{"id":"cb4aef76-b93c-4779-ab6d-628469143bc3","arxiv_id":"2606.11296","paper_version":3,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":6.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"Computes entanglement negativities for the tripartite spin system in e+e- -> ttZ and projects that collective entanglement is accessible but genuine multipartite entanglement has limited sensitivity at a polarized ILC with expected luminosity.","lead":"The paper reconstructs the 12x12 spin density matrix for the tripartite system in e+e- to ttZ from Standard Model helicity amplitudes and computes one-to-one, one-to-other, and genuine multipartite negativities at varying integration levels. A smart generalist might read it to understand how quantum entanglement measures can be applied to high-energy collider processes and what sensitivity future machines like the ILC might achieve.","discovery_kind":"new_application","skeptic_critique":{"model":"grok-4.3","headline":"Tree-level SM helicity amplitudes may miss NLO QCD corrections that alter spin correlations and negativity measures","rationale":"The reader's weakest assumption directly identifies the same load-bearing step. Because the full text was not supplied in the initial query, the UNVERDICTED verdict is appropriate; the NLO omission supplies a concrete, falsifiable reason to keep the verdict conditional rather than accept the accessibility claims at face value.","tokens_in":1798,"tokens_out":317,"duration_ms":12484,"concrete_test":"Recompute the integrated one-to-other and genuine multipartite negativities after replacing the tree-level helicity amplitudes with NLO QCD-corrected amplitudes (or a validated effective correction factor) for the same three phase-space integration levels; if either negativity changes by more than 15 % at the benchmark polarisation, the projected sensitivities at ILC luminosity require revision.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The reconstruction of the 12×12 spin density matrix (and all derived negativities) begins from tree-level SM helicity amplitudes. In tt̄ production, NLO QCD corrections are known to modify spin-density-matrix elements at the few-to-ten-percent level; because genuine multipartite negativity is a nonlinear functional of off-diagonal coherences, even modest corrections can shift the reported accessibility thresholds. The manuscript provides no estimate or bound on these corrections, nor any comparison to NLO amplitudes, leaving the quantitative claims about collective vs. genuine entanglement at √s=1 TeV dependent on an unverified leading-order approximation.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The manuscript investigates multipartite entanglement in e⁺e⁻ → t t̄ Z at a future lepton collider. Starting from Standard Model helicity amplitudes, it reconstructs the full 12×12 spin density matrix for the tripartite system (t, t̄, Z) and characterizes its entanglement structure via one-to-one negativities, one-to-other negativities, and genuine multipartite negativity, evaluated at three levels of phase space integration. Pairwise entanglement is suppressed relative to collective and genuine measures, with all quantities decreasing upon integration. Projections assuming quantum tomography in the fully leptonic channel at √s=1 TeV indicate that collective entanglement should be accessible at a realistic high-luminosity polarized lepton collider, while certifying genuine multipartite entanglement has only limited sensitivity for a specific polarization benchmark within expected ILC luminosity. The work provides a general mixed-state framework applicable to any tripartite spin system.","tokens_in":1944,"tokens_out":570,"duration_ms":16933,"significance":"If the quantitative projections hold, the paper establishes e⁺e⁻ → t t̄ Z as an attractive laboratory for probing multipartite entanglement in high-energy collisions and supplies a reusable mixed-state formalism for tripartite spin systems. The explicit comparison of entanglement measures across integration levels and the experimental accessibility estimates at a polarized ILC add concrete value to the field.","major_comments":[{"comment":"The reconstruction of the 12×12 spin density matrix (and all derived negativities) begins from tree-level Standard Model helicity amplitudes. NLO QCD corrections are known to modify spin-density-matrix elements at the few-to-ten-percent level in t t̄ production; because genuine multipartite negativity is a nonlinear functional of off-diagonal coherences, even modest corrections can shift the reported accessibility thresholds. The manuscript provides no estimate or bound on these corrections, nor any comparison to NLO amplitudes, leaving the quantitative claims about collective vs. genuine entanglement at √s=1 TeV dependent on an unverified leading-order approximation.","section":"reconstruction of the spin density matrix from helicity amplitudes"}],"minor_comments":[{"comment":"The three increasingly inclusive levels of phase space integration are mentioned but not explicitly defined or labeled in the abstract or summary; a clear enumeration (e.g., fully differential, single-particle integrated, fully integrated) would improve