{"id":"c83e838a-3102-424c-973a-a1c7dd2425ab","arxiv_id":"2412.11860","paper_version":1,"verdict":"REJECT","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":15,"one_line_summary":"Using BLFQ proton wave functions, the authors compute parton spin and momentum entanglement and report that a dynamical gluon enhances quark entanglement.","lead":"This paper calculates how strongly quarks and gluons inside a proton are quantum-entangled, using wave functions obtained from a light-front Hamiltonian model. It finds that adding a dynamical gluon increases the entanglement, and suggests such correlations might one day be measured in scattering experiments.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The central comparison is uncontrolled: the |qqq> and |qqq>+|qqqg> wave functions come from different Hamiltonians, truncations, and fitted parameters, so the entropy increase cannot be attributed to the dynamical gluon.","rationale":"The reader's weakest assumption is exactly the load-bearing concern. The central claim is a statement of causation: the dynamical gluon significantly enhances entanglement. Causal attribution requires a controlled comparison, but the two wave functions are generated from different Hamiltonians, different basis truncations, and different fitted parameters. The manuscript itself describes them as distinct models in Sec. II, so the numerical comparison in Sec. III is not a controlled experiment. No fundamental error in the entanglement computation is alleged; the issue is that the evidence does not support the conclusion. The x-resolved analysis in Sec. IV also relies on post-selected conditional states, and the Bell-CH result is secondary, but these are not the primary weakness. A simple projection test on the existing wave function would settle the main concern. I agree with the reader's assessment and recommend rejection, while noting that a revised version with a controlled baseline could potentially support the conclusion.","tokens_in":13860,"tokens_out":3810,"duration_ms":37462,"concrete_test":"Take the |qqq>+|qqqg> wave function of Ref. [25] and compute S_spin for the valence-quark component alone, obtained by projecting out the |qqqg> Fock sector and renormalizing. If this projected |qqq> state already yields S_spin approximately 0.4, or if it differs substantially from the |qqq> state of Refs. [23,24], then the entropy increase is a Hamiltonian/model artifact rather than a gluon effect. Conversely, if the projected valence state gives S_spin approximately 0.2 and the full mixed state gives 0.414, the gluon-sector amplitudes are responsible; then repeat the comparison with a single Hamiltonian at matched Nmax to confirm the effect.","verdict_should_be":"REJECT","load_bearing_attack":"The paper's central claim (Abstract, Sec. V) rests on comparing S_spin computed from the |qqq> state of Refs. [23,24] with S_spin from the |qqq>+|qqqg> state of Ref. [25]. These are not the same model with and without a gluon: they use different Hamiltonians (Eq. 3 vs Eq. 6), different truncations (Nmax=10 vs Nmax=9), and different fitted parameters (e.g., confinement strength kappa=0.34 GeV vs 0.54 GeV; different quark masses and couplings). Thus the observed rise in S_spin for u quarks (0.219 to 0.414) and the large gluon entropy (0.766) could be driven by parameter and basis changes rather than by the dynamical gluon itself. The paper provides no controlled test, such as turning off the |qqqg> sector inside one Hamiltonian, and no check that the valence sector of Ref. [25] alone already produces S_spin around 0.4. If the valence component of the mixed-state wave function alone gives similar entropy, the conclusion that the gluon enhances entanglement collapses. This is load-bearing: the main physical conclusion is not established by the presented evidence.