{"id":"7a0e1daf-67c7-486b-a53e-6038574e3925","arxiv_id":"2508.05484","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":5.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"A framework certifies high-dimensional entanglement in bipartite pure states under LOCC, and the sample cost of certifying a fixed degree drops as the local dimension grows.","lead":"This paper proposes a general framework for certifying high-dimensional entanglement in two-party quantum systems using restricted operations like local measurements with classical communication. It claims that certifying a fixed level of entanglement becomes cheaper as the quantum systems grow larger, an unusual and practically useful property.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The certificate and proof behind the monotone sample-cost claim are unreadable in the delivered file; a fixed-Schmidt-rank reading may conflict with embedding invariance.","rationale":"I read the abstract in good faith: the claimed result is striking and potentially valuable, but the full text as delivered is unreadable and even appears to be a different paper (math.AP 2508.05478). The reader's UNVERDICTED judgment is therefore the correct one. My main concern is the same unverifiability: the central theorem relies on an unstated certificate, and no proof can be inspected. I add a sharper technical worry: if the certificate is Schmidt rank at fixed rank r, the monotone-in-d claim seems to violate embedding invariance for LOCC protocols, because padding a state with zero amplitudes does not change any local-measurement statistics. This is not a proof of error, but it identifies a concrete condition under which the claim would fail. I do not change the reader's verdict because the missing text prevents a decisive technical check; UNVERDICTED remains appropriate. I do not attribute any intent to the authors; the issue is the state of the delivered manuscript.","tokens_in":17990,"tokens_out":6680,"duration_ms":80747,"concrete_test":"Obtain a clean copy of arXiv:2508.05484 (TeX source or PDF) and locate the definition of 'degree of HDE' and the theorem asserting monotone decreasing sample cost. Then perform an embedding-invariance test: take a Schmidt-rank-r state in C^r⊗C^r, embed it into C^d⊗C^d for d>r by padding with zeros, and apply the paper's proposed certification strategy. If the claimed sample cost depends on d for fixed r, the theorem conflicts with the fact that all local-measurement statistics are unchanged by embedding. If the theorem assumes full Schmidt rank d, then the abstract's phrase 'given degree' must be reinterpreted.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The delivered full text is not assessable: it is mojibake and contains a header for a different arXiv ID (2508.05478v1 [math.AP]). The abstract therefore cannot be checked against any definition or proof. The central claim—that sample cost for certifying a given degree of HDE decreases monotonically with local dimension—depends on an unnamed certified quantity. If that quantity is the Schmidt rank r, and the local dimension d is merely the embedding dimension (d > r), then any LOCC protocol's outcome statistics on a Schmidt-rank-r state embedded in C^d⊗C^d are identical to its statistics on the same state in C^r⊗C^r, because the extra dimensions are never populated. Sample cost cannot strictly decrease with d for such a fixed state. The monotonicity claim therefore needs either a different definition of 'degree' (e.g., full Schmidt rank or a dimension-dependent measure) or an additional assumption that excludes embedded states; otherwise it is internally suspect. The reader's secondary concern about purity is not a flaw for a pure-state claim, but the purity assumption should be stated as a scope limit. No machine-checked proof or reproducible code is supplied. The concern is not about author intent; it is that the paper as delivered cannot be verified.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper (arXiv:2508.05484) claims a general framework for certifying high-dimensional entanglement (HDE) in bipartite pure states under restricted operations such as LOCC. The central advertised results are: (i) efficient certification with a sample cost that decreases monotonically with the local dimensions for a given degree of HDE, and (ii) an optimal entanglement-certification strategy for two-qubit pure states based on separable operations, which is LOCC-realizable when the target state is sufficiently entangled. The abstract is readable, but the delivered full text is corrupted mojibake and includes a header for a different arXiv ID (2508.05478v1 [math.AP]), making it impossible to inspect definitions, theorems, or proofs.","tokens_in":18165,"tokens_out":1799,"duration_ms":19122,"significance":"If the claims are correct, the main result is significant and counterintuitive: certifying a fixed degree of high-dimensional entanglement would become statistically cheaper as the local Hilbert-space dimension grows, and the proposed framework would unify restricted-operation certification across many resources. The two-qubit optimality claim is also notable because separable operations are generally strictly more powerful than LOCC. However, because the manuscript cannot be read, I cannot assess whether these claims are supported. The paper contains no machine-checked proofs or reproducible code; the claimed derivations are not inspectable in the delivered file. The significance therefore remains conditional on a readable