{"id":"79166b68-e1eb-4d37-b668-39c63d75fb39","arxiv_id":"2607.05643","paper_version":1,"verdict":"ACCEPT","confidence":"HIGH","novelty_score":6.5,"correctness_risk":"low","formal_verification":"none","parameter_count":0,"one_line_summary":"Coherent control of unitarily equivalent Stinespring dilations of the amplitude-damping channel activates temporal CHSH violations up to γ≈0.83, beyond both the deterministic threshold and independent-environment control.","lead":"Coherent control of two equivalent physical realizations of the same noisy channel can revive temporal Bell inequality violations that ordinary noise would destroy. The result shows that the concrete Stinespring dilation, not only the reduced channel, can matter for temporal quantum correlations.","discovery_kind":"extension","skeptic_critique":{"model":"grok-4.5","headline":"No significant objection identified","rationale":"The manuscript supplies every intermediate formula needed to reconstruct both activation thresholds from the Choi matrices. The load-bearing mathematical steps (cross maps \to conditional channels \to correlation tensors \to S_T) are free of gaps. The only residual uncertainty is experimental engineering of the inverse dilation and control coherence, which the reader already flags and which does not affect the correctness of the derived claim. Consequently the ACCEPT verdict stands without adjustment.","tokens_in":18294,"tokens_out":370,"duration_ms":4780,"concrete_test":"Independently recompute the two largest eigenvalues of T_D^T T_D from the normalized Choi matrix J^D_+ (Eq. A13) and verify that S_T^D = 4√(2-2γ)/(2-γ) recovers the reported threshold γ_c ≃ 0.83 under the X–Y measurement set of Eq. (6); any algebraic discrepancy would falsify the headline activation range.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim rests on fully explicit analytic expressions (Eqs. 53–54) for the two post-selected temporal CHSH values, derived from the corresponding Choi operators (Appendix A). The comparison between independent-environment control and dilation-level control is mathematically self-contained, and the setting-independent post-selection probability for the chosen ADC dilations U_SE(\theta) and U_SE(-\theta) follows directly from the Kraus structure. No internal inconsistency, hidden assumption that fails inside the stated model, or circular step appears. The reader’s weakest assumption (experimental realizability of the dilations plus control coherence) is a standard engineering caveat for the subfield and does not undermine the theoretical result as written.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.5","summary":"The paper shows that coherent control of noisy evolutions can revive temporal CHSH violations suppressed by amplitude damping. It compares two constructions that realize the same reduced ADC deterministically: (i) coherent control of independent system–environment interactions and (ii) coherent control of two unitarily equivalent Stinespring dilations (U_SE(\theta) and U_SE(-\theta)). Post-selection on the control yields distinct conditional maps; analytic expressions for the temporal CHSH parameter (Eqs. 53–54) and the associated Choi operators (Appendix A) show that dilation-level control extends violation from the deterministic threshold γ_c=0.5 up to γ≃ 0.83, strictly beyond the γ≃ 0.65 reachable with independent environments. Under setting-independent post-selection (X–Y measurements), the same activation certifies that the ADC is not strongly CHSH nonlocality-breaking in that range. The work therefore identifies the choice of Stinespring dilation as an operationally relevant resource for temporal nonclassicality tests.","tokens_in":18446,"tokens_out":1164,"duration_ms":39794,"significance":"If correct, the result supplies a concrete, analytically controlled mechanism by which implementation-level distinctions among Stinespring dilations become operationally visible under coherent control, even though they are invisible for deterministic channel use. The explicit comparison of activation thresholds (0.5 vs ≃0.65 vs ≃0.83), the matching with the optimal filtering threshold of Ref. [42] via an entirely different physical route, and the clean link to strong nonlocality-breaking via setting-independent post-selection are all valuable. The derivations are fully explicit (conditional channels, success probabilities, Choi matrices and correlation tensors), which makes the central claim falsifiable and reproducible. The paper therefore advances both the theory of temporal Bell inequalities under noise and the broader program of coherent control of quantum processes.","major_comments":[{"comment":"Sec. III B and Eqs. (32)–(33): the dilation-level construction is specialized to the single pair U_SE(\theta) and U_SE(-\theta) (i.e., one particular environment unitary V_E). While this choice is natural (reverse Hamiltonian, Kraus separation K0 vs K1) and already demonstrates a clear advantage over independent-environment control, the broader claim that “the choice of