{"id":"fb09d526-e265-4ee5-826c-44a44c3613fb","arxiv_id":"2607.28724","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"Quantum-information measures of the DIS final electron-quark state are shown to be sensitive to transversity PDFs and can discriminate between different tensor-charge extractions.","lead":"This paper proposes that quantum correlations — entanglement, discord, steering, and magic — between the scattered electron and the struck quark in deep-inelastic scattering can serve as a new probe of the proton's internal spin structure. If measurable at the Electron-Ion Collider, these correlations could help pin down the proton's tensor charges, quantities relevant for searches for new physics.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The claimed direct mapping from QI measures to tensor charges is model-mediated and not one-to-one: measures at one (x,Q) determine only α(x,Q), while δu,δd are x-integrals, so the mapping relies on the same fits whose moments define the charges.","rationale":"The reader's verdict is CONDITIONAL; our concern does not change it. We agree with the reader that the forward calculation is likely correct and the idea is novel. However, while the reader selected observability (jet spin transfer) as the weakest assumption, we identify a more fundamental issue with the central claim as stated: the 'direct mapping' to tensor charges is not a direct mapping. The QI measures depend on α at the measured kinematic point; tensor charges are x-integrals. The paper's Fig. 4 only shows a correlation because the same five fits are used to compute both axes. This is a circular step that inflates the strength of the claim. If a measurement of a QI invariant at x=0.5 is made, it tells you α(0.5); translating that to δu,δd requires assuming a specific x-dependence. That assumption comes from the same global fits the method claims to complement. Thus the central claim 'directly informs δu,δd' is overstated, though the more modest claim of sensitivity to transversity and discrimination among fits is supported. The concrete test with modified PDFs would demonstrate whether the mapping is actually one-to-one. This does not change the CONDITIONAL verdict; the paper remains a promising proposal but needs a multi-x analysis or a clear statement that the mapping is prior-dependent. We also note the reader's observability concern is valid and separately acknowledged by the authors as future work ('realistic fragmentation and detector effects'), so we do not base our verdict on it.","tokens_in":14665,"tokens_out":9702,"duration_ms":98497,"concrete_test":"Construct artificial transversity distributions that exactly match each of the five fits' α(0.5,12) but differ in their high-x and low-x tails (e.g., modify h1(x) with functions vanishing at x=0.5 but altering the moment integral). Compute δu,δd via Eq. (17) and the QI measures at the reference kinematics. If the resulting (measure, δq) points fall outside the corresponding bands of Fig. 4 for the same measure value, the 'direct mapping' fails. A second, simpler check: within the existing fit replicas, randomly permute which replica's α at x=0.5 is paired with which replica's δq and recompute the correlation; if the scatter increases substantially, the Fig. 4 correlation is a fit artifact.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim of a 'direct, calculable mapping' between the measured quantum correlations and the tensor charges δu,δd (Constraints on Tensor Charges) is not supported by the analysis. The QI measures in Figs. 1 and 3 depend on the density matrix ρ_eq, whose nonperturbative input enters only through α(x,Q) in Eq. (15) at the sampled kinematics (x=0.5, Q=12 GeV). The tensor charges, Eq. (17), are integrals of h_{1,q}(x) over all x. A single measurement of α at one x cannot determine an integral moment without assuming the full x-dependence. The correlation bands in Fig. 4 are generated by propagating the same transversity fits through both α and δq, so the 'mapping' is an internal projection of the fit ensemble, not a property derivable from the density matrix alone. The statement that 'this inference proceeds entirely from invariants of the measured density matrix, and is thus distinct from ... conventional global analyses' is therefore misleading: the inversion from invariant to δq relies on the functional forms and extrapolations of those same global fits. If the true transversity has a different x-dependence than all five fits, the same measured α could correspond to δu,δd outside the plotted bands. Thus the strongest claim is overstated; what is actually demonstrated is that QI measures are sensitive to transversity at a chosen point and can discriminate among the specific fits considered.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes using quantum-information measures of the bipartite spin state of the final-state electron and struck quark in deep-inelastic scattering (DIS) as a probe of transversity PDFs and tensor charges. The authors derive the final-state density matrix rho_eq from leading-order partonic amplitudes (Supplemental Material), express it in Fano-Bloch form, and compute concurrence, stabilizer magic, quantum discord, and steering as functions of the initial transverse polarizations and the scattering angle. They parametrize the struck-quark transverse polarization by Eq. (15) as alpha(x,Q) times the proton polarization, where alpha is a charge-weighted ratio of transversity to unpolarized PDFs. Using five transversity fit ensembles (with and without lattice-QCD constraints), they show that at x=0.5, Q=12 GeV the quantum measures