{"id":"252ed9a0-082b-4ceb-b99c-8ebcbc6869a8","arxiv_id":"2507.15588","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"A one-sided witness based on quantum memory effects can conclusively show that the gravitational interaction is quantum, using measurements on only one of the two interacting masses.","lead":"This paper designs a new table-top experiment to test whether gravity behaves quantum mechanically by watching only one of two interacting masses. The method uses the idea of a 'quantum memory': if the single watched system's past information returns after being stored in the other mass, gravity must have transferred quantum information.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Appendix B omits the proof of Q⪰0 in Eq. (B4), the step that makes w<0 imply quantum memory; until Q is exhibited, the central witness is unproven.","rationale":"The reader's verdict was CONDITIONAL with moderate confidence, and the weakest assumption identified was the locality and state-preparation assumptions of the intermediate gates. I agree those are relevant experimental conditions. However, the single most load-bearing concern in the logical argument is the unverified Q⪰0 step in Appendix B, because the paper's headline statement 'A qubit dynamics D=(E1,E2) requires quantum memory if we find w<0' is true only if the witness decomposition is valid. The reader did flag this as issue (2) among required revisions, so there is partial agreement, but the reader did not treat it as the primary weakest assumption. My proposed test — explicit computation of Q — would settle the matter: if Q is PSD, the analytical witness stands and the main result is sound (subject to the usual physical assumptions); if not, the central claim would need to be revised. Since the paper's own argument is incomplete at this point, the CONDITIONAL verdict remains appropriate: acceptance should require the PSD verification. No change to the reader's verdict is needed.","tokens_in":14598,"tokens_out":17702,"duration_ms":191239,"concrete_test":"Explicitly compute the 16×16 operator Q = W1^{AD}⊗1^{D'B} + W2^{AB}⊗Φ_+^{DD'} − R^{⊤_{D'B}} using W1, W2, and R as defined in Eqs. (B3) and (B5), respecting the paper's convention σ_z|1⟩=|1⟩. Verify Q⪰0 by exact diagonalization (or an SDP feasibility check) and report the minimum eigenvalue. If the minimum eigenvalue is negative, Eq. (10) is not a valid quantum-memory witness and the central claim is unsupported; if all eigenvalues are nonnegative, the omitted step is resolved and the witness proof is complete.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that w<0 in Eq. (10) certifies quantum memory rests entirely on the witness proof in Appendix B. The proof reduces to finding positive semidefinite operators Q and R satisfying Eq. (B4) for W1, W2 in Eq. (B3). The paper defines R=|κ⟩⟨κ| with κ=(|0111⟩−|1110⟩)/√2 and then states: 'It is then straightforward to verify that the operator Q resulting from Eq. (B4) is also positive semidefinite.' No expression for Q is given, and no verification is shown. If Q has a negative eigenvalue, then Eq. (10) is not a valid witness: a dynamics with classical memory could yield w<0, and the paper's central inference — that negative w for the two-qubit gravitational protocol proves a quantum memory — collapses. This is an omitted proof at the logical core of the Letter, not merely a cosmetic gap. A secondary issue is that Eq. (10) contains trσ_zE1[1], an identity input that is not one of the stated Pauli-eigenstate preparations; it can be obtained by summing two preparations, but the advertised 'three correlators' measure is imprecise.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a one-sided witness for the quantum nature of gravitational dynamics, based on the concept of verifiable quantum memory. Two gravitationally coupled qubits P and M interact through a Newtonian-potential Hamiltonian, with intermediate local phase gates inserted. The reduced dynamics of P at two times defines D=(E1,E2); the witness w in Eq. (10), built from three measured correlators on P alone, is claimed to certify that D cannot be realized with a classical-memory decomposition of the form Eq. (2). For the proposed two-qubit protocol the authors derive w=λ(1/3+cos(4gτ)) and give experimental parameters for which w<0. The paper argues that a negative w requires either that gravity is non-LOCC or that the gravitational field itself acts as a quantum memory, and it extends the framework numerically and to a qubit-oscillator setup in the appendices.","tokens_in":14839,"tokens_out":28381,"duration_ms":307601,"significance":"If the proof gap identified below is repaired, this would be a significant new tool: it is a genuinely one-sided test in the sense that measurements and state tomography are performed only on the probe, and the analytical witness is falsifiable and experimentally