{"id":"21ddf17e-b962-4971-a846-302f5bda2192","arxiv_id":"1908.09939","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"In holographic CFTs, the Bures information metric of locally excited reduced density matrices vanishes outside the entanglement wedge and matches the AdS time-slice metric inside, giving a CFT-side derivation of wedge geometry.","lead":"The authors show that the Bures metric, a quantum information measure of how easily two states can be told apart, reproduces the shape of entanglement wedges in AdS/CFT when computed in holographic conformal field theories. For a single interval the metric vanishes outside the wedge and equals the AdS time-slice metric inside; for two intervals the wedge is reproduced approximately with the correct phase transitions.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The fidelity replica continuation collapses at k=1: Eq. (17) gives A=1, so Eq. (19) and the single-interval Bures metric are not derived as written.","rationale":"Good faith reading: the paper's program is attractive and the single-interval I(rho,rho') plot plus the free-scalar exact result are genuine evidence. However, the headline 'precisely reproduce' rests on Eq. (19), and Eq. (19) is the output of the replica calculation in Section 3. The reader flagged the analytic continuation as unproven; the stress-test shows it is worse than unproven: at the stated continuation point the formula degenerates to A=1 and loses w'. This is not an external-consensus disagreement; it is an internal consistency check of Eqs. (16)-(19). The double-interval analysis explicitly uses I rather than the Bures metric and admits percent-level deviations, so it cannot substitute for the single-interval Bures derivation. Therefore the central claim is currently unsupported by the manuscript's own equations, and the conditional verdict should be kept with the requirement that Section 3 be repaired or rewritten.","tokens_in":11238,"tokens_out":18708,"duration_ms":188177,"concrete_test":"Directly evaluate Eq. (17) at n=m=1/2 (k=1) using the stated z1,z2: A = |z1-z2|^{-4h} * |z1-z2|^{4h} * 1 = 1, independent of w'. Then repeat the intended derivation for k>1 with the full set of 2k insertions containing both w and w' (2mn copies of the pair and 2n copies of the primed pair) and take the limit k→1 with w' fixed; check whether the inside-wedge contraction yields Eq. (19) or whether the w' dependence is lost. A numerical evaluation of the fidelity on a small lattice realization would provide an independent cross-check.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"Section 3's derivation of the central single-interval result is undermined by the analytic continuation to n=m=1/2. With k=(2m+1)n, the fidelity point n=m=1/2 gives k=1. In Eq. (16)-(17) the trace is then a 2k=2 point function, and the points are z1=(-x-iτ)/(L-x-iτ) and z2=(-x+iτ)/(L-x+iτ)=bar z1; the loop generating z_{2s+1},z_{2s+2} is empty. Substituting k=1 into Eq. (17), the conformal prefactors cancel the two-point function and A_{1/2,1/2}=1, with no w' dependence. The claimed Eq. (19) contains w' and is therefore not a consequence of the formula shown. The 'inside-wedge' contraction chosen in Eq. (18) also degenerates: for k=1 the two competing contractions reduce to the same pair z1,z2, so there is no regime in which the nontrivial contraction dominates. If the authors intend a limit k→1 from k>1, the analytic continuation and the fate of the w' insertions must be specified; as written the Bures metric derivation collapses.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript proposes that, in two-dimensional holographic CFTs, the Bures metric of the reduced density matrix of a locally excited state, viewed as a function of the excitation point, reproduces the AdS time-slice metric inside the entanglement wedge and vanishes outside it. The single-interval case is treated in Sec. 3 by a replica calculation with analytic continuation to n=m=1/2, leading to the claimed result dD_B^2 = (h/τ^2)(dx^2+dτ^2) inside the wedge. The two-interval case is analyzed in Sec. 4 using the surrogate quantity I(ρ,ρ') = Tr[ρρ']/sqrt(Tr[ρ^2]Tr[ρ'^2]) instead of the genuine Bures metric; the region where a nontrivial Wick contraction dominates is compared with the holographic entanglement wedge, including the connected/disconnected transition. A free scalar CFT is analyzed as a contrast and is argued to show no sharp wedge structure. The broad conceptual claim is that entanglement-wedge geometry can be derived from CFT distinguishability data alone, without assuming the bulk metric.","tokens_in":11496,"tokens_out":15241,"duration_ms":160835,"significance":"If the derivation were made rigorous, the paper would offer a genuinely new route to the emergence of entanglement-wedge geometry from CFT data, and it would provide a sharp, falsifiable criterion distinguishing holographic CFTs from free CFTs. The comparison with free scalars is instructive, and the paper is honest that the double-interval computation uses an alternative to the Bures metric. However, the load-bearing fidelity calculation in Sec. 3 has a