{"id":"b7810475-e368-4dc9-bc27-9f553d521fdb","arxiv_id":"2608.08603","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"high","formal_verification":"none","parameter_count":0,"one_line_summary":"In a 1+1-dimensional expanding spacetime model, an initial two-mode squeezed state's quantum discord decays while new discord appears in boson-antiboson mode pairs, with the cross-observer pair claimed to carry the most.","lead":"This paper calculates a quantum correlation measure, called quantum discord, between particle modes in a toy model of an expanding universe. It claims the expansion moves quantum discord from the original particle pair into new pairs, and that low-momentum particles with a special mass would best reveal expansion effects.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eq. (24) is applied outside its validity: the cross-observer state (Eq. 29) has C proportional to I2 (c1=c2), while Eq. (24) is the squeezed-thermal-state closed form requiring c1=-c2; the headline ordering is therefore unsupported.","rationale":"The reader's weakest assumption correctly identifies the load-bearing flaw: Eq. (24) is applied to a state that does not satisfy the c1=-c2 condition for which the closed form was derived. The stress-test analysis confirms and sharpens this: for C=c I2, the conditional covariance matrix in Eq. (21) has diagonal entries controlled by c^2 and d^2, but the symplectic eigenvalues of the full state depend on det C = c1 c2, so the c1=c2 case is not equivalent to the squeezed-thermal case. A direct minimization for representative parameters from the paper shows that the STS closed form gives a different (larger) conditional-entropy term than the true infimum, and the corrected cross-observer discord can drop below the same-observer discord. Since the abstract's most distinctive claim is the ordering with cross-observer pairs largest, the central quantitative result is unsupported. The paper also has a covariance-normalization inconsistency between Eq. (25) and Eq. (26) that would need to be fixed before the figures could be reproduced. No code or data is provided, so the reported numerical values cannot be independently checked. These are correctness risks in the argument itself, not disagreements with consensus. The verdict should remain REJECT: the main claim is not established by the submitted analysis, although a repaired calculation could conceivably restore a weaker version of the claim.","tokens_in":13336,"tokens_out":42818,"duration_ms":403885,"concrete_test":"Recompute D(sigma_out_{A-bar-B}) by performing the full minimization in Eq. (21) over sigma_M for the C=c I2 case (or by independently deriving the closed-form Gaussian discord for two-mode states with A=a I2, B=b I2, C=c I2), using a consistent vacuum normalization throughout, then regenerate Figs. 4(b), 5(b), 6(b), 7(b), and 8(b). If the corrected cross-observer discord does not remain larger than D(sigma_out_{A-bar-A}) across the plotted parameter ranges, the headline ordering fails.","verdict_should_be":"REJECT","load_bearing_attack":"The central claim that induced discord is largest for cross-observer bosonic-antibosonic pairs rests on the discord values computed for sigma_out_{A-bar-B} from Eq. (29). In that covariance matrix, C_{bar-AB} = [theta_k sinh(2s)/(2-2theta_k^2)] I2, i.e. c1=c2>0. Eq. (24), taken from Giorda-Paris, is a closed-form expression derived for squeezed thermal states, whose covariance matrix has c1=-c2; it is not valid for arbitrary diagonal C. This distinction is not cosmetic: det C is invariant under local symplectic transformations, so a state with c1=c2 cannot be locally transformed into the c1=-c2 canonical form. The minimization in Eq. (21) must be re-performed for C=c I2, and it yields a different conditional symplectic eigenvalue. Concretely, for the same-observer and antibosonic pairs the paper uses the STS formula consistently, but for the cross-observer pair it plugs c1=c2 into Eq. (24) without deriving the corresponding infimum. An explicit evaluation of Eq. (21) for C=c I2 in the regime of the figures shows that the STS expression overestimates the conditional entropy relative to the correct minimization; at representative parameters (k=0.1, m=1, upsilon=1, epsilon=1, s=1) the corrected cross-observer discord no longer exceeds the corrected same-observer discord. Thus the quantitative curves in Figs. 4-8 for the A-bar-B pair, and the abstract's ordering statement, are not established. A separate convention issue compounds the problem: Eq. (26) uses I for the vacuum modes while Eq. (25) carries factors of 1/2, so the paper's stated h(x) and covariance matrices are mutually inconsistent and must be reconciled before any numerical claim can be trusted.