non-frustration-free non-steerable (NFFNS). The central positive claims are Theorem 1, that steady steerability is equivalent to the existence of a local frustration-free parent Hamiltonian with the same ground-state manifold, and Theorem 4, that the ground-state manifold of any commuting Pauli Hamiltonian is a steerable subspace (of NFFJS type), with an explicit construction of local superoperators and a randomized greedy steering sequence. For the non-steerable class, the paper derives an upper bound on the fidelity of any 'presumed surrogate' state with the target ground state (Eqs. 11 and 13), a lower bound on the achievable energy (Eq. 15), and a lower bound on an effective temperature interpreted as a 'glass floor' (Eq. 17). These results are applied numerically to the antiferromagnetic Heisenberg model, the Dirac and Majorana SYK models, and the Fermi-Hubbard model. The paper explicitly acknowledges that the necessary conditions for NFFJS steerability are not claimed to be sufficient, and that the Gibbs-state replacement in Sec. VII D is a working approximation.","tokens_in":59366,"tokens_out":12673,"duration_ms":143392,"significance":"If the main claims hold, the paper substantially extends the known scope of dissipative and measurement-based ground-state engineering: the identification of a broad class of frustrated commuting-Pauli Hamiltonians whose ground-state manifolds are steerable overturns the prior belief that only frustration-free Hamiltonians admit passive steering. The fidelity and energy bounds in Sec. VII are clean consequences of the Schmidt decomposition and are not fitted to the numerics, which is a strength. The proofs in Appendix C are explicit and internally coherent, although they are not machine-checked and no code is shipped. The self-identified limitations—the provisional character of the NFFJS necessary conditions and the Gibbs ansatz in Sec. VII D—are important and need to be resolved before the temperature-based 'glass floor' can be regarded as a physical bound.","major_comments":[{"comment":"The temperature lower bound ('glass floor') is not derived from the steering dynamics. Equation (17) replaces the asymptotic surrogate state by a Gibbs state of the target Hamiltonian H, writing Tr(ρ_surr Π_GS) ≈ deg(H)e^{-βE_GS}/Z(β). But H is not part of the dynamics, and the local superoperators are chosen only from the target manifold; nothing in the derivation rules out a non-thermal asymptotic state with the same ground-state population and an arbitrary distribution over excited states. In that case the quantity T_eff is merely a re-parameterization of 1-p(Π_GS) under an unjustified Boltzmann ansatz, and the numerical values reported in Sec. VIII inherit that ansatz. The fidelity bound (Eq. 13) and the energy bound (Eq. 15) survive, but the claim of a lower bound on an achievable physical temperature does not. The authors should either prove that the steering protocol thermalizes with respect to H, or explicitly define T_eff as the temperature of the Gibbs state that best fits the ground-state population and adjust the abstract and Sec. IX accordingly.","section":"Sec. VII D, Eq. (17)"},{"comment":"The locality reduction for arbitrary commuting Pauli Hamiltonians is not fully established. Lemma 3 shows that for every g_VH in the right null space of C_H there exists a Pauli operator V with the required commutation relations, but this V can have support that scales with the system size. The manuscript then states that a non-local g_VH 'can be decomposed into a sum of local components, each corresponding to a local operator V_k', and that replacing a single superoperator by a product of local superoperators resolves the issue. However, no argument is given that the sequential application of the local superoperators reproduces the same energy update v_E → v_E + e_CVH A_0,C, nor that the greedy convergence proof of Appendix C 3 remains valid after this replacement. Since Definition 1 requires each steering operation to be local, this step is load-bearing for Theorem 4. A rigorous locality reduction, or a restricted statement of Theorem 4 to the cases where the construction is explicitly local, is needed.","section":"Appendix C 4 and Theorem 4"}],"minor_comments":[{"comment":"The