take different values for different fits, and they plot correlations between these measures and the tensor charges delta u, delta d defined by Eq. (17). The paper claims a direct, calculable mapping from the quantum invariants to tensor charges, with quark steerability as a binary discriminant between lattice-constrained and unconstrained fits, and discusses implications for BSM physics.","tokens_in":15055,"tokens_out":9754,"duration_ms":101705,"significance":"The parton-level derivation of rho_eq and the demonstration that multiple quantum-information measures have distinct sensitivity to transversity at a chosen DIS kinematic point are useful and timely contributions to the growing collider-QI literature. The paper goes beyond the previously studied back-scattering concurrence limit and shows that discord, magic, and steering have different angular and polarization dependence, which is a genuine addition. The use of five modern transversity fits, including lattice-constrained variants, makes the sensitivity study concrete and gives a sharp, in-principle falsifiable criterion: the presence or absence of quark steerability at a specified kinematic point. However, the central claim that these measures provide a direct mapping to the tensor charges is currently overstated: the mapping is mediated by the same PDF fits whose moments define the charges, and the experimental observability of the parton-level spin state is deferred. The paper's strengths are the analytic density-matrix formalism and the explicit fit comparison; its weakness is the gap between parton-level sensitivity and a demonstrated observable constraint on delta u, delta d.","major_comments":[{"comment":"The central claim that a measurement of quantum correlations maps directly to delta u and delta d is not supported by the analysis as presented. The QI measures depend on the struck-quark polarization only through alpha(x,Q^2) at the single sampled point (x=0.5, Q=12 GeV; Eq. (15)), whereas delta u and delta d are x-integrals of the transversity PDFs (Eq. (17)). The bands in Fig. 4 are obtained by propagating the same five transversity fit ensembles through both alpha and the moment integral; they are therefore an internal projection of the fit ensembles, not an inference that proceeds 'entirely from invariants of the measured density matrix' as stated in the text. A state with the same measured invariants could correspond to different tensor charges if the true h_{1,q}(x) has an x-dependence not represented by the five fits. To make the 'direct mapping' claim defensible, the authors sho","section":"Constraints on Tensor Charges, Eq. (17) and Fig. 4"},{"comment":"The experimental program assumes that the spin state of the final-state struck quark can be reconstructed. The density matrix rho_eq in Eqs. (1)-(2) is defined for the electron and the parton-level quark, but the quark is not an asymptotic state; it is observed only through its fragmentation into a jet. The Conclusions state that the quark spin is 'accessed through its fragmentation into a jet' and that 'realistic fragmentation and detector effects' are left to future work. This is not a minor technicality: without a quantitative relation between the parton-level quark spin and the measured hadronic/jet observables (e.g., through spin-dependent fragmentation functions or jet polarimetry), the proposed quantum tomography of rho_eq cannot be performed. At present the paper demonstrates sensitivity at the parton level, not an observable prescription. The claims that steerability is a 'binar","section":"Conclusions; Quantum State of DIS"},{"comment":"The binary steerability criterion is the sharpest advertised result, but its robustness is not quantified. The paper states that fits with lattice-QCD constraints are 'consistently quark-steerable at the 1 sigma level, unlike the latter,' but no number is given: what fraction of replicas in each of the five ensembles satisfies the steering inequality (Eq. (13)) at the reference point? How stable is this fraction under variation of x, Q, and sqrt(s) within the ranges shown in Fig. 1, or under higher-order QCD corrections to the hard-scattering matrix? Because the PDF ensembles carry probability distributions, a deterministic binary statement needs a statistical characterization. As written, the 'strong discriminator' could be a property of the specific fits at one kinematic point rather than a robust prediction. Please provide replication-level statistics or soften the claim accordingly.","section":"Connection to Nonperturbative Models, Fig. 3 (lower left) and Fig. 4 (lower panels)"}],"minor_comments":[{"comment":"The caption does not define the white-dashed line in the middle panels. The text says it delineates the separable region as identified by the concurrence, but the caption should state this explicitly for the reader.","section":"Fig. 1"},{"comment":"The steering inequality is presented without a citation to the original two-qubit steering criterion (e.g., Cavalcanti et al., Phys. Rev. Lett. 103, 170404 (2009)). A citation would help the uninitiated reader locate the derivation of Eq. (13).","section":"Eq. (11)"},{"comment":"The definition of the second stabilizer Renyi entropy for mixed states is not discussed; a brief remark on its validity for the mixed rho_eq considered here, or a reference, would be useful.","section":"Eq. (6)"},{"comment":"The phrase 'the true classical-quantum boundary is measured through quantum discord' is imprecise; discord is one measure of non-classical correlations, not a unique boundary. Consider rewording to avoid overstatement.","section":"Quantum