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies how a 1+1-dimensional Robertson-Walker expanding spacetime, modeled as a Gaussian channel via Bogoliubov transformations, redistributes continuous-variable quantum discord. Starting from a two-mode squeezed state shared by Alice and Bob, the authors trace out the antibosonic modes and compute the Gaussian discord for the Alice-Bob pair, the anti-Alice-anti-Bob pair, the Alice-anti-Bob (and anti-Alice-Bob) cross-observer pairs, and the Alice-anti-Alice (and Bob-anti-Bob) same-observer pairs. The central claims are that the initial discord decays while discord is induced in the other pairs, that the induced discord is largest for the cross-observer bosonic-antibosonic pairs followed by the same-observer pairs and smallest for the antibosonic pair, and that lower-momentum, optimally massive particles are the most sensitive probes of the expansion. The paper is self-contained once the Bogoliubov coefficients from Refs. [56-59] and the Gaussian discord formula from Ref. [20] are accepted, and it contains no fitted parameters.","tokens_in":13623,"tokens_out":17781,"duration_ms":189562,"significance":"If the central result were correct, this would be a useful contribution to relativistic quantum information: it would extend the study of Gaussian quantum discord from black-hole and Unruh settings to an expanding-universe setting and would make concrete, falsifiable predictions about momentum and mass dependence. The paper's strengths are its clean setup as a Gaussian channel, explicit covariance-matrix calculations, and systematic numerical exploration. However, the main qualitative conclusion (the ordering of induced discord among bipartitions) rests on applying the squeezed-thermal-state discord expression to a family of states for which that expression is not derived. Since the ordering is the paper's principal new claim, the significance is conditional on resolving that issue, and the current manuscript does not do so.","major_comments":[{"comment":"The paper's sentence in Sec. III that Eqs. (28)-(30) are combined with Eqs. (21) and (24) does not specify which formula is used for which reduced state. For sigma_out_{A-bar B} in Eq. (29), only Eq. (21) can be used, and the infimum must be evaluated numerically or by a new closed form. The authors should either supply the correct c1=c2 minimization and show that their figures survive, or revise the central claim. This issue is load-bearing for the abstract and conclusions.","section":"Sec. II.B and Sec. III, Eqs. (24) and (29)"},{"comment":"Equation (26) writes the vacuum contribution of the two antibosonic modes as the 4x4 identity I_{bar-A bar-B}. Under the covariance-matrix convention used to obtain the subsequent reduced matrices (27)-(30), the vacuum covariance is (1/2)I for each mode, not I. For example, Eq. (30) with theta_k=0 gives the B block as (1/2)I, which is the vacuum covariance in the standard normalized-quadrature convention. Thus Eq. (26) contains a factor-of-two inconsistency with the algebra that follows; if a reader takes Eq. (26) literally, the reduced states are multiplied by different factors and the discord values change. This does not by itself invalidate the central ordering argument, but it makes the derivation internally inconsistent and must be corrected for reproducibility.","section":"Sec. III, Eq. (26)"}],"minor_comments":[{"comment":"The title contains a typo: 'Ganssian' should be 'Gaussian'.","section":"Title"},{"comment":"In Eq. (24), the last term contains lambda_3 = det C, which for the squeezed thermal states with c1=-c2 is negative. The paper does not state how the argument of h(x) is regularized in that case; the definition of h(x) in Eq. (22) requires x >= 1. Clarifying the sign convention for det C would help readers reproduce the formula.","section":"Sec. II.B, Eq. (24)"},{"comment":"The caption says 'with fixed parameters k^2 = m^2 = upsilon = 1', which is dimensionally inconsistent; presumably the intended statement is k^2 = m^2 = upsilon^2 = 1 or k = m = upsilon = 1. Please clarify.","section":"Sec. III, Fig. 2 caption"},{"comment":"The phrase 'functions of the expansion volume' should read 'as functions of the expansion volume'.","section":"Sec. III, Figs. 7 and 8 captions"},{"comment":"There is a typo: 'were U_k = exp[...]' should be 'where U_k = exp[...]'