concrete. The connection between quantum memory in the reduced dynamics and the quantumness of the joint gravitational interaction is clearly articulated in Fig. 1 and Appendix A, and the paper gives explicit, order-of-magnitude experimental estimates. The numerical SDP in Appendix C is a concrete computational procedure that could certify witnesses for arbitrary interaction times, which is a useful contribution in its own right. The main caveat is that the analytical proof of the specific witness Eq. (10) is load-bearing and is not supplied correctly as written.","major_comments":[{"comment":"The proof that Eq. (10) is a valid quantum-memory witness is incomplete and, as written, appears to be incorrect. The paper defines R=|κ⟩⟨κ| with κ=(|0111⟩−|1110⟩)/√2 and states that 'It is then straightforward to verify that the operator Q resulting from Eq. (B4) is also positive semidefinite.' No expression for Q is given. A direct calculation using the stated definitions shows that this claim fails: in the subspace spanned by |Φ+⟩_AB⊗|00⟩_DD' and |Φ+⟩_AB⊗|11⟩_DD', with the paper's unnormalized |Φ+⟩=|00⟩+|11⟩, the matrix of Q is [[2/3,−4/3],[−4/3,−5/6]], whose determinant is −7/3. Hence Q has a negative eigenvalue and Eq. (B4) is not satisfied by the proposed R. Because w<0 in Eq. (10) is the logical core of the central inference, this is not a cosmetic omission: the authors must either exhibit a valid pair (Q,R) for their specific W1,W2 or replace the analytical witness with a certified one.","section":"Appendix B (Eqs. B3-B5)"},{"comment":"The numerical SDP in Eq. (C4) optimizes over the coefficients w11, w1z, wxx, wzz and produces valid witnesses for each τ/g, but it does not certify the particular analytical W1,W2 used in Eqs. (B3). Consequently, Figure 5 supports the existence of some witness of the restricted form for every τ/g, but it does not support the claim that the closed-form witness in Eq. (10), with its specific coefficients, is valid. Given the failure of the Appendix B verification, the analytical result w=λ(1/3+cos(4gτ)) and the associated statement that a measured w<0 proves quantum memory remain unsupported. The authors should either provide a correct proof for Eq. (10) or restate Eq. (11) as a numerically certified example and include the SDP certificate.","section":"Appendix C (Eq. C4)"},{"comment":"The protocol is advertised as one-sided and as requiring no detailed knowledge of M, but the two-qubit circuit requires preparing M in the specific state |1⟩ and applying the local phase gates S⊗S to M. This means that the experimenter must have sufficient control over M to implement these gates, even though no measurements are made on M. The paper should clarify that the one-sidedness refers to state preparation and readout of the probe only, and that control of M, including its initial state, is still part of the protocol.","section":"Main text, Eq. (10) and Fig. 4"}],"minor_comments":[{"comment":"The text says the witness requires measurement of 'only three correlators', but the term tr σ_z E1[𝟙] is not a single Pauli-eigenstate preparation: it requires preparing both σ_z eigenstates (or a maximally mixed ensemble) and summing the outcomes. The experimental counting of preparation/measurement settings should be clarified.","section":"Eq. (10)"},{"comment":"The statement that the witness 'becomes negative if we choose an interaction time τ>3s' is imprecise because w=λ(1/3+cos(4gτ)) is periodic; negativity occurs only in intervals where cos(4gτ)<−1/3. Please specify the allowed intervals rather than a single threshold.","section":"Experimental estimates"},{"comment":"There are several typographical and grammatical errors, including 'do not conclusively proof the quantum nature' (should be 'prove') and 'were λ>0' in Eq. (10) (should be 'where λ>0').","section":"Abstract and Introduction"},{"comment":"The qubit-oscillator example is a useful extension, but the statement that it is 'similar to the one in Refs. [15,16]' would benefit from an explicit remark that the revival dynamics in those references are locally classically realizable, which is the motivation for the additional local Hamiltonian introduced here.","section":"Appendix D"}],"recommendation":"major_revision","confidential_remarks":"The main risk is Appendix B: if the authors cannot supply a valid Q,R for the specific witness in Eq. (10), the analytical central claim collapses and the paper would need to be restructured around the numerical SDP witnesses. The paper is otherwise interesting and the concept is worth publishing if the proof is corrected. I also recommend that the editor ask the authors to clarify the control requirements on M, since the 'one-sided' wording may overstate the experimental asymmetry."