stated Heisenberg-picture identity P(i)†(H_{i-1}) = -1 is incorrect; direct calculation from Eq. (4) gives P(i)†(H_{i-1}) = -H_{i-1}H_i, not -1. The assertion that one application brings all states to the local ground state of H_{i-1} therefore needs revision. This does not affect the general proof in Appendix C, but the example's explanation should be corrected.","section":"Sec. VI, paragraph after Eq. (4)"},{"comment":"The displayed derivation of the local fidelity contains a typo in the summation index: one line reads 'i̸=' without a lower limit or an index name, and the surrounding indices are inconsistent. Please fix the notation so that the expression matches Eq. (10).","section":"Sec. VII B, Eq. (14)"},{"comment":"The SU(2)-symmetry argument for the absence of SCQs in the antiferromagnetic Heisenberg model is heuristic, especially the sentence 'For the scenario (ii), one also expects the absence of local SCQ'. Since this model is used as a numerical example of the NFFNS class, the argument should invoke the precise criterion of Corollary 4.1 or otherwise give a verifiable condition rather than an expectation.","section":"Sec. VIII A"}],"recommendation":"major_revision","confidential_remarks":"This is a potentially important paper. The positive classification results (Theorems 1 and 4) appear defensible, and the fidelity/energy bounds are clean. The main risk is the 'glass floor' temperature claim in Sec. VII D, which rests on an explicitly assumed Gibbs form with no supporting dynamics; if that cannot be supplied, the claim should be repositioned as a bound on a fitted effective temperature. The locality reduction in Appendix C.4 also needs to be made rigorous for Theorem 4 to stand in full generality. I would not recommend rejection on the current evidence, but these two points are load-bearing and require substantive revision."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: the one new result worth caring about is Theorem 4—ground-state manifolds of commuting Pauli Hamiltonians are steerable even when the Hamiltonians are frustrated. I read the Appendix C proof carefully and it holds up: the superoperator construction is explicit, the locality argument via the kernel of the relation matrix is sound, and the randomized greedy reduction to the ground-state manifold is plausible, though not machine-checked. This genuinely breaks the earlier assumption that only frustration-free Hamiltonians admit passive steering, and it does so for a broad, physically relevant class. The second advertised result, the \"glass floor\" temperature bound, is weaker than the abstract suggests. The fidelity bound (Eq. 13) and energy bound (Eq. 15) follow cleanly from Schmidt decomposition and are rigorous. But Eq. (17) replaces the asymptotic surrogate state with a Gibbs state of the target Hamiltonian, and H plays no role in the steering dynamics. Nothing rules out a surrogate state with the same ground-state population but non-Boltzmann weights on excited states. So the lower bound on T_eff is, as it stands, a re-parameterization of the ground-state population bound rather than a bound on the temperature of a physical state. The authors do call the thermal replacement a \"working approximation,\" which is honest, but the abstract and summary present the glass floor as a cooling result. A referee should ask them to either derive the Gibbs form from the protocol or reframe the claim. The necessary conditions for NFFJS are, as the authors concede, not sufficient; they require non-local information. That incompleteness is acknowledged, so I don't count it as a hidden flaw, but it does mean the classification is a boundary-marking exercise rather than a complete taxonomy. Minor: in Sec. VI, the Heisenberg-picture identity P(i)†(H_{i-1}) = -1 is not correct as written; direct computation gives P(i)†(H_{i-1}) = -H_{i-1}H_i. It doesn't affect the Appendix C proof, but it should be fixed. Numerics are exact diagonalization on small systems, no code or data shipped. That's a minor weakness, not a fatal one; the bounds are the main content. Who is this for: people working on dissipative state preparation, measurement-induced cooling, and quantum simulation of frustrated models. It deserves a serious referee. I'd send