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper uses light-front wave functions for the proton generated by Basis Light-front Quantization (BLFQ) in the |qqq> and |qqq>+|qqqg> Fock spaces to compute von Neumann entanglement entropies for the spin and longitudinal momentum of individual partons. It also evaluates a three-body Bell-CH inequality for the valence-quark spin state and studies spin entanglement at fixed longitudinal momentum fractions, comparing the proton with a dressed quark. The central claim is that the dynamical gluon significantly enhances entanglement among the proton's partons, as evidenced by larger spin entanglement entropies in the two-sector wave function than in the valence-only wave function.","tokens_in":14134,"tokens_out":9581,"duration_ms":87061,"significance":"If the central comparison were controlled, the paper would provide a useful nonperturbative, Hamiltonian-based estimate of parton-level entanglement in the proton, complementing existing DIS-based entanglement studies. The manuscript is transparent about the model parameters and uses wave functions from prior BLFQ publications, and the entanglement calculations are clearly described. The paper also attempts to connect the computed quantities to helicity distributions, although this connection remains qualitative. The main limitation is that the headline comparison is not controlled: the two wave functions come from different Hamiltonians, truncations, and parameter sets, so the attribution of the entropy increase to the dynamical gluon is not currently established. There is no circularity issue, because the model parameters were fitted to the proton mass and form factors, not to entanglement entropies.","major_comments":[{"comment":"The central claim that the dynamical gluon 'significantly enhances entanglement' is based on comparing the spin entanglement entropies S_spin of the |qqq> wave function (Fig. 1) with those of the |qqq>+|qqqg> wave function (Fig. 2). These two wave functions are not the same model with and without a gluon: they are generated from different Hamiltonians [Eqs. (3) and (6)], with different Fock-space truncations (Nmax=10 vs Nmax=9) and different fitted parameters (Table I: kappa=0.34 GeV, m_q/k=0.3 GeV, alpha_s=1.1; Sec. II A 2: kappa=0.54, m_u=0.31 GeV, m_d=0.25 GeV, m_g=0.5 GeV, gS_tilde=2.4). The increase in S_spin from 0.219 to 0.414 for the u quark and the gluon entropy 0.766 could therefore be caused by the change of Hamiltonian, basis, or parameters rather than by the dynamical gluon. To support the headline conclusion, the authors need a controlled test, e.g., computing S_spin for the valence-sector projection of the [25] eigenstate alone (or setting the |qqqg> amplitude to zero within the same Hamiltonian and truncation) and showing that it does not already produce S_spin approximately 0.4 for the valence quarks. Without such a test, the Abstract's attribution of the enhancement to the gluon is not established.","section":"Abstract and Secs. III A, III B, V (Figs. 1-2)"},{"comment":"The x-resolved 'entanglement entropy' is not the entanglement of a parton at fixed x with the rest of the proton in the global state. In Eqs. (14)-(16) (and similarly Eqs. (18)-(19)), the authors select all configurations containing a parton with longitudinal momentum x_f, form a new wave function, and renormalize its norm to 1. The von Neumann entropy of this post-selected, renormalized state is a property of a conditional subensemble, not of the original proton wave function; renormalization discards the probability weight of the selected configurations, and the entropy of a conditional state is not the conditional entropy S(A|B) of quantum information theory. The conclusions of Sec. IV, including the claim that gluons amplify information exchange between quarks at fixed x, therefore need either a clear operational definition of the quantity being computed or a computation from the global state (e.g., by tracing out all other degrees of freedom without post-selection and then conditioning the reduced density matrix on x_f). As written, the physical interpretation in Sec. V is not supported by the quantity defined in Sec. IV.","section":"Sec. IV A and IV B, Eqs. (14)-(19)"},{"comment":"The comparison between the proton and the dressed quark is also uncontrolled. The dressed quark state is computed with a different Fock-space truncation ({Nmax,K}={7,15.5} rather than {9,16.5}) and represents a different physical system. The conclusion that 'most entanglement of the dynamical gluon in the proton arises from exchange interactions among quarks' (Sec. IV B) relies on the assertion that the dressed quark simulates a quark embedded in the proton, but no quantitative test of this assertion is provided. The smaller S_spin in the dressed quark could be due to the smaller Hilbert space or to other differences unrelated to the self-energy/exchange distinction. This conjecture should be either derived from a controlled