Stinespring dilation is an operationally relevant resource” would be stronger if the manuscript either (a) optimized over a one-parameter family of V_E or (b) briefly argued why other unitarily equivalent dilations cannot improve (or can only degrade) the activation range. A short remark or numerical scan would close this gap without changing the central result.","section":null},{"comment":"Sec. IV and Appendix A: the main-text expression S^D_T = 4√(2-2γ)/(2-γ) (Eq. 54) and the quoted threshold γ_c≃0.83 are obtained with the fixed equatorial measurement set of Eq. (6). The conditional Choi operator (A13) itself admits a larger CHSH value (violation for all γ<1) when measurements are allowed in the X–Z plane, but those measurements make the post-selection probability setting-dependent. This distinction is explained only at the end of the Appendix; it should be stated explicitly in Sec. IV so that readers do not misinterpret Eq. (54) as the absolute maximum of the conditional Choi state, which would affect the nonlocality-breaking certification claim.","section":null}],"minor_comments":[{"comment":"Section headings contain spurious spaces (“IMPLEMENTA TIONS”, “ACTIV A TION THRESHOLDS”); these should be corrected.","section":null},{"comment":"Fig. 1 caption and labels refer to environments E1 and E2 while the text (Eqs. 14–15) uses E0 and E1; unify the notation.","section":null},{"comment":"Fig. 1 and Fig. 3: the phrases “which path qubit” and “Coherent recombiner” would read more cleanly as “which-path qubit” and “coherent recombiner”.","section":null},{"comment":"A one-sentence experimental outlook (possible platforms for controlled U and U†, sensitivity to control decoherence) would help readers assess the practical reach of the dilation-level advantage; this can remain brief.","section":null},{"comment":"In Appendix A the formatting of the closed-form S expressions (e.g., “8√2-2γ/4-γ”) is occasionally ambiguous in plain text; ensure the published version uses unambiguous LaTeX fractions.","section":null}],"recommendation":"minor_revision","confidential_remarks":"The central analytic results are solid and the comparison between the two control architectures is clean. I see no hidden circularity or load-bearing error. The coincidence with the optimal filtering threshold of Ref. [42] is a strength rather than a weakness, provided the authors keep the physical mechanisms clearly distinguished (as they already do). Suitable for a solid theory journal after the minor clarifications above; I would not insist on a full multi-channel generalization for acceptance."},"author_rebuttal":null,"desk_editor":{"model":"grok-4.5","letter":"The one thing worth knowing is that they give an explicit, checkable distinction between two coherent-control architectures that look identical at the CPTP level. For the amplitude-damping channel, controlling two unitarily equivalent Stinespring dilations (U_SE(θ) and its inverse) plus Hadamard post-selection on the control pushes temporal CHSH violation from the deterministic threshold γ_c=0.5 all the way to ≃0.83. Controlling independent-environment realizations of the same channel only reaches ≃0.65. Both numbers come straight from the eigenvalues of the post-selected Choi correlation tensors (Appendix A, Eqs. 53–54 and Figs. 4–5).\n\nWhat is new is the systematic side-by-side comparison itself. Superposition of channels is already standard; treating the choice of dilation as an operational resource for temporal nonclassicality is not. The paper does the bookkeeping carefully: same measurement settings, same success-probability formulas, setting-independent post-selection for the chosen dilations, and a clean link to the known hidden-nonlocality threshold of the ADC Choi state. The coincidence with the optimal filtering result of Ku et al. (2021) is noted as a posteriori, not assumed.\n\nSoft spots are minor and standard for the subfield. Everything is analytic for one channel and one pair of dilations; there is no experimental noise model on the control qubit and no claim that the construction is easy to engineer. The paper does not pretend otherwise. The citation pattern is appropriate and the derivations start from the ordinary Stinespring unitary, so there is no circularity.\n\nThis is for people who already care about temporal Bell inequalities, coherent control of channels, or nonlocality-breaking maps. It is not a foundational earthquake, but it is a solid, self-contained advance that a serious referee should see. I would accept it for peer review and would cite the quantitative comparison if I were writing on temporal correlations or process control.","headline":"Clean analytic comparison: dilation-level coherent control of the ADC revives temporal CHSH up to γ≃0.83, beating independent-environment control at ≃0.65, and the math checks out.","tokens_in":19043,"tokens_out":519,"would_cite":true,"duration_ms":5054,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.5","headline":"Coherent control of a channel's own dilations revives temporal Bell