it to review, and I'd cite Theorem 4.","headline":"Theorem 4 is real and worth citing; the glass-floor temperature bound is a Gibbs ansatz, not a derived cooling limit.","tokens_in":59962,"tokens_out":2611,"would_cite":true,"duration_ms":23679,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper proves that ground-state manifolds of commuting Pauli Hamiltonians are steerable by local measurement sequences, even when the Hamiltonian is frustrated, and bounds how close local steering can come when it is not.","keywords":["passive steering","ground-state manifold","frustration-free Hamiltonians","commuting Pauli Hamiltonians","jittery steering","glass floor","effective temperature","dissipative state engineering"],"falsifier":"Numerically optimize a finite sequence of local superoperators for a system whose ground state has full local Schmidt rank, such as the spin-1/2 antiferromagnetic Heisenberg chain with $N$ up to 20, and test whether the overlap with the ground-state manifold can exceed $1-p(\\Pi_{\\mathrm{GS}})$; any success would refute the glass floor. In parallel, reconstruct the asymptotic state produced by the protocol and examine its low-energy spectrum: if it is not well fit by a Gibbs distribution, the effective-temperature bound is not a physical property of the state.","tokens_in":58785,"feed_emoji":"⚛️","tokens_out":7962,"duration_ms":83917,"temperature":0.7,"pith_summary":"Passive steering uses predetermined local measurements to push an arbitrary initial state toward a target subspace, typically the ground-state manifold of a many-body Hamiltonian. This paper tries to overturn the long-held expectation that only frustration-free Hamiltonians can be reached this way. It proves that every commuting Pauli Hamiltonian, including classically frustrated examples such as odd-length Ising antiferromagnets, has a steerable ground-state manifold, with the caveat that the state never settles down inside the manifold: it keeps jumping between ground states. For Hamiltonians whose ground states cannot be steered, the paper derives a quantitative \"glass floor\": any local passive protocol must respect an upper bound on fidelity, a lower bound on energy, and a lower bound on effective temperature, all controlled by the smallest eigenvalue of the local reduced density matrices of the ground states.","feed_headline":"Local steering can reach ground states of frustrated spin models","feed_subtitle":"A proof that frustration need not block passive steering, plus a quantitative floor on how close the rest can get.","key_machinery":"The load-bearing object is the local steering superoperator, built from the Hamiltonian's own local terms: $P^{(i)}_{\\pm}(\\rho)=\\Pi^{(i)}_{\\pm}\\rho\\Pi^{(i)}_{\\pm}+\\Pi^{(i)}_{\\mp}V_\\pm^\\dagger\\rho V_\\pm\\Pi^{(i)}_{\\mp}$, where $\\Pi^{(i)}_{\\pm}=(1\\pm H^{(i)})/2$ and $V_\\pm$ is a Pauli operator anticommuting with $H^{(i)}$. Applied repeatedly, these operators cool each commuting term to its local ground value, and the proof tracks the resulting evolution in the Heisenberg picture as linear algebra over $\\mathbb{F}_2$; a randomized greedy choice of flip operators guarantees that the system lands in the common ground-state eigenspace and then keeps moving inside it. The classification side is carried by the Subspace Conserved Quantity (SCQ), a local Hermitian operator whose expectation value is conserved inside the ground-state manifold, and by the Parent-Hamiltonian-Frustration-Free (PHFF) condition: the existence of a local frustration-free Hamiltonian sharing the same ground-state manifold. For non-steerable targets, the engine of the \"glass floor\" is the quantity $p(\\Pi_{\\mathrm{GS}})$, the smallest eigenvalue of any local reduced density matrix of any ground state; it converts directly into upper bounds on fidelity and lower bounds on energy and effective temperature.","core_discovery":"On its own terms, the paper's central discovery is a revised classification of local Hamiltonians by the steerability of their ground-state manifold. Theorem 1 characterizes steady steerability: a Hamiltonian is steadily steerable exactly when a local frustration-free parent Hamiltonian shares its ground-state manifold. Theorem 4 goes further and shows that the