serious gap that must be repaired before the central claim is established; as it stands, the main result is not derived by the equations shown.","major_comments":[{"comment":"At the claimed analytic-continuation point n=m=1/2, the replica parameter is k=(2m+1)n=1. Substituting k=1 into Eq. (17) makes the conformal prefactors cancel the two-point function, giving A_{1/2,1/2}=1 identically, with no dependence on w'. The displayed expression A_{1/2,1/2}=|w-\\bar w|^{2h}|w'-\\bar w'|^{2h}|w'-\\bar w|^{-4h} therefore does not follow from Eq. (17). Moreover, the two Wick contractions compared in Eq. (18) coincide when k=1, so the distinction between the 'inside-wedge' and 'outside-wedge' regimes is not defined in this formula. Consequently Eq. (19) and the central claim that the Bures metric equals (h/τ^2)(dx^2+dτ^2) inside the wedge are not derived as written. Please specify a well-defined analytic continuation that keeps the w'-dependent insertions, or provide a direct computation of the fidelity at n=m=1/2.","section":"Sec. 3, Eqs. (16)-(19)"},{"comment":"The insertion points assigned in Eq. (17), namely z_{2s+1}=e^{2πi s/k}z_1 and z_{2s+2}=e^{2πi s/k}z_2, are all expressed in terms of the unprimed coordinate w only; the points belonging to ρ' (which should depend on w') are never written down. Even for k=2 this would give z_3=-z_1, whereas the Section 2 calculation of Tr[ρρ'] has z_3=-z' with z' depending on w'. Without an explicit assignment of the w'-dependent points, the replica representation cannot encode the distinguishability between ρ_A(w) and ρ_A(w'), which is the very object needed for the Bures metric.","section":"Sec. 3, definitions after Eq. (17)"},{"comment":"The approximation of all multi-point correlators by generalized free field Wick contractions is load-bearing for both the I(ρ,ρ') wedge boundary and the claimed Bures metric. The citation to Ref. [22] supports generalized free fields in a large-c limit, but the regime used here involves arbitrary excitation positions and operator weight h with 1≪h≪c; the paper does not analyze competing conformal blocks or 1/c corrections in this kinematics. If subleading contributions are not negligible, the sharp wedge boundary and the vanishing of the metric outside the wedge would be modified. This may be a standard approximation in the holographic CFT literature, but its validity for the specific 2k-point functions and kinematics used here should be justified.","section":"Secs. 2 and 3, Eqs. (12) and (18)"}],"minor_comments":[{"comment":"The closing paragraph of Sec. 4 states that computing the genuine Bures metric for the double-interval case is 'very complicated' and that obtaining the expected metric (7) 'might not be surprising'; this is an admission that the double-interval Bures claim is not established and should be labeled as a conjecture rather than presented as a consequence.","section":"Sec. 4, final paragraph"},{"comment":"The abstract's phrase 'up to a very small error' for the double-interval wedge is not quantified; the deviation in Fig. 5 should be defined precisely, for example through a distance between the two boundary curves, so that the claimed few-percent accuracy can be checked.","section":"Abstract and Sec. 4"},{"comment":"The free-scalar Bures metric in Eq. (22) is presented without derivation; since this is the only case where the Bures metric is computed without the problematic replica collapse, a derivation or a precise reference for the direct fidelity calculation would substantially help the reader.","section":"Sec. 3, Eq. (22)"},{"comment":"There are typographical errors, including 'furture' in Sec. 5 and 'intstructive' in Sec. 3; these should be corrected in revision.","section":"General"}],"recommendation":"major_revision","confidential_remarks":"The stress-test concern is confirmed by direct substitution: at n=m=1/2 the replica parameter k equals 1, and Eq. (17) yields A_{1/2,1/2}=1 with no w' dependence. This is a load-bearing gap in the central single-interval Bures-metric derivation. The paper's conceptual idea is interesting and the I(ρ,ρ') analysis provides partial evidence, but the main result needs either a corrected analytic continuation or a reframing of the central claim."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: the single-interval I(ρ,ρ') computation is a genuine contribution, and the double-interval phase transition is intriguing. But the paper's flagship Bures metric result, Eq. (19), is not derived as written. The stress-test note lands. At the fidelity point n=m=1/2, k=(2m+1)n=1, and Eq. (17) collapses to A=1: the conformal prefactors cancel the two-point function, no w' dependence survives, and the two competing Wick contractions become the same pair. The w' dependence in Eq. (19) cannot come from that formula. The analytic continuation from integer k needs to be spelled out; as it stands, the derivation is unsupported.