Hierarchy of DIS"},{"comment":"The neutron EDM relation should specify the renormalization scale at which delta q^n and d_q are evaluated; this matters for the SMEFT interpretation of tensor charges.","section":"Eq. (18)"}],"recommendation":"major_revision","confidential_remarks":"The paper is likely to be of interest to the collider-QI community, but the title and abstract overstate the directness of the tensor-charge connection. The key issues are not the parton-level QI calculation, which appears clean at leading order, but the fit-mediated inference from alpha to delta u, delta d and the unresolved experimental chain from the struck quark to a jet. These are fixable in a revision by softening the claims and moving the fragmentation/detector limitation from 'future work' to a central caveat, but they are load-bearing for the paper's main message."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"What you should know: this is a clean, well-executed proposal, and the new piece is real—Cheng/Han/Trifinopoulos already did concurrence and magic for transversely polarized e-p at the EIC, but this paper extends the hierarchy to discord and steering and explicitly maps all the measures to transversity PDFs and tensor charges via α. The forward calculation from the density matrix to the quantum measures is straightforward and I see no issue with it. The strongest practical idea is the steering threshold: whether the final state is quark-steerable separates the transversity fits with and without lattice-QCD input at 1σ. That's a crisp, binary observable, and the authors are right that it could complement lattice and low-energy constraints.\n\nThe soft spots are real, though. The 'direct, calculable mapping' to δu and δd is not as direct as advertised. The measures at one kinematic point determine α(x,Q²) at that point—a ratio of weighted transversity to unpolarized PDFs—and the tensor charges are x-integrals of h1. The correlation bands in Fig. 4 are generated by propagating the same transversity fits through both α and δq; so the inferred band is a projection of the fit ensemble, not an independent constraint. If the true h1 has a different x-dependence than all five fits, the same measured α could correspond to tensor charges outside the plotted band. The sentence claiming the inference 'proceeds entirely from invariants of the measured density matrix' is overstated.\n\nThe other structural caveat is observability: the quark polarization must survive through fragmentation into the observed jet. That's a big assumption, and the paper acknowledges it only as future work. If depolarization is significant, the whole chain from measured invariants to α to δu/δd collapses. Also, the discrimination is shown at one hand-picked kinematic point; we don't know how the 1σ separation evolves with x and Q².\n\nNone of this kills the paper. The central observation—that QI measures of the DIS final state are genuinely sensitive to transversity and can separate competing fits—holds up. What doesn't hold up is the stronger claim that this constitutes a direct, self-contained measurement of the tensor charges. That's a revision, not a rejection.\n\nI'd send this out to a serious referee. It's a legitimate contribution to the QI-at-colliders program and to transversity phenomenology, and the critique above gives a referee something concrete to work with. A careful reader gets value from the figures and the steering discriminator, even if the headline claim needs tempering.","headline":"Clean proof-of-concept connecting DIS quantum correlation measures to transversity, with a real new extension to steering and discord—but the claimed direct mapping to tensor charges is a projection of the same fits, not an independent constraint.","tokens_in":15538,"tokens_out":2298,"would_cite":true,"duration_ms":23662,"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":"Quantum correlations in deep-inelastic scattering can map the proton's internal transverse spin structure.","keywords":["deep inelastic scattering","quantum entanglement","quantum steering","quantum discord","quantum magic","transversity parton distribution functions","tensor charges","hadron structure"],"falsifier":"Measure the spin-correlation matrix of the final-state electron and a jet in transversely polarized electron–proton scattering at a single kinematic point (e.g., x≈0.5, Q≈12 GeV). If the reconstructed density matrix shows a quark-steerable state for a transversity fit that predicts non-steerability (or vice versa), the mapping from quantum measures to tensor charges is falsified; alternatively, if the quark's reconstructed spin is systematically smaller than α b^p_⊥, the depolarization assumption fails.","tokens_in":14546,"feed_emoji":"⚛️","tokens_out":5271,"duration_ms":46254,"temperature":0.7,"pith_summary":"The paper argues that the quantum correlations between the scattered electron and the struck quark in deep-inelastic scattering are a direct probe of the proton's transversity parton distribution functions, which encode the transverse spin of quarks inside a proton. Because these correlations are invariants of a reconstructed density matrix, measuring any one of them—entanglement, discord, steering, or magic—selects a band of allowed values for the proton's tensor charges δu and δd. The sharpest result is that the binary question of whether the final state is quark-steerable cleanly separates transversity fits that include lattice-QCD constraints from those that do not. This matters because the tensor charges are poorly determined and feed into searches for physics beyond the Standard Model, such as the