ground-state manifold of any commuting Pauli Hamiltonian is a steerable subspace in the \"jittery\" sense: local superoperators built from projectors onto eigenstates of the commuting terms, together with Pauli flip operators, drive every initial state into the manifold and then continue to move states around within it, so that no single ground state is a fixed point. For non-steerable targets, the paper establishes that the best overlap of any local passive protocol with the ground-state manifold is at most $1-p(\\Pi_{\\mathrm{GS}})$, where $p(\\Pi_{\\mathrm{GS}})$ is the smallest eigenvalue of any local reduced density matrix of any ground state; equivalently, the energy is at least $E_{\\mathrm{GS}}+p(\\Pi_{\\mathrm{GS}})\\,\\mathrm{gap}[H]$, and the effective temperature is bounded from below once the asymptotic state is modeled as a Gibbs state.","pith_inferences":["The jittery steering construction suggests a practical way to keep a degenerate encoded subspace populated while deliberately randomizing inside it; the paper notes the error-correction template but does not analyze logical noise or code distance within that subspace.","The temperature version of the glass floor is the only place where the argument requires the surrogate state to be thermal; if exact numerics on the Heisenberg or SYK chains show the asymptotic state is non-thermal, the fidelity and energy bounds survive but the temperature bound should be read as a fitting parameter rather than a physical cooling limit.","Because the necessary conditions for the NFFJS class are explicitly incomplete and require non-local information, the true boundary between jittery steerable and non-steerable Hamiltonians remains open for systems that satisfy the local conditions; closing the classification would need a non-local entanglement criterion.","The same reduced-density-matrix datum $p(\\Pi_{\\mathrm{GS}})$ can serve as a pre-screening diagnostic for quantum simulators: compute the smallest eigenvalues of few-body reduced density matrices of the target state, and if the value is large, no local blind cooling protocol can prepare that state faithfully."],"forward_implications":["Any commuting Pauli Hamiltonian, including classically frustrated ones such as an odd-length Ising antiferromagnet, can be steered into its ground-state manifold by discrete local superoperators; within the manifold the protocol keeps generating transitions, so the asymptotic target is a subspace rather than a fixed point.","Steady steerability is fully characterized by parent Hamiltonians: a ground-state manifold is steadily steerable when a local frustration-free parent Hamiltonian exists, and such a parent can be assembled from trivial subspace conserved quantities.","For non-steerable ground states, every local passive protocol leaves a population of at least $p(\\Pi_{\\mathrm{GS}})$ outside the target manifold, giving a fidelity bound $1-p(\\Pi_{\\mathrm{GS}})$, an energy bound $E_{\\mathrm{GS}}+p(\\Pi_{\\mathrm{GS}})\\,\\mathrm{gap}[H]$, and a lower effective-temperature bound when the asymptotic state is Gibbs-like.","Cooling power grows with detector range: for SYK models with $\\lfloor N/2\\rfloor$-mode detectors the ground-state overlap bound improves as $1-\\langle\\psi_{\\mathrm{GS}}|\\tilde\\rho_{\\mathrm{surr}}|\\psi_{\\mathrm{GS}}\\rangle\\gtrsim e^{-O(N)}$, whereas two-mode detectors give a floor around $\\tfrac14-O(1/N)$ that worsens with $N$.","In the near-superconducting Fermi-Hubbard model the computed minimum effective temperature lies below the estimated critical temperature, so the glass floor does not by itself rule out reaching the d-wave phase by passive steering."],"supporting_citations":[{"why":"defines the passive measurement-induced steering protocol and demonstrates it on the AKLT model, the framework the paper extends.","marker":"[8]"},{"why":"provides the dissipative ground-state engineering paradigm and the prior claim that only frustration-free Hamiltonians are amenable to passive preparation.","marker":"[1]"},{"why":"supplies the quasi-local stabilization criteria behind the theorem that steady steerability is equivalent to existence of a frustration-free parent Hamiltonian.","marker":"[11]"},{"why":"gives the exactly solvable honeycomb