{"id":"ea1e90c4-636b-441d-bc84-44065ad01cc4","arxiv_id":"2605.26240","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":6.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"Gravity-induced entanglement in pulsed optomechanics has an input-state-independent threshold g_G > 2 γ_m N_th set by gravitational coupling versus thermal decoherence, with amplification via nonclassical states.","lead":"The paper derives that gravity-induced entanglement between optical outputs in two pulsed optomechanical systems can be amplified using squeezed or Fock input states, but the generation threshold remains fixed at g_G > 2 γ_m N_th regardless of input choice. A smart generalist might read it to understand fundamental limits on lab tests of quantum gravity effects.","discovery_kind":"extension","skeptic_critique":{"model":"grok-4.3","headline":"Central claim that no input state lowers the threshold g_G>2γ_m N_th is only explicitly proven for Gaussian and Fock inputs","rationale":"Reader's weakest assumption targets the physical model (beam-splitter swap and thermal dominance). The more direct threat to the headline claim is the scope of the 'any input state' assertion, which is narrower than stated. This moves the verdict from UNVERDICTED to CONDITIONAL pending confirmation that the bound is input-independent in general.","tokens_in":1726,"tokens_out":375,"duration_ms":20704,"concrete_test":"Extract the section deriving the threshold (likely the Gaussian case) and re-derive it for a non-Gaussian input such as a two-mode cat state |α⟩|α⟩ + |-α⟩|-α⟩ (normalized); compute the output logarithmic negativity as a function of g_G / (γ_m N_th) and check whether entanglement appears below the quoted threshold.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The abstract asserts the threshold 'cannot be lowered by any choice of input state' yet immediately qualifies this by stating 'We prove this bound for two-mode Gaussian inputs and show that it continues to hold for Fock-state inputs.' The load-bearing step is therefore the unstated extension from these two classes to arbitrary states. If the derivation of the bound relies on properties specific to Gaussians (e.g., covariance-matrix evolution under the beam-splitter swap) or on the photon-number statistics of Fock states, a different non-Gaussian state could in principle alter the effective competition between g_G and thermal noise without violating the model assumptions. The full manuscript must contain either a general argument that input-state dependence drops out for any state or an explicit statement that the claim is restricted to the proven cases.","agreement_with_reader":"disagree"},"referee_report":{"model":"grok-4.3","summary":"The paper investigates gravity-induced entanglement between the output optical fields of two red-detuned pulsed optomechanical systems whose masses interact gravitationally. Using rectangular pulses to realize beam-splitter state swaps, it shows that preparing input states in squeezed or Fock form amplifies the generated entanglement, but derives a threshold g_G > 2 γ_m N_th for entanglement generation that is set by competition with thermal decoherence and cannot be lowered by input-state choice. The bound is proven for two-mode Gaussian inputs and shown to hold for Fock inputs; the work also analyzes imperfect detection and identifies entanglement-annihilating and entanglement-breaking regimes independent of g_G.","tokens_in":1895,"tokens_out":375,"duration_ms":18645,"significance":"If the central bound holds, the result supplies a concrete, input-state-independent limit on gravity-induced entanglement generation in pulsed optomechanics, together with explicit amplification mechanisms for nonclassical inputs. The explicit proofs for Gaussian and Fock cases, the identification of detection-modified regimes, and the parameter-free character of the threshold (arising directly from g_G versus thermal terms) are strengths that would guide experimental efforts to observe quantum gravity effects.","major_comments":[{"comment":"Abstract: the claim that the threshold 'cannot be lowered by any choice of input state' is not supported by the proofs that are explicitly limited to two-mode Gaussian inputs and Fock-state inputs. If the manuscript contains no general argument showing that input-state dependence drops out for arbitrary states (e.g., via properties of the beam-splitter swap or thermal noise that are state-independent), the claim must be qualified to the cases actually proven; otherwise the central assertion about the threshold is over-stated.","section":"Abstract"}],"minor_comments":[],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for their careful reading of the manuscript and for highlighting the need to align the abstract claim with the scope of the proofs. We address the single major comment below and will make the corresponding revision.","responses":[{"response":"We agree that the abstract statement is stronger than the explicit proofs provided. The threshold g_G > 2 γ_m N_th originates from the additive thermal noise contributed by the mechanical baths during the interaction time; because this noise is independent of the input state and the beam-splitter swap merely transfers the gravitational phase accumulation to the optical outputs, the minimal coupling required to overcome the noise is expected to be state-independent. Nevertheless, we have only derived the bound rigorously for two-mode Gaussian states and verified it for Fock states. To correct the overstatement we will (i) revise the abstract to read that the threshold “cannot be lowered by the choice of Gaussian or Fock input states” and (ii) add a short paragraph after the Fock-state section explaining why the same bound is anticipated for general states on the basis of the state-independent thermal channel. These changes will be implemented in the revised manuscript.","revision_made":"yes","referee_comment":"[Abstract] Abstract: the claim that the threshold 'cannot be lowered by any choice of input state' is not supported by the proofs that are explicitly limited to two-mode Gaussian inputs and Fock-state inputs. If the manuscript contains no general argument showing that input-state dependence drops out for arbitrary states (e.g., via properties of the beam-splitter swap or thermal noise that are state-independent), the claim must be qualified to the cases actually proven; otherwise the central assertion about the threshold is over-stated."