neutron electric dipole moment.","feed_headline":"Steerable quarks rule out some proton spin models","feed_subtitle":"A yes-or-no quantum test can constrain the proton's tensor charges, key inputs to new-physics searches.","key_machinery":"The central object is the Fano–Bloch decomposition of the two-qubit density matrix ρ_eq for the final-state electron and struck quark, whose coefficients are the measured single-spin polarizations and spin–spin correlation matrix. The argument is carried by the ratio α(x,Q²) = Σ_q e_q² h_{1,q}(x,Q²) / Σ_q e_q² f_q(x,Q²), which converts the proton's transverse polarization into the struck quark's transverse polarization, and by the steering inequality whose violation provides a binary steerability test that separates transversity scenarios.","core_discovery":"The paper establishes a calculable mapping from the quantum-information measures of the final-state electron–quark spin density matrix to the proton's tensor charges. At parton level, the struck quark inherits a fraction α(x,Q²) of the proton's transverse polarization, where α is the charge-weighted ratio of transversity to unpolarized PDFs. Quantum-information measures such as concurrence, quantum discord, steering, and magic are all functions of this α and the scattering angle, so different transversity fits produce distinct values of these measures at fixed kinematics. In particular, quark steerability acts as a threshold criterion: fits informed by lattice QCD predict steerable states at","pith_inferences":["If the mapping survives realistic fragmentation and detector effects, the same technique could extend to other hard processes such as Drell-Yan, where a quark's transverse polarization enters the final-state density matrix, giving independent handles on transversity-like distributions.","The binary nature of steerability suggests a natural experimental test at a future electron-ion collider: simply establishing that the final state is steerable at one kinematic point would rule out all transversity fits that predict separable states, without needing precise values of the other measures.","Because α is flavor-charge-weighted, flavor-tagged final states (e.g., identifying charm or strangeness in the jet) would isolate individual quark flavors and could turn the quantum measures into flavor-by-flavor tensor-charge constraints.","The hierarchy among the measures—entanglement nested within steering, with discord extending beyond—could serve as a consistency check: if steering and concurrence disagree about the same state, that would signal unmodeled depolarization or higher-twist effects."],"forward_implications":["A measurement of any of the four quantum measures at a fixed DIS kinematic point maps to a definite band of allowed tensor charges (δu, δd), independent of the model assumptions of global fits.","Establishing quark steerability in the final state is a sharp, binary criterion that can distinguish transversity extractions made with lattice-QCD input from those made without.","The quantum measures constrain a flavor combination distinct from the isovector tensor charge g_T = δu − δd, offering a new handle for BSM searches such as the neutron electric dipole moment.","Quantum discord remains nonzero in regions where entanglement vanishes, so discord extends the probe to a wider range of scattering angles than concurrence alone.","The asymmetry between electron and quark discord and steering suggests the possibility of inferring the quark's quantum state from electron measurements alone, which is valuable since the quark is observed only through its jet."],"fun_headline_variants":["Steerable quarks set new constraints on proton spin","Quantum discord probes proton's parton-level spin","Steering thresholds test proton spin models","Entanglement and magic map proton's tensor charge","DIS quantum correlations expose hidden proton spin"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The calculation assumes the struck quark's transverse polarization is exactly the PDF ratio α times the proton's polarization, and that the quark's final-state spin is faithfully read out through its fragmentation into a jet; if hadronization or detector effects depolarize the quark, the measured quantum correlations no longer map to α, and the tensor-charge connection collapses.","fun_headline_variants_meta":{"raw":{"variants":["Steerable quarks set new constraints on proton spin","Quantum discord probes proton's parton-level spin","Steering thresholds test proton spin models","Entanglement and magic map proton's tensor charge","DIS quantum correlations expose hidden proton spin"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000176,"raw_usage":{"total_tokens":1071,"prompt_tokens":637,"completion_tokens":434,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":381,"completion_tokens_details":{"reasoning_tokens":365}},"tokens_in":381,"tokens_out":434,"duration_ms":5321,"temperature":1.0,"reasoning_tokens":365,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-03T00:33:19.689706+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the spin-correlation matrix of the final-state electron and a jet in transversely polarized electron–proton scattering at a single kinematic point (e.g., x≈0.5, Q≈12 GeV). If the reconstructed density matrix shows a quark-steerable state for a transversity fit that predicts non-steerability (or vice versa), the mapping from quantum measures to tensor charges is falsified; alternatively, if the quark's reconstructed spin is systematically smaller than α b^p_⊥, the depolarization assumption fails.","supporting_citations":[],"review_version":1}