\n\nWhat is actually new and good: using the Bures metric of reduced density matrices as a wedge diagnostic for locally excited states is a fresh idea. The single-interval I(ρ,ρ') analysis is coherent under the stated large-c, generalized-free-field, and large-h assumptions, and it gives a sharp wedge boundary in the holographic case. The free scalar CFT contrast, where no sharp wedge structure appears, strengthens the claim that the effect is holographic. The double-interval analysis is honest about using the surrogate I(ρ,ρ') instead of the genuine Bures metric, and the connected/disconnected phase transition comes out at the right place within a few percent. The citation pattern looks fine; the reliance on [22] for generalized free fields is standard, though not independently justified for the specific operator dimensions used here.\n\nThe soft spots are the analytic continuation at k=1, which is load-bearing, and the generalized free field approximation for the 2k-point functions. The latter is a standard assumption in this literature and may be acceptable, but the former is not. The double-interval approximation is explicitly acknowledged by the authors, so that is only a minor weakness.\n\nThis paper deserves a serious referee: the idea is important, the I-based wedge result is a real step, and the Bures metric gap is addressable. As is, I would not accept it without a fix to the n=m=1/2 continuation. If the authors can repair that, the paper becomes solid. I would send it to peer review with a clear request to address the k=1 issue.","headline":"The wedge-from-I result is real and worth a look, but the advertised Bures metric derivation has a k=1 collapse and needs repair.","tokens_in":11995,"tokens_out":3436,"would_cite":false,"duration_ms":37688,"reading_group":"maybe","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The Bures metric of reduced density matrices in a holographic CFT reproduces the AdS entanglement wedge geometry from boundary data alone.","keywords":["entanglement wedge","Bures metric","information metric","holographic CFT","locally excited states","AdS/CFT correspondence","generalized free fields","reduced density matrix"],"falsifier":"Compute $A_{n,m}$ for a concrete large-central-charge CFT beyond the Wick contraction, including subleading conformal blocks or the first $1/c$ corrections, and continue to $n=m=1/2$; the central claim collapses if $dD_B^2$ fails to vanish identically outside the wedge or fails to equal $\\frac{h}{\\tau^2}(dx^2+d\\tau^2)$ inside it.","tokens_in":11068,"feed_emoji":"📐","tokens_out":7844,"duration_ms":75165,"temperature":0.7,"pith_summary":"This paper claims that the geometry of an entanglement wedge in AdS/CFT can be derived directly from conformal field theory data, without first assuming a bulk metric. For a locally excited state in a two-dimensional holographic CFT, the Bures information metric of the reduced density matrix on an interval is shown to coincide with the vacuum pure-state metric and with the induced anti-de Sitter metric on a time slice whenever the excitation lies inside the entanglement wedge, and to vanish identically outside it. The same computation in a free massless scalar CFT shows no sharp wedge, so the effect appears to be special to holographic CFTs. For a subsystem made of two disjoint intervals, a closely related distinguishability quantity reproduces the expected connected and disconnected entanglement wedges, including the phase transition, within a few percent. If correct, this provides a purely boundary route to emergent bulk geometry.","feed_headline":"Bures metric redraws AdS entanglement wedges","feed_subtitle":"In a 2d holographic CFT, this distance measure reproduces the bulk time-slice metric inside the wedge and vanishes outside it.","key_machinery":"The load-bearing object is the Bures distance $D_B(\\rho,\\rho')^2=2(1-\\operatorname{Tr}[\\sqrt{\\sqrt{\\rho}\\,\\rho'\\sqrt{\\rho}}])$ and its replica evaluation through $A_{n,m}=\\operatorname{Tr}[(\\rho^m\\rho'\\rho^m)^n]$, analytically continued to $n=m=1/2$. In holographic CFTs the multi-point functions are evaluated by generalized free-field Wick contractions: the trivial contraction makes the two reduced states indistinguishable, while the nontrivial contraction dominates precisely inside the entanglement wedge and reproduces the pure-state metric. Conformal maps---$z^2=w/(w-L)$ for the single interval, and an elliptic map onto a torus for two intervals---convert the two density matrices into a single correlation function whose dominant contraction selects the wedge boundary. The sharpness of the boundary comes from the $h\\gg1$ limit, and the free scalar CFT fails because its correlation functions lack this dominance structure.","core_discovery":"The central claim is that state distinguishability inside the boundary theory encodes the shape of the bulk. In a two-dimensional holographic CFT, the Bures metric $dD_B^2$ computed from the reduced density matrix $\\rho_A(w,\\bar w)$ of a locally excited primary operator equals $\\frac{h}{\\tau^2}(dx^2+d\\tau^2)$ when the excitation lies inside the entanglement wedge, and vanishes when it lies outside; the paper obtains the same structure for the circle and finite-temperature backgrounds, with the metric factors $1/\\sinh^2\\tau$ and $\\sin^{-2}(2\\pi T\\tau)$ respectively. For