nonclassicality deeper into noise than control of independent environments.","keywords":["temporal CHSH inequality","Stinespring dilation","coherent control","amplitude damping channel","post-selection","nonlocality-breaking channels","temporal correlations"],"falsifier":"Implement both the independent-environment and the equivalent-dilation coherent-control protocols for amplitude damping on a controllable qubit platform and measure the temporal CHSH value versus damping strength; the dilation protocol must continue to violate past γ ≈ 0.65 and up to ≈ 0.83 while the independent-environment protocol does not.","tokens_in":19214,"feed_emoji":"⚛️","tokens_out":658,"duration_ms":5693,"temperature":0.7,"pith_summary":"Temporal CHSH inequalities detect nonclassical correlations in sequential measurements on one system, but amplitude damping destroys the violation past a damping strength of 0.5. The paper shows that placing two realizations of that noisy evolution in quantum superposition and post-selecting the control can push the violation threshold higher. The key comparison is between two physically different constructions that look identical when used deterministically: coupling the system to independent environments versus controlling two unitarily equivalent Stinespring dilations of the same channel. For amplitude damping the dilation-level control extends the violation up to roughly 0.83, well past the independent-environment limit of about 0.65 and matching the best known stochastic-filtering result. Because the post-selection probability does not depend on the first measurement setting, the revived violation also certifies that the channel is not strongly nonlocality-breaking. The choice of how a channel is dilated therefore becomes an operational resource for protecting temporal quantum correlations.","feed_headline":"Channel dilations revive temporal Bell violation deeper into noise","feed_subtitle":"Controlling equivalent Stinespring dilations beats independent environments, extending violation to γ≈0.83","key_machinery":"Coherent control of unitarily equivalent Stinespring dilations: a control qubit places the system–environment unitaries U_SE(θ) and U_SE(−θ) in superposition; post-selection on the control then yields conditional maps that cleanly separate the Kraus operators and generate stronger interference than independent-environment superpositions.","core_discovery":"Coherent control of two unitarily equivalent Stinespring dilations of the amplitude-damping channel revives temporal CHSH violation from the deterministic threshold γ = 0.5 all the way to γ ≃ 0.83, strictly beyond the γ ≃ 0.65 reachable by coherent control of independent-environment realizations of the same channel, even though both constructions produce identical reduced dynamics when used without control.","pith_inferences":[],"forward_implications":[],"fun_headline_variants":["Coherent control of Stinespring dilations revives temporal CHSH to γ≃0.83","Equivalent dilations of ADC extend temporal Bell violation past γ=0.5","Unitarily equivalent dilations beat independent environments for temporal CHSH","Controlled channel dilations push temporal nonclassicality deeper into noise","Stinespring choice revives temporal CHSH violation beyond deterministic limit"],"cache_read_input_tokens":128,"weakest_assumption_plain":"The concrete pair of dilations—one unitary and its inverse—must be experimentally realizable with post-selection whose success probability stays independent of the first measurement setting; if that engineering fails, the extended activation range disappears.","fun_headline_variants_meta":{"raw":{"variants":["Coherent control of Stinespring dilations revives temporal CHSH to γ≃0.83","Equivalent dilations of ADC extend temporal Bell violation past γ=0.5","Unitarily equivalent dilations beat independent environments for temporal CHSH","Controlled channel dilations push temporal nonclassicality deeper into noise","Stinespring choice revives temporal CHSH violation beyond deterministic limit"]},"model":"grok-4.5","effort":"low","cost_usd":0.005112,"raw_usage":{"total_tokens":1392,"prompt_tokens":762,"num_sources_used":0,"completion_tokens":100,"cost_in_usd_ticks":51120000,"prompt_tokens_details":{"text_tokens":762,"audio_tokens":0,"image_tokens":0,"cached_tokens":128},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":530,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":762,"tokens_out":100,"duration_ms":4029,"temperature":1.0,"reasoning_tokens":530,"cache_read_input_tokens":128,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-11T04:26:12.809012+00:00","model_set":{"reader":"grok-4.5"},"falsifier":"Implement both the independent-environment and the equivalent-dilation coherent-control protocols for amplitude damping on a controllable qubit platform and measure the temporal CHSH value versus damping strength; the dilation protocol must continue to violate past γ ≈ 0.65 and up to ≈ 0.83 while the independent-environment protocol does not.","supporting_citations":[],"review_version":1}