readability.","section":"abstract"},{"comment":"The Hilbert space notation ℜ = ℂ² ⊗ ℂ² ⊗ ℂ³ is introduced without an accompanying statement of the chosen basis ordering for the 12-dimensional space; adding this would aid readers reconstructing the density matrix.","section":"introduction or formalism section"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for the detailed review and for highlighting the importance of higher-order corrections in assessing the robustness of our quantitative projections. We address the major comment below.","responses":[{"response":"We agree that the analysis is performed at leading order and that NLO QCD corrections to the spin-density-matrix elements in tt̄ production are known to reach the few-to-ten-percent level. Because genuine multipartite negativity is a nonlinear functional, such corrections could in principle affect the precise numerical thresholds for experimental accessibility. The present work is an exploratory study that establishes the general mixed-state formalism and demonstrates the qualitative hierarchy (pairwise entanglement suppressed relative to collective and genuine measures) already at tree level. To strengthen the manuscript we will add a dedicated paragraph in the revised version that (i) cites the existing NLO literature on spin correlations in tt̄ and tt̄Z, (ii) provides a conservative estimate of the expected shift in the negativity measures based on those results, and (iii) explicitly states that a full NLO computation lies beyond the scope of this paper but would be a natural follow-up. This addition will make the dependence on the leading-order approximation transparent without altering the central conclusions of the work.","revision_made":"partial","referee_comment":"The reconstruction of the 12×12 spin density matrix (and all derived negativities) begins from tree-level Standard Model helicity amplitudes. NLO QCD corrections are known to modify spin-density-matrix elements at the few-to-ten-percent level in t t̄ production; because genuine multipartite negativity is a nonlinear functional of off-diagonal coherences, even modest corrections can shift the reported accessibility thresholds. The manuscript provides no estimate or bound on these corrections, nor any comparison to NLO amplitudes, leaving the quantitative claims about collective vs. genuine entanglement at √s=1 TeV dependent on an unverified leading-order approximation."}],"tokens_in":1510,"tokens_out":402,"duration_ms":14762,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The headline result is a set of negativity calculations for the 12x12 spin density matrix in e+e- to ttZ, done at three levels of phase-space integration, plus projections for detecting collective versus genuine multipartite entanglement at a 1 TeV ILC with polarized beams and full leptonic decays. Pairwise entanglement comes out weaker than the collective measures, and everything drops when more kinematics are integrated out.\n\nWhat the work does cleanly is take standard negativity functionals and apply them systematically to a mixed tripartite system built from SM helicity amplitudes. The framework is general enough that it could be reused for other three-spin final states, and the comparison across integration levels shows how much information is lost when moving from differential to inclusive observables.\n\nThe main soft spot is the starting point: everything rests on tree-level amplitudes. NLO QCD corrections are known to shift spin-density-matrix elements at the few-to-ten-percent level in top-pair production, and because genuine multipartite negativity is a nonlinear function of the off-diagonal terms, those shifts can move the accessibility thresholds. The manuscript gives no estimate or comparison to NLO amplitudes, so the quantitative ILC claims sit on an unverified leading-order approximation.\n\nThis is aimed at the small group working on quantum information at future colliders. A reader already interested in negativity measures or top-spin correlations will get usable numbers and a reusable setup. The paper is coherent on its own terms and shows clear engagement with the literature, so it deserves a serious referee even though the LO limitation needs to be addressed in revision.","headline":"The paper gives a concrete tree-level calculation of tripartite negativity measures for the ttZ final state and ILC projections, but the lack of NLO checks on the spin density matrix is a real gap.","tokens_in":2431,"tokens_out":398,"would_cite":false,"duration_ms":11332,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"In e+ e- to t tbar Z at future lepton colliders, collective tripartite entanglement is accessible via tomography while genuine multipartite entanglement shows only limited sensitivity.","keywords":["tripartite entanglement","top-antitop-Z production","spin density matrix","negativity measures","lepton collider","quantum tomography","multipartite negativity","polarised beams"],"falsifier":"An experimental reconstruction of the genuine multipartite negativity or one-to-other negativity in the fully leptonic channel at 1 TeV that lies outside the projected sensitivity band for the ILC luminosity benchmark would falsify the accessibility