calculation (e.g., a dressed quark with the proton's truncation, or a proton calculation with the gluon restricted to self-energy-type couplings) or explicitly labeled as speculative.","section":"Sec. IV B, Fig. 5 and inset"}],"minor_comments":[{"comment":"Equation (10) is missing the minus sign in the von Neumann entropy formula: S = Tr(rho log2 rho) should be S = -Tr(rho log2 rho); the Shannon form on the right is correct.","section":"Sec. II B, Eq. (10)"},{"comment":"The text states that the maximal spin entanglement entropy is 1, but for the gluon, which is described as a qutrit, the maximum is log2(3) ~ 1.585; this should be stated for a fair comparison with the quarks.","section":"Sec. III B"},{"comment":"The definition of the large-x region appears to contain a typo: 'xmin >= 5.5/15.5' should read 'xmax >= 5.5/15.5'.","section":"Sec. IV A"},{"comment":"The longitudinal momentum fraction conventions are inconsistent: parton momenta are summed to 16.5 (Sec. III A), but x_f and x_g are written with denominators 15.5 (Sec. IV A) and 15 (Sec. IV B); please clarify the normalization of x.","section":"Sec. IV"},{"comment":"The statement that the entanglement entropies are 'experimentally accessible' through helicity distributions is not substantiated: no formula or reference connects S_spin(x) to a measurable parton-helicity observable.","section":"Abstract and Sec. V"},{"comment":"The Bell-CH violation of 0.0905553 is reported without an uncertainty; since Table I gives alpha_s = 1.1 +/- 0.1, the authors should state whether the violation persists within the parameter uncertainty or treat it as a fixed-parameter result.","section":"Sec. III A"}],"recommendation":"major_revision","confidential_remarks":"For the editor: the paper is not circular, since the BLFQ parameters were fitted to the proton mass and form factors rather than to the entanglement observables. The problem is that the two wave functions compared in the central claim come from different Hamiltonians, truncations, and parameter sets, so the observed entropy increase cannot be attributed unambiguously to the dynamical gluon. A controlled computation with and without the gluon sector within a single Hamiltonian would address this. The x-resolved analysis also needs a clearer operational meaning. Given the exploratory nature of the calculation, I recommend major revision rather than outright rejection, contingent on the authors supplying the controlled test or substantially qualifying the central claim."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague, this one is worth a look but not a citation yet. The paper computes spin and longitudinal-momentum entanglement entropy, and a Bell-CH inequality, for two BLFQ proton wave functions—one with only |qqq> and one with |qqq>+|qqqg>. The computation is straightforward and the authors are transparent: they list all basis truncations, model parameters, and even use a cloud quantum simulator for the partial traces. The x-resolved analysis in Sec. IV is a nice attempt to connect entanglement to momentum fraction, including a dressed-quark comparison to separate self-energy from exchange effects.\n\nThe problem is the comparison that anchors the main claim. The |qqq> state comes from Refs. [23,24] with Nmax=10, kappa=0.34 GeV, and one set of quark masses; the |qqq>+|qqqg> state comes from Ref. [25] with Nmax=9, kappa=0.54 GeV, and a different mass scheme. So when the u-quark spin entropy rises from 0.219 to 0.414 and the gluon shows 0.766, that increase cannot be cleanly attributed to the dynamical gluon—any of the parameter shifts could be responsible. The paper offers no controlled test, such as turning off the gluon sector inside one Hamiltonian, or checking the entropy of the |qqq> component projected from the mixed-state wave function. Without that, the abstract's claim that the gluon 'significantly enhances entanglement' is not established.\n\nTwo smaller concerns. The Bell-CH violation in the |qqq> state is 0.0906, a small number with no estimate of model or numerical uncertainty; I'd treat the claimed nonlocality as fragile. And the x-resolved entropies are computed on post-selected, renormalized subsets of the wave function, so they describe conditional states, not directly measurable quantities. The suggested link to parton helicity distributions is speculative.