}],"tokens_in":1360,"tokens_out":370,"duration_ms":24309,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The core result is a lower bound g_G > 2 γ_m N_th on the gravitational coupling needed to generate entanglement between the output fields; the bound is independent of the input state and arises from competition with mechanical thermal decoherence. They show that squeezed or Fock inputs can increase the amount of entanglement above threshold, and they track how finite detection efficiency raises the effective threshold and carves out entanglement-breaking regimes set only by accumulated thermal noise.\n\nThe work is clearest on the Gaussian case, where the beam-splitter swap and covariance-matrix evolution let them prove the bound directly, and the Fock-state extension is checked explicitly. That part is solid and useful for experiment design. The model assumptions (rectangular pulses realizing a clean state swap, thermal decoherence as the sole competing process) are stated plainly.\n\nThe soft spot is the reach of the claim. The abstract says the threshold cannot be lowered by any input state, yet the proofs cover only two-mode Gaussians and Fock states. Nothing in the provided text supplies a general argument that input dependence drops out for every possible state; if a different non-Gaussian state alters the effective competition between g_G and thermal terms under the same interaction Hamiltonian, the bound could shift. The paper would be stronger with either a general proof or an explicit restriction to the cases shown.\n\nThis is for groups working on pulsed optomechanics and proposals for gravity-entanglement tests. A reader who needs concrete bounds on lab parameters will find the threshold and detection analysis helpful. It is worth sending to referees because the central claim is sharp and the derivations for the checked cases are reproducible, even though the generality step needs tightening.","headline":"The paper derives a thermal-noise threshold for gravity-induced entanglement that holds for Gaussian and Fock inputs but asserts it for arbitrary states without a general proof.","tokens_in":2362,"tokens_out":412,"would_cite":false,"duration_ms":15757,"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":"Gravity-induced entanglement in pulsed optomechanics requires gravitational coupling to exceed twice the thermal decoherence rate, and no input state lowers this threshold.","keywords":["gravity-induced entanglement","pulsed optomechanics","entanglement threshold","thermal decoherence","Gaussian states","Fock states","beam-splitter swap"],"falsifier":"An experiment that generates detectable entanglement with g_G less than or equal to 2 gamma_m N_th using either Gaussian or Fock inputs would falsify the claimed bound.","tokens_in":2622,"feed_emoji":"⚛️","tokens_out":551,"duration_ms":14226,"temperature":0.7,"pith_summary":"The paper studies two red-detuned pulsed optomechanical systems whose mechanical modes interact gravitationally. Each system uses rectangular pulses to first swap a nonclassical optical state onto its mechanical mode and then read the gravitationally induced entanglement back into the outgoing light. Squeezed or Fock inputs increase the amount of entanglement that appears in the optical outputs. The generation threshold itself, however, remains fixed by the inequality g_G greater than 2 gamma_m N_th. This bound is proven for two-mode Gaussian inputs and shown to hold as well for Fock inputs; imperfect detection further splits the parameter space into entanglement-annihilating and entanglement-breaking regimes governed solely by accumulated thermal decoherence.","feed_headline":"Gravity entanglement bound set by thermal decoherence, not input state","feed_subtitle":"The threshold g_G > 2 gamma_m N_th holds for both Gaussian and Fock inputs in pulsed optomechanical systems.","key_machinery":"The beam-splitter state swap performed by the red-detuned optomechanical interaction under rectangular pulses, which transfers the effect of the gravitational coupling from the mechanical modes to the optical outputs.","core_discovery":"In two red-detuned pulsed optomechanical systems with gravitationally coupled masses, the optomechanical interaction realizes a beam-splitter state swap. Two rectangular pulses per system first imprint a nonclassical state on the mechanics and then read the gravitationally generated entanglement onto the outgoing optical fields. While squeezed or Fock inputs amplify the resulting entanglement, the threshold condition g_G > 2 gamma_m N_th cannot be lowered by any choice of input state; the bound is established for two-mode Gaussian inputs and remains valid for Fock-state inputs. Imperfect detection modifies the accessible regimes, which are ultimately set by thermal decoherence accumulated ov","pith_inferences":[],"forward_implications":[],"fun_headline_variants":["Thermal decoherence fixes gravity entanglement bound","Input state cannot lower g_G > 2 gamma_m N_th threshold","Entanglement bound unchanged by squeezed or Fock inputs","Thermal decoherence sets gravity entanglement threshold"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"The optomechanical interaction must realize an ideal beam-splitter swap with rectangular pulses while thermal decoherence in the mechanical modes is the only competing noise.","fun_headline_variants_meta":{"raw":{"variants":["Thermal decoherence fixes gravity entanglement bound","Input state cannot lower g_G > 2 gamma_m N_th threshold","Entanglement bound unchanged by squeezed or Fock inputs","Thermal decoherence sets gravity entanglement threshold"]},"model":"grok-4.3","cost_usd":0.006415,"raw_usage":{"total_tokens":3023,"prompt_tokens":699,"num_sources_used":0,"completion_tokens":59,"cost_in_usd_ticks":64149500,"prompt_tokens_details":{"text_tokens":699,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":2265,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":699,"tokens_out":59,"duration_ms":21925,"temperature":1.0,"reasoning_tokens":2265,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-29T21:25:02.165305+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"An experiment that generates detectable entanglement with g_G less than or equal to 2 gamma_m N_th using either Gaussian or Fock inputs would falsify the claimed bound.","supporting_citations":[],"review_version":1}