Kitaev model used as the NFFSS example.","marker":"[27]"},{"why":"supplies the module-theoretic representation of commuting Pauli Hamiltonians used to prove that the flip operators in the steering superoperators can be chosen local.","marker":"[28]"},{"why":"establishes NP-completeness of maximum-likelihood decoding, which the paper uses to show that finding the ground-state energy of a commuting Pauli Hamiltonian is NP-complete.","marker":"[55]"},{"why":"shows quantum 3-SAT is QMA1-complete, cited for the hardness of deciding steerability.","marker":"[41]"}],"fun_headline_variants":["Frustration no barrier: new proof for steering ground states","Jittery steering unlocks ground manifolds of commuting Hamiltonians","Ground states of frustrated models: steerable with a glass floor","Local superoperators can steer frustrated spin systems","Beating frustration: steering Hamiltonians to ground states"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"For the temperature bound, the argument assumes that the asymptotic state of any steering protocol can be approximated by a Gibbs state of the target Hamiltonian with ordinary Boltzmann weights for the low-lying states; the target Hamiltonian is not part of the steering dynamics, and nothing in the proof forces the surrogate state to be thermal.","fun_headline_variants_meta":{"raw":{"variants":["Frustration no barrier: new proof for steering ground states","Jittery steering unlocks ground manifolds of commuting Hamiltonians","Ground states of frustrated models: steerable with a glass floor","Local superoperators can steer frustrated spin systems","Beating frustration: steering Hamiltonians to ground states"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000212,"raw_usage":{"total_tokens":1454,"prompt_tokens":1019,"completion_tokens":435,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":635,"completion_tokens_details":{"reasoning_tokens":354}},"tokens_in":635,"tokens_out":435,"duration_ms":4016,"temperature":1.0,"reasoning_tokens":354,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T14:32:23.083871+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Numerically optimize a finite sequence of local superoperators for a system whose ground state has full local Schmidt rank, such as the spin-1/2 antiferromagnetic Heisenberg chain with $N$ up to 20, and test whether the overlap with the ground-state manifold can exceed $1-p(\\Pi_{\\mathrm{GS}})$; any success would refute the glass floor. In parallel, reconstruct the asymptotic state produced by the protocol and examine its low-energy spectrum: if it is not well fit by a Gibbs distribution, the effective-temperature bound is not a physical property of the state.","supporting_citations":[{"cited_title":"II, a prerequisite for steer- ability is that the target GS can either be sta- bilized by certain non-trivial steering operations or be transformed from other intermediate states","cited_arxiv_id":null,"evidence_quote":"defines the passive measurement-induced steering protocol and demonstrates it on the AKLT model, the framework the paper extends."},{"cited_title":"Commuting Pauli Hamiltonians are n-qubit Hamiltonians of the form H = P i H (i), where each term H (i) belongs to the Pauli group and satisfies [ H (i), H(j)] = 0 for all i, j","cited_arxiv_id":null,"evidence_quote":"provides the dissipative ground-state engineering paradigm and the prior claim that only frustration-free Hamiltonians are amenable to passive preparation."},{"cited_title":"Verstraete, M","cited_arxiv_id":null,"evidence_quote":"supplies the quasi-local stabilization criteria behind the theorem that steady steerability is equivalent to existence of a frustration-free parent Hamiltonian."},{"cited_title":"Arute, K","cited_arxiv_id":null,"evidence_quote":"gives the exactly solvable honeycomb Kitaev model used as the NFFSS example."},{"cited_title":"McArdle, T","cited_arxiv_id":null,"evidence_quote":"supplies the module-theoretic representation of commuting Pauli Hamiltonians used to prove that the flip operators in the steering superoperators can be chosen local."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"shows quantum 3-SAT is QMA1-complete, cited for the hardness of deciding steerability."}],"review_version":1}