\n\nFor whom is this? People working on quantum information probes of hadron structure will find the pipeline useful, and the authors are clearly not hiding anything—the parameters are all in the paper. But the central physical conclusion needs a controlled baseline to survive. I'd send this to a serious referee requesting major revision, not desk-reject. As is, I wouldn't cite the claim, but I'd watch for the revised version.","headline":"A transparent numerical study whose central claim about gluon-enhanced entanglement is undermined by an uncontrolled comparison between wave functions from two different Hamiltonians and parameter sets.","tokens_in":14709,"tokens_out":4209,"would_cite":false,"duration_ms":37390,"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":"Adding a gluon to the proton's valence state roughly doubles quark spin entanglement.","keywords":["entanglement entropy","light-front Hamiltonian","proton structure","gluon entanglement","Basis Light-front Quantization","Bell-CH inequality","parton helicity","Fock sector"],"falsifier":"Repeat the computation in a single controlled Hamiltonian where the |qqq> and |qqq>+|qqqg> spaces are solved with identical parameters and truncation; if the quark spin entanglement entropy does not rise when the gluon sector is added, the paper's central claim would be refuted. A less direct test would be to measure parton helicity distributions and check whether the predicted x-dependent entanglement pattern is visible.","tokens_in":13582,"feed_emoji":"⚛️","tokens_out":4484,"duration_ms":36614,"temperature":0.7,"pith_summary":"This paper tries to establish that including one dynamical gluon in the proton's light-front wave function substantially increases quantum entanglement among its partons. Using wave functions from a Hamiltonian diagonalization in two Fock sectors, |qqq> and |qqq>+|qqqg>, it computes spin and longitudinal-momentum entanglement entropies for each parton relative to the rest. The reported numbers show the u-quark spin entanglement rising from 0.219 to 0.414, and the gluon carrying the largest spin entropy, 0.766. If correct, this provides a concrete, calculable sense in which gluons mediate quantum information exchange inside the proton, and it suggests entanglement could be probed experimentally through parton helicity distributions.","feed_headline":"Adding a gluon doubles quark spin entanglement in proton","feed_subtitle":"Light-front wave functions show the gluon carries the largest spin entropy (0.766), signaling QCD information flow.","key_machinery":"The central objects are the light-front wave functions generated by Basis Light-front Quantization, a nonperturbative method that solves relativistic bound states by diagonalizing the light-front Hamiltonian in a basis. The paper uses two truncations: one with only the valence sector |qqq> and one that adds the single-gluon sector |qqqg>. Entanglement is quantified by the von Neumann entropy of reduced density matrices obtained by partially tracing over all other degrees of freedom, separately for spin and for longitudinal momentum. The gluon is treated as a spin-1 qutrit with an extra 'no gluon' state, while quarks are spin-1/2 qubits, which matters for encoding and for why no Bell-CH inequality is applied to the full system.","core_discovery":"The authors find that spin entanglement entropy of a valence quark with the remainder of the proton increases when the Fock space is expanded from |qqq> to |qqq>+|qqqg>. In the gluon-included wave function, the reported entropies are S_spin = {0.414, 0.483, 0.414, 0.766} for u, d, u, and gluon, versus {0.219, 0.172, 0.219} in the valence-only state. The longitudinal momentum entropies remain large for quarks (about 3.35-3.47) and drop to 2.722 for the gluon. They also report a marginal Bell-CH inequality violation (maximum 0.0905553) in the pure three-quark spin state, which disappears when the gluon is traced out, and they observe that the spin entanglement of a quark at fixed longitudinal momentum fraction xf is roughly symmetric with that of the gluon at 1-xf, a symmetry that holds exactly in a dressed quark test state.","pith_inferences":["Because the comparison uses different model parameters, the quantitative increase in entropy may not survive a controlled calculation; the paper's qualitative claim that gluons carry extra entanglement is more robust than the specific numbers.","The approximate symmetry S_spin(xf) ≈ S_spin(1-xf) for quark versus