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Best to know: this is a genuinely new idea — using quantum memory witnesses from open-system theory to certify the quantumness of gravity from probe-only measurements. The echo protocol with local gates that turns pure dephasing into a dynamics requiring quantum memory is clever, and the analytical witness with only a handful of correlators (Eq. 10) is a real step beyond the SDP-based witnesses in [49]. The paper also does the right thing by being explicit about what the witness can and cannot prove: a negative w rules out classical-memory decompositions, which implies either non-LOCC gravity or gravity itself acting as a quantum memory. That is a clear and honest logical structure.\n\nThe main text's two-qubit derivation is self-consistent. I checked the maps E1, E2 and the expression w=λ(1/3+cos(4gτ)); they follow from the Hamiltonian and gate sequence. The experimental estimates are in the same ballpark as the original GIE proposals, which is credible.\n\nNow the soft spots. The biggest one is Appendix B. The witness validity rests on finding positive semidefinite Q,R satisfying Eq. (B4). The authors give R explicitly, then say it is 'straightforward to verify' that Q is also PSD — without showing Q or giving any numerical check. That is the load-bearing step, and as written it is unproven. A referee should demand the explicit Q matrix or a script that verifies PSD. This is fixable, but it is not cosmetic; if Q were not PSD, w<0 would not certify quantum memory.\n\nSecond, Appendix D has an error: the Hamiltonian written after the RWA is σ+ a† + σ- a, which is anti-Jaynes-Cummings, not the Jaynes-Cummings model. The supplemental equations are consistent with the anti-JC choice, so it is not just a typo. This affects the oscillator example, not the central two-qubit result, but the example should be corrected or re-derived.\n\nThird, the 'one-sided' claim is slightly oversold. The protocol's maps E1,E2 assume the memory M starts in a specific state |1>. The paper says the experimenter can remain ignorant of M, but the derivation does not show the witness works for arbitrary ρM. That is a gap between the advertised generality and the concrete calculation.\n\nFourth, the premise that the intermediate local gates act only locally and do not create joint P-M dynamics is stated but not error-analyzed. This is an important assumption for any experiment.\n\nOverall: the central idea is sound and the two-qubit result is likely correct, but the paper needs revision to close the App B gap, fix App D, and clarify the memory-state assumption. I would send this to a serious referee. The result, if repaired, would be a solid contribution to the quantum-gravity phenomenology literature.","headline":"A clever and genuinely new probe-only witness for quantum gravity, with a fixable but load-bearing proof gap in Appendix B and a wrong Hamiltonian in the oscillator appendix.","tokens_in":15363,"tokens_out":4818,"would_cite":true,"duration_ms":47454,"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":"The paper claims that a negative value of a three-correlator witness, measured on one gravitationally coupled mass alone, proves the interaction cannot be described by classical memory and therefore is a conclusive one-sided signature of…","keywords":["quantum gravity","quantum memory witness","one-sided test","gravitationally induced entanglement","table-top experiments","non-LOCC dynamics","open quantum systems"],"falsifier":"Run the same local-gate sequence with gravity switched off or shielded and measure the three probe correlators that define $w$; if the control run gives $w<0$, the witness fires without any gravitational quantum effect and the claim that $w<0$ certifies gravitational quantumness is falsified.","tokens_in":14395,"feed_emoji":"🪐","tokens_out":12799,"duration_ms":121880,"temperature":0.7,"pith_summary":"The paper proposes a conclusive one-sided test of whether the gravitational interaction between two quantum masses is quantum in nature. The central idea is quantum memory: if the reduced dynamics of one mass—the probe—cannot be reproduced by a classical-memory decomposition, then the joint gravitational dynamics must be either non-LOCC (not realizable by local operations and classical communication) or gravity itself must store quantum information at intermediate times. The authors construct an explicit two-qubit protocol in which the gravitational unitary is interrupted by local phase gates, and they derive an analytical witness, $w=\\lambda(1/3+\\cos(4g\\tau))$, that requires measuring only three correlators on the probe. If the measured $w$ is negative, the probe dynamics provably requires quantum memory. Unlike earlier local signatures that can be reproduced by classical models, this witness rules out classical dynamics and works with measurements on only one subsystem.","feed_headline":"A lone probe can witness gravity's quantum nature","feed_subtitle":"Three correlators on one mass rule out any