two disjoint intervals, the region favored by the nontrivial Wick contraction in a four-point function approximates the true entanglement wedge to within a few percent, and switches from connected to disconnected at the expected phase-transition point. The paper also shows that a free scalar CFT does not produce any sharp wedge, indicating that the derivation relies on the holographic, large-central-charge character of the CFT.","pith_inferences":["A consequence the authors leave implicit: the Bures metric gives an operational, measurement-based definition of bulk locality --- points in the boundary parameter space are geometrically separated exactly to the extent that their reduced states can be distinguished.","One testable extension is to track the first $1/c$ correction: if it moves the wedge boundary or produces a nonvanishing metric outside the wedge, the present sharp wedge picture is only approximate, and the exact wedge boundary would be defined by the genuine Bures metric rather than by $I(\\rho,\\rho')$.","The few-percent discrepancy in the two-interval case suggests a precise computation of the genuine Bures metric there, which the paper hints should yield the pure-state metric; if confirmed, the discrepancy quantifies how far $I(\\rho,\\rho')$ is from the true fidelity."],"forward_implications":["If the derivation survives, the entanglement wedge geometry can be obtained from boundary correlation functions alone, without assuming the bulk metric.","The wedge boundary becomes a sharp transition in state distinguishability: inside the wedge the Bures metric equals the pure-state metric, outside it vanishes.","The method extends to circle and finite-temperature backgrounds, recovering the corresponding time-slice metrics of the dual spacetime.","In the two-interval case the connected/disconnected phase transition is captured by the torus calculation, with only a few-percent discrepancy relative to the true wedge.","Free scalar CFTs show no sharp wedge, so a sharp wedge in this construction is a diagnostic of holographic dynamics."],"supporting_citations":[{"why":"Supplies the generalized free-field approximation for holographic CFT correlation functions used in Eq. (12).","marker":"[22]"},{"why":"Defines the locally excited state reduced density matrix and the replica setup for its entanglement entropy.","marker":"[14]"},{"why":"Already noted that the pure-state information metric is proportional to the AdS time-slice metric, the starting point extended here to reduced density matrices.","marker":"[17]"},{"why":"Introduced the quantity $I(\\rho,\\rho')$ used throughout as an estimate of state distinguishability.","marker":"[18]"},{"why":"Defines holographic entanglement entropy, whose extremal surface delimits the expected entanglement wedge.","marker":"[5]"},{"why":"Supplies the elliptic conformal map used to analyze the two-interval subsystem in Section 4.","marker":"[25]"},{"why":"Provides the black-hole phase transition that the torus computation maps onto the connected/disconnected wedge transition.","marker":"[26]"}],"fun_headline_variants":["Bures metric carves entanglement wedges in CFT","Information metric reveals AdS entanglement wedge","Bures metric reproduces holographic wedge geometry","State distinguishability encodes bulk entanglement wedges","Bures metric gives sharp wedges only in holographic CFT"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that in a large-central-charge holographic CFT, multi-point correlation functions are accurately captured by generalized free-field Wick contractions, and that the replica expression $A_{n,m}$ can be analytically continued to $n=m=1/2$; if either fails, the sharp wedge boundary and the vanishing of the Bures metric outside the wedge would be disturbed.","fun_headline_variants_meta":{"raw":{"variants":["Bures metric carves entanglement wedges in CFT","Information metric reveals AdS entanglement wedge","Bures metric reproduces holographic wedge geometry","State distinguishability encodes bulk entanglement wedges","Bures metric gives sharp wedges only in holographic CFT"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000915,"raw_usage":{"total_tokens":3908,"prompt_tokens":901,"completion_tokens":3007,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":517,"completion_tokens_details":{"reasoning_tokens":2933}},"tokens_in":517,"tokens_out":3007,"duration_ms":22299,"temperature":1.0,"reasoning_tokens":2933,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T10:57:42.009357+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute $A_{n,m}$ for a concrete large-central-charge CFT beyond the Wick contraction, including subleading conformal blocks or the first $1/c$ corrections, and continue to $n=m=1/2$; the central claim collapses if $dD_B^2$ fails to vanish identically outside the wedge or fails to equal $\\frac{h}{\\tau^2}(dx^2+d\\tau^2)$ inside it.","supporting_citations":[{"cited_title":"It from Qubit","cited_arxiv_id":null,"evidence_quote":"Defines holographic entanglement entropy, whose extremal surface delimits the expected entanglement wedge."}],"review_version":1}