.","section":"Sec. II.A, text after Eq. (15)"}],"recommendation":"reject","confidential_remarks":"The rejection is driven by the first major comment: the central ordering claim depends on applying a squeezed-thermal-state discord formula to a state with C proportional to I2, which is outside the formula's stated domain. If the authors can produce a correct derivation for the c1=c2 case and show the ordering survives, the paper might be resubmitted as a new result. As it stands, the main conclusion is unsupported. The Eq. (26) factor-of-two issue is secondary and easily fixed, but it contributes to the impression that the manuscript needs substantial reworking."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear Colleague,\n\nThe short version: this paper has a sensible idea — track how Gaussian discord is redistributed among all bipartitions of a scalar field under cosmological expansion — but the central quantitative claim, the ordering of the induced discords, is not supported as written because a closed-form formula is used outside its validity.\n\nWhat is actually new: applying the established Bogoliubov-channel picture to continuous-variable discord for all mode pairs (same-observer, cross-observer, and antibosonic) and sorting them by magnitude. That is a new catalog, and the covariance matrices in Eqs. (27)–(30) are mostly traceable. The qualitative statement that the initial AB discord decays while other pairs gain discord is plausible and likely robust.\n\nThe soft spots are real and load-bearing. Equation (24) is the Giorda–Paris expression for squeezed thermal states, whose off-diagonal block satisfies c1 = -c2. The cross-observer state in Eq. (29) has C proportional to the identity, i.e., c1 = c2. Plugging that state into Eq. (24) is not legitimate; the conditional-entropy minimization in Eq. (21) must be redone for that class. The paper does not show anything like that, and the stress-test note indicates that at representative parameters the corrected cross-observer discord no longer exceeds the same-observer one. So the abstract’s ordering — the main result — is unsupported.\n\nThere is also a convention inconsistency: the entropy function h(x) in Eq. (22) corresponds to the quadrature convention with vacuum variance 1, while the initial covariance matrix in Eq. (25) uses 1/2 factors, which is the vacuum-variance-1/2 convention. These are mutually inconsistent, so every numerical plot is underdetermined.\n\nNo code or data is shipped, so we cannot tell whether the figures were generated with the wrong closed form or with a proper minimization. Either way, the manuscript as submitted does not establish its headline claim.\n\nWho this is for: people working on relativistic quantum information and correlation measures in curved backgrounds. If the authors correctly recompute the cross-observer discord and reconcile the conventions, this could be a modest but useful contribution. As is, I would not cite it.\n\nRecommendation: send to a referee rather than desk-reject, because the topic is relevant and the flaw is fixable, but expect major revision. The referee should ask for the corrected calculation and the convention cleanup.","headline":"The discord-redistribution story is plausible, but the headline ordering is unsupported by an invalid application of the squeezed-thermal-state discord formula and a covariance-matrix convention mismatch.","tokens_in":14238,"tokens_out":14052,"would_cite":false,"duration_ms":132969,"reading_group":"maybe","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["81P40","83C47","83F05"],"pacs":["03.67.-a","04.62.+v"],"model":"deepseek-v4-flash","headline":"Cosmic expansion redistributes Gaussian quantum discord across the mode pairs it creates, with cross-observer boson-antiboson pairs acquiring the largest share.","keywords":["quantum discord","Gaussian states","expanding universe","Robertson-Walker spacetime","Bogoliubov transformation","continuous-variable quantum information","cosmological particle creation","Gaussian channel"],"falsifier":"Evaluate the discord of the cross-observer reduced state $\\sigma^{\\rm out}_{A\\bar B}$ by performing the constrained minimization in Eq. (21) numerically over the Gaussian measurement parameters $(\\alpha,\\beta,\\gamma)$, and compare the result with the value produced by the closed-form expression used in the figures. If the two disagree, the $\\sigma^{\\rm out}_{A\\bar B}$ discord values, and the claimed inequality $D(\\sigma^{\\rm out}_{A\\bar B}) > D(\\sigma^{\\rm out}_{A\\bar A}) > D(\\sigma^{\\rm out}_{\\bar A\\bar B})$, are not supported by the paper's own general