classical explanation of the gravitational coupling.","key_machinery":"The load-bearing object is the classical-memory decomposition of a two-time probe dynamics, Eq. (2): $E_1[\\rho]=\\sum_i K_i\\rho K_i^\\dagger$ and $E_2[\\rho]=\\sum_i \\Phi_i[K_i\\rho K_i^\\dagger]$ with $\\Phi_i$ completely positive trace-preserving maps. Dynamics of this form can be simulated by storing the measurement outcome $i$ as classical data, so ruling out such a decomposition certifies that quantum memory is required. The witness $w$ in Eq. (10), built from the three correlators $\\mathrm{tr}\\,\\{\\sigma_j E_n[\\sigma_i]\\}$, does exactly that: for the gravitational circuit it evaluates to $w=\\lambda(1/3+\\cos(4g\\tau))$, and $w<0$ implies no classical-memory decomposition exists. The intermediate local gates $S$ and $Z$ are the crucial device: they convert the bare gravitational dephasing, which is always classically realizable, into a dynamics that provably requires quantum memory.","core_discovery":"The paper's central claim is that the quantum nature of the gravitational interaction can be certified by local measurements on one subsystem only. The certification uses the notion of verifiable quantum memory: a two-time dynamics $D=(E_1,E_2)$ on the probe is classical-memory-realizable if $E_2$ can be obtained by conditioning subsequent completely positive trace-preserving maps on classical outcomes of a measurement that already realized $E_1$; if no such decomposition exists, a quantum memory must have stored information at the intermediate time. In the proposed two-qubit circuit, the gravitational unitary $U=\\exp(-ig\\tau\\,\\sigma_x\\otimes\\sigma_x)$ is interrupted by local gates $S=\\exp(-i\\pi\\sigma_z/4)$ and a local $Z$-gate, giving $E_1$ as a partial amplitude-damping map and $E_2$ as the identity, so every input state is restored at time $t_2$. The paper derives the analytical witness $w=\\lambda(1/3+\\cos(4g\\tau))$ from three probe correlators and proves that $w<0$ implies the absence of a classical-memory decomposition. Hence a negative $w$ measured on the probe alone proves that the gravitational coupling coherently transfers quantum information, i.e., the interaction is non-LOCC or gravity itself provides the quantum memory.","pith_inferences":["One natural control experiment, not discussed in the Letter, is to run the same gate sequence with gravity shielded or replaced by a known classical force; a negative $w$ in that control would show the witness can fire without gravitational quantum memory.","The same three-correlator witness could be applied to any suspected quantum mediator between a probe and an unmeasured partner, provided a local-interrupted interaction sequence can be engineered.","Because the intermediate gates are essential, the certified object is the combined 'gravity plus local control' dynamics; whether this weakens the protocol as a test of bare gravity is an interpretive question the paper leaves open."],"forward_implications":["A negative $w$ measured on the probe alone rules out every dynamics that can be written with classical memory in Eq. (2), including random-unitary dephasing models that mimic local decoherence.","The one-sided nature means the memory system $M$ never needs to be measured or fully characterized, so the test works when $M$ is much heavier than the probe and only requires ground-state cooling in the oscillator version.","The analytical witness requires only three correlators, so it can be implemented without full process tomography of the probe dynamics.","For the qubit-qubit setup, the estimated parameters—two masses of about $10^{-14}$ kg with interaction times above roughly 3 seconds under the stated geometry—are comparable to those needed for gravitationally induced entanglement witnesses.","For the qubit-oscillator setup, a 1 mg oscillator with a $10^{-14}$ kg probe and interaction time near 100 seconds could give a measurable witness, whereas a single-atom probe would require an unreachable precision of order $10^{-28}$."],"supporting_citations":[{"why":"Defines the classical-memory decomposition in Eq. (2) and establishes that detecting quantum memory in local dynamics certifies non-Markovian quantum memory; this is the theoretical basis of the witness.","marker":"[48]"},{"why":"Supplies the witness-construction method (operator decomposition and semidefinite program in Eq. (B4)) that the paper's analytical three-correlator witness simplifies.","marker":"[49]"},{"why":"Provides the baseline gravitationally induced entanglement proposal whose setup and experimental parameters the paper uses for comparison and extends to one-sided verification.","marker":"[10]"},{"why":"Establishes that gravitationally induced entanglement between two masses is sufficient evidence of quantum effects in gravity, the two-sided reasoning the paper contrasts with its one-sided