claims.","tokens_in":2711,"feed_emoji":"⚛️","tokens_out":779,"duration_ms":19851,"temperature":0.7,"pith_summary":"The paper reconstructs the full 12x12 spin density matrix for the tripartite system of top, antitop, and Z spins from Standard Model helicity amplitudes in e+ e- to t tbar Z. It then evaluates one-to-one negativities, one-to-other negativities, and genuine multipartite negativity at three levels of phase space integration to map the entanglement structure. Pairwise entanglement turns out suppressed relative to collective and genuine forms, with all measures falling as more kinematics are integrated away. A sympathetic reader would care because the work positions this process as a concrete laboratory for testing multipartite quantum correlations at high-energy colliders using realistic luminosities and polarisation.","feed_headline":"Collective entanglement accessible in top-Z production at lepton colliders","feed_subtitle":"Tomography at 1 TeV shows one-to-other negativity reachable with ILC luminosity, but genuine multipartite certification remains limited.","key_machinery":"The 12x12 spin density matrix of the tripartite spin system (top, antitop, Z) reconstructed from tree-level SM helicity amplitudes, together with negativity-based entanglement measures evaluated after successive phase-space integrations.","core_discovery":"Starting from the Standard Model helicity amplitudes, the full 12x12 spin density matrix is reconstructed for the tripartite Hilbert space of the top, antitop, and Z spins. Entanglement is characterised through one-to-one negativities, one-to-other negativities, and the genuine multipartite negativity at three increasingly inclusive levels of phase space integration. Pairwise entanglement is generally suppressed relative to the collective and genuine multipartite measures, and all quantities decrease when more kinematic information is integrated out. Assuming quantum tomography in the fully leptonic decay channel at sqrt(s)=1 TeV, collective entanglement is accessible at a realistic high-lum","pith_inferences":["The mixed-state negativity framework developed here can be applied directly to other tripartite final states involving vector bosons or heavy fermions at colliders.","Observation of the predicted collective negativity would constitute a direct test of quantum coherence in SM production amplitudes beyond classical spin correlations.","Including next-to-leading-order QCD corrections or hypothetical BSM contributions would shift the predicted negativity values and could be constrained by the same tomography setup.","The approach suggests that spin tomography at lepton colliders offers a systematic route to quantify multipartite entanglement in any process whose final-state spins span a product of low-dimensional Hilbert spaces."],"forward_implications":["Pairwise entanglement is suppressed relative to collective and genuine multipartite entanglement.","All entanglement measures decrease as more kinematic information is integrated out.","Collective entanglement should be accessible via quantum tomography in the fully leptonic decay channel at sqrt(s)=1 TeV with realistic high-luminosity polarised lepton colliders.","Certifying genuine multipartite entanglement has only limited sensitivity for a specific polarisation benchmark within expected ILC luminosity."],"fun_headline_variants":["Tripartite entanglement in ttbar Z at lepton colliders","Negativities characterize entanglement in e+e- to ttZ","Collective and genuine multipartite negativity in top Z system","Spin density matrix reveals suppressed pairwise entanglement in ttZ","Multipartite entanglement accessible in 12x12 ttbarZ state"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"The spin density matrix reconstructed from tree-level Standard Model helicity amplitudes fully captures the entanglement structure relevant for experimental tomography, without significant contamination from higher-order QCD corrections, beyond-Standard-Model contributions, or decay-channel-specific reconstruction biases.","fun_headline_variants_meta":{"raw":{"variants":["Tripartite entanglement in ttbar Z at lepton colliders","Negativities characterize entanglement in e+e- to ttZ","Collective and genuine multipartite negativity in top Z system","Spin density matrix reveals suppressed pairwise entanglement in ttZ","Multipartite entanglement accessible in 12x12 ttbarZ state"]},"model":"grok-4.3","cost_usd":0.006759,"raw_usage":{"total_tokens":3200,"prompt_tokens":778,"num_sources_used":0,"completion_tokens":70,"cost_in_usd_ticks":67587000,"prompt_tokens_details":{"text_tokens":778,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":2352,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":778,"tokens_out":70,"duration_ms":14061,"temperature":1.0,"reasoning_tokens":2352,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-27T12:27:42.339561+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"An experimental reconstruction of the genuine multipartite negativity or one-to-other negativity in the fully leptonic channel at 1 TeV that lies outside the projected sensitivity band for the ILC luminosity benchmark would falsify the accessibility claims.","supporting_citations":[],"review_version":1}