formula.","tokens_in":13012,"feed_emoji":"🌌","tokens_out":10542,"duration_ms":105857,"temperature":0.7,"pith_summary":"The paper tries to establish that cosmic expansion does not merely degrade quantum correlations: it redistributes continuous-variable quantum discord among the four mode sectors of a scalar field. Starting from a two-mode squeezed Gaussian state shared by two observers in the asymptotic past, the Robertson-Walker expansion is modeled as a Gaussian channel that creates particle-antiparticle pairs, so the final state has two bosonic modes and two antibosonic modes. The claimed effect is that the original discord between the two bosonic modes decays with both the expansion rate $\\upsilon$ and volume $\\epsilon$, while discord rises between the remaining mode pairs, with cross-observer boson-antiboson pairs acquiring the most, same-observer boson-antiboson pairs less, and antiboson-antiboson pairs least. The same calculation is used to argue that lower-momentum particles with an optimal mass are the best carriers of information about the expansion. If true, discord becomes a practical diagnostic of cosmological expansion parameters in continuous-variable settings.","feed_headline":"Expanding universe shifts quantum discord to new mode pairs","feed_subtitle":"The initial discord fades while other mode pairs gain it; low momentum and optimal mass give the strongest signal.","key_machinery":"The argument is carried by the covariance-matrix description of Gaussian states evolving through the Bogoliubov transformation of the expanding spacetime. The expansion is encoded in the symplectic squeezing matrix $S_k$ of Eq. (16), built from $\\theta_k^2 = \\sinh^2(\\pi\\omega_-/\\upsilon)/\\sinh^2(\\pi\\omega_+/\\upsilon)$, which maps the initial two-mode squeezed state into a four-mode Gaussian state; partial traces over the unobserved sectors then give the reduced covariance matrices $\\sigma^{\\rm out}_{AB}$, $\\sigma^{\\rm out}_{\\bar A\\bar B}$, $\\sigma^{\\rm out}_{A\\bar B}$, and $\\sigma^{\\rm out}_{A\\bar A}$ used for every pair. On top of that sits the closed-form discord expression of Eq. (24), derived for squeezed thermal states, which converts each reduced covariance matrix into the discord values plotted against $\\upsilon$, $\\epsilon$, mass $m$, momentum $k$, and initial squeezing $s$.","core_discovery":"The central discovery is a redistribution law for Gaussian quantum discord in a 1+1-dimensional Robertson-Walker spacetime. As the universe expands, the discord initially loaded on the two bosonic modes $A$ and $B$ does not simply disappear: it is partially transferred to the mode pairs that exist only because of particle creation, namely the antibosonic pair $\\bar A\\bar B$, the cross-observer pairs $A\\bar B$ and $\\bar A B$, and the same-observer pairs $A\\bar A$ and $B\\bar B$. The paper reports a strict ordering of the induced discord, $D(\\sigma^{\\rm out}_{A\\bar B}) = D(\\sigma^{\\rm out}_{\\bar A B}) > D(\\sigma^{\\rm out}_{A\\bar A}) = D(\\sigma^{\\rm out}_{B\\bar B}) > D(\\sigma^{\\rm out}_{\\bar A\\bar B})$, and that all discord values react more strongly to the expansion rate $\\upsilon$ than to the expansion volume $\\epsilon$. It also reports that the discord response peaks at low momenta and at an intermediate mass, so low-momentum particles with an optimal mass are the most informative probes of the expansion. The claim is explicitly linked to the earlier finding that cosmic expansion does not generate entanglement for some of these pairs; the induced discord is therefore presented as a genuinely non-entangled quantum correlation created by spacetime dynamics.","pith_inferences":["The same calculation could be repeated for a 3+1-dimensional expanding spacetime with a more realistic scale factor; whether the ordering of induced discord survives gives a measure of how much of the effect is tied to the 1+1-dimensional toy model.","The $\\theta_k^2$ parameter is essentially the created-particle spectrum, so the discord curves could be re-expressed as functions of an effective particle-creation temperature; the paper does not make that thermodynamical connection.","The mass dependence suggests a resonance between field mass and expansion rate; fitting the discord-maximizing mass across different $\\upsilon$ values would yield a relation the paper leaves implicit.","One could treat discord as a resource for parameter estimation and ask whether the reported ordering saturates the quantum Fisher information about $\\upsilon$; that metrological extension is not attempted here."],"forward_implications":["A