witness.","marker":"[11]"},{"why":"Shows how to test the quantumness of gravity without entanglement via simulability of the expected unitary dynamics by LOCC maps, locating the paper's witness in the hierarchy of non-classicality tests.","marker":"[35]"},{"why":"Demonstrates that dephasing from the gravitational coupling can be described as a random unitary evolution and hence as classically realizable, motivating the need for the intermediate local gates.","marker":"[44]"},{"why":"Shows limits on inferring gravitational entanglement from local measurements, supporting the paper's claim that one-sided signatures must explicitly rule out classical models.","marker":"[45]"},{"why":"Provides the previous one-sided atom-interferometry proposal whose qubit-oscillator model is reanalyzed with the new witness to estimate required probe masses.","marker":"[15]"}],"fun_headline_variants":["One-sided witness: gravity's quantum nature from local data","Verifiable quantum memory turns one probe into a gravity witness","Three correlators on one mass certify quantum gravity","Probe-only test: gravitational coupling leaves a quantum memory","Single mass's noisy evolution betrays non-classical gravity"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The protocol assumes that the intermediate local gates $S$ and $Z$ are purely local operations on each mass that do not jointly couple the probe and memory or otherwise mimic the quantum-memory signature; if they do introduce any joint dynamics, the witness could turn negative without any quantum gravitational effect.","fun_headline_variants_meta":{"raw":{"variants":["One-sided witness: gravity's quantum nature from local data","Verifiable quantum memory turns one probe into a gravity witness","Three correlators on one mass certify quantum gravity","Probe-only test: gravitational coupling leaves a quantum memory","Single mass's noisy evolution betrays non-classical gravity"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000635,"raw_usage":{"total_tokens":2929,"prompt_tokens":949,"completion_tokens":1980,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":565,"completion_tokens_details":{"reasoning_tokens":1901}},"tokens_in":565,"tokens_out":1980,"duration_ms":17597,"temperature":1.0,"reasoning_tokens":1901,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T15:28:46.366167+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the same local-gate sequence with gravity switched off or shielded and measure the three probe correlators that define $w$; if the control run gives $w<0$, the witness fires without any gravitational quantum effect and the claim that $w<0$ certifies gravitational quantumness is falsified.","supporting_citations":[{"cited_title":"Carney, H","cited_arxiv_id":null,"evidence_quote":"Defines the classical-memory decomposition in Eq. (2) and establishes that detecting quantum memory in local dynamics certifies non-Markovian quantum memory; this is the theoretical basis of the witness."},{"cited_title":"Bäcker, K","cited_arxiv_id":null,"evidence_quote":"Supplies the witness-construction method (operator decomposition and semidefinite program in Eq. (B4)) that the paper's analytical three-correlator witness simplifies."},{"cited_title":"Carney, P","cited_arxiv_id":null,"evidence_quote":"Provides the baseline gravitationally induced entanglement proposal whose setup and experimental parameters the paper uses for comparison and extends to one-sided verification."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Establishes that gravitationally induced entanglement between two masses is sufficient evidence of quantum effects in gravity, the two-sided reasoning the paper contrasts with its one-sided witness."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Shows how to test the quantumness of gravity without entanglement via simulability of the expected unitary dynamics by LOCC maps, locating the paper's witness in the hierarchy of non-classicality tests."},{"cited_title":"Temporal Entanglement and Witnesses of Non-Classicality","cited_arxiv_id":"2506.15474","evidence_quote":"Demonstrates that dephasing from the gravitational coupling can be described as a random unitary evolution and hence as classically realizable, motivating the need for the intermediate local gates."},{"cited_title":"Hosten, Constraints on probing quantum coherence to infer gravitationalentanglement,PhysicalReviewResearch 4,013023 (2022)","cited_arxiv_id":null,"evidence_quote":"Shows limits on inferring gravitational entanglement from local measurements, supporting the paper's claim that one-sided signatures must explicitly rule out classical models."},{"cited_title":"Krisnanda, G","cited_arxiv_id":null,"evidence_quote":"Provides the previous one-sided atom-interferometry proposal whose qubit-oscillator model is reanalyzed with the new witness to estimate required probe masses."}],"review_version":1}