gluon suggests a form of momentum-helicity complementarity that, if confirmed, would tie entanglement entropy directly to the shape of helicity distributions.","The gluon spin being a qutrit with a 'no gluon' state means standard qubit Bell inequalities do not apply; constructing a qutrit Bell test for the |qqqg> sector could give a sharper nonlocality probe.","The method can be extended to higher Fock sectors (sea quarks, multiple gluons) to see how entanglement grows with resolution scale, which the paper lists as a next step."],"forward_implications":["Adding a dynamical gluon sector raises the spin entanglement of valence quarks with the rest of the proton, e.g., u quark from 0.219 to 0.414.","The gluon itself has the largest spin entanglement (0.766), suggesting it is the dominant carrier of quantum information among quarks.","In the pure |qqq> spin state the Bell-CH inequality is violated only marginally (maximum 0.0905553), indicating weak nonlocal correlations among the three valence quarks; tracing out the gluon removes the violation.","The spin entanglement of a quark at momentum fraction xf is approximately symmetric with that of the gluon at 1-xf, hinting at an exchange-like role for the gluon.","The computed entanglement entropies are in principle accessible through measurements of parton helicity distributions."],"supporting_citations":[{"why":"Provides the valence-only |qqq> wave function and its fitted parameters used for the baseline entanglement calculation.","marker":"[23]"},{"why":"Supplies an alternative valence |qqq> wave function from the same BLFQ framework, serving as part of the baseline comparison.","marker":"[24]"},{"why":"Gives the |qqq>+|qqqg> wave function with one dynamical gluon, which is the central object whose entanglement properties are studied.","marker":"[25]"},{"why":"Introduces the Basis Light-front Quantization method on which both wave function calculations rely.","marker":"[22]"}],"fun_headline_variants":["Gluon boosts quark spin entanglement in proton","Gluon tops spin entropy among proton's partons","Bell violation disappears when gluon is traced out","Dynamical gluon amplifies parton entanglement","Spin symmetry at xf hints gluon-quark swap"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The comparison between the two wave functions assumes they differ only by the inclusion of the gluon sector, but they actually come from different Hamiltonians, different truncations (Nmax=10 vs 9), and different fitted parameters (e.g., confinement strength 0.34 vs 0.54 GeV), so the reported increase in entanglement could partly be an artifact of these model differences.","fun_headline_variants_meta":{"raw":{"variants":["Gluon boosts quark spin entanglement in proton","Gluon tops spin entropy among proton's partons","Bell violation disappears when gluon is traced out","Dynamical gluon amplifies parton entanglement","Spin symmetry at xf hints gluon-quark swap"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000467,"raw_usage":{"total_tokens":2335,"prompt_tokens":955,"completion_tokens":1380,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":571,"completion_tokens_details":{"reasoning_tokens":1304}},"tokens_in":571,"tokens_out":1380,"duration_ms":10456,"temperature":1.0,"reasoning_tokens":1304,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T14:30:58.955789+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Repeat the computation in a single controlled Hamiltonian where the |qqq> and |qqq>+|qqqg> spaces are solved with identical parameters and truncation; if the quark spin entanglement entropy does not rise when the gluon sector is added, the paper's central claim would be refuted. A less direct test would be to measure parton helicity distributions and check whether the predicted x-dependent entanglement pattern is visible.","supporting_citations":[{"cited_title":"Dumitru, A","cited_arxiv_id":null,"evidence_quote":"Provides the valence-only |qqq> wave function and its fitted parameters used for the baseline entanglement calculation."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies an alternative valence |qqq> wave function from the same BLFQ framework, serving as part of the baseline comparison."},{"cited_title":"Dumitru and E","cited_arxiv_id":null,"evidence_quote":"Introduces the Basis Light-front Quantization method on which both wave function calculations rely."}],"review_version":1}