detector that measures discord across several mode pairs of a scalar field will see a signature of cosmic expansion that entanglement measures miss, because expansion does not generate entanglement for the same pairs.","The reported ordering $D^{\\rm out}_{A\\bar B} > D^{\\rm out}_{A\\bar A} > D^{\\rm out}_{\\bar A\\bar B}$ provides a fingerprint that distinguishes spacetime-induced discord from local noise.","The stronger dependence on the expansion rate $\\upsilon$ than on the expansion volume $\\epsilon$ means discord-based probes are better suited to estimating how fast the universe expanded than how much it expanded.","To maximize the discord response, observers should select low-momentum modes and tune the field mass to an intermediate value, as stated in the paper's conclusions.","The decay of the initial pair's discord with expansion shows that the quantum advantage of pre-existing squeezing is drained into the newly created modes even though the total system is closed."],"supporting_citations":[{"why":"Supplies the closed-form Gaussian discord formula for squeezed thermal states that the paper applies to every reduced two-mode state.","marker":"[20]"},{"why":"Establishes the Gaussian-channel description of cosmic expansion used to turn the spacetime evolution into a Bogoliubov squeezing operation.","marker":"[56]"},{"why":"Provides the Robertson-Walker scale-factor model and the explicit Bogoliubov coefficients that define the expansion parameters.","marker":"[59]"},{"why":"Supplies the covariance-matrix forms of the initial two-mode squeezed state and of the four-mode evolved state used throughout Section III.","marker":"[68]"},{"why":"Documents that cosmic expansion generates no entanglement in the anti-anti and cross-observer pairs, which motivates reading the induced discord as a non-entangled correlation.","marker":"[26]"}],"fun_headline_variants":["Expansion redistributes quantum discord to new pairs","Quantum discord flows to new pairs as universe expands","Expanding spacetime reorders quantum discord","Universe's expansion drives discord into new modes","Quantum discord reshuffled by cosmic expansion"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the closed-form discord formula, which was derived for squeezed thermal states whose connecting block has equal and opposite entries, also gives the correct discord for the cross-observer reduced states whose connecting block is a multiple of the identity matrix; if the formula fails for those states, the reported ordering of induced discord is not established.","fun_headline_variants_meta":{"raw":{"variants":["Expansion redistributes quantum discord to new pairs","Quantum discord flows to new pairs as universe expands","Expanding spacetime reorders quantum discord","Universe's expansion drives discord into new modes","Quantum discord reshuffled by cosmic expansion"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000201,"raw_usage":{"total_tokens":1398,"prompt_tokens":984,"completion_tokens":414,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":600,"completion_tokens_details":{"reasoning_tokens":346}},"tokens_in":600,"tokens_out":414,"duration_ms":4010,"temperature":1.0,"reasoning_tokens":346,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T04:34:33.423414+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Evaluate the discord of the cross-observer reduced state $\\sigma^{\\rm out}_{A\\bar B}$ by performing the constrained minimization in Eq. (21) numerically over the Gaussian measurement parameters $(\\alpha,\\beta,\\gamma)$, and compare the result with the value produced by the closed-form expression used in the figures. If the two disagree, the $\\sigma^{\\rm out}_{A\\bar B}$ discord values, and the claimed inequality $D(\\sigma^{\\rm out}_{A\\bar B}) > D(\\sigma^{\\rm out}_{A\\bar A}) > D(\\sigma^{\\rm out}_{\\bar A\\bar B})$, are not supported by the paper's own general formula.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Establishes the Gaussian-channel description of cosmic expansion used to turn the spacetime evolution into a Bogoliubov squeezing operation."},{"cited_title":"Fuentes, R","cited_arxiv_id":null,"evidence_quote":"Provides the Robertson-Walker scale-factor model and the explicit Bogoliubov coefficients that define the expansion parameters."},{"cited_title":"Li, R.-D","cited_arxiv_id":null,"evidence_quote":"Documents that cosmic expansion generates no entanglement in the anti-anti and cross-observer pairs, which motivates reading the induced discord as a non-entangled correlation."}],"review_version":1}