and internally consistent manuscript.","major_comments":[{"comment":"The delivered full text is unreadable mojibake. No equation, theorem, proof, or figure can be checked. The abstract cannot be verified against any underlying definition. This is not a peripheral issue: the paper's central claims are precise sample-cost statements, and none of the supporting derivations is accessible. The authors must provide a correctly encoded, readable manuscript before the claims can be evaluated.","section":"Full text (entire manuscript)"},{"comment":"The abstract states that the sample cost for certifying a given degree of HDE decreases monotonically with the local dimensions, but it never defines the certified quantity. If 'degree of HDE' means Schmidt rank r and the local dimension d is merely the embedding dimension (d > r), the claim appears internally problematic: a Schmidt-rank-r state embedded in C^d⊗C^d has the same LOCC statistics as the same state in C^r⊗C^r, since the extra dimensions are unpopulated. Sample cost therefore cannot strictly depend on d in the way suggested unless the certified quantity is dimension-dependent or the statement explicitly excludes embedded states. The authors should state the definition of 'degree' and the exact dependence of the sample cost on r and d.","section":"Abstract, monotone sample-cost claim"},{"comment":"The two-qubit optimality claim is stated without a comparison class or error-metric specification. It is not clear whether optimality is in sample complexity, success probability, or both, and whether the separable-operations benchmark is for one-shot or multi-copy certification. These details are needed to assess the LOCC-realizability threshold, especially because the abstract says LOCC realizability holds only when the target state has 'sufficiently high entanglement'—this threshold is not quantified.","section":"Abstract, optimal two-qubit strategy"}],"minor_comments":[{"comment":"The full text carries the arXiv identifier 2508.05478v1 [math.AP], which is inconsistent with the claimed arXiv number 2508.05484 (quant-ph). This suggests a file-assembly error that should be corrected in resubmission.","section":"Header"},{"comment":"The text encoding is corrupted throughout; mathematical symbols and Latin letters are replaced by mojibake. A clean PDF must be produced.","section":"Presentation"},{"comment":"The abstract uses 'HDE' and 'given degree of HDE' without formal definition. Please include a precise definition of the certified resource and the sample-cost function in the introduction if the full version is revised.","section":"Abstract"}],"recommendation":"uncertain","confidential_remarks":"The submitted file is unreadable due to encoding corruption, so I cannot reach a soundness verdict. The embedding-invariance concern I raise is not a hidden agenda; it follows directly from the abstract's ambiguity. The editor may wish to ask the authors for a clean, machine-readable PDF before sending the paper to any further referee. If the cleaned manuscript resolves the definitional issue, the claims may be significant, but the current version cannot be assessed."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe bottom line: I can only assess the abstract. The delivered full text is corrupted mojibake (it even contains a header for a different arXiv ID), so no equation, proof, or definition is inspectable. That makes this a paper to return to the authors for a clean version rather than to referee as-is.\n\nWhat the abstract promises is genuinely interesting. A simple and general framework for certifying high-dimensional entanglement in bipartite pure states under LOCC-type restrictions, with sample cost that falls monotonically as local dimension grows, plus an optimal two-qubit separable-operations strategy that is LOCC-realizable at sufficiently high entanglement—these are concrete, experiment-relevant claims. If the derivations hold, it is a solid subfield advance. Nothing in the abstract suggests hidden fitting or circular benchmarks, and the pure-state scope is honestly implicit.\n\nBut there is a load-bearing subtlety that the stress-test note gets right. \"Degree of HDE\" is never named in the abstract. If it means Schmidt rank r, then a rank-r state embedded in C^d⊗C^d with d>r produces exactly the same statistics under any LOCC protocol as the same state in C^r⊗C^r, because the extra dimensions are never populated. Sample cost cannot strictly decrease with d for such fixed states. So either \"degree\" is defined through something else, like full Schmidt rank or a dimension-dependent entanglement measure, or the claim needs an extra assumption excluding embedded states. The abstract as written does not resolve this. It may be resolved in the proofs—I simply cannot tell from the delivered file.\n\nSecondary points: purity is a scope limit, not a flaw, for a pure-state certification paper, but it should be stated as such. No code or machine-checked proofs are supplied, which is fine for a theory paper, but it means verification rests entirely on the text.\n\nMy verdict is unverdictable, not negative. The right move is to ask the authors for a clean PDF and then send it to a serious referee. The monotone sample-cost claim is surprising enough to deserve scrutiny, and the two-qubit optimality result is worth checking. I would not desk-reject the science. I would not cite it from the abstract alone.\n\nRecommendation: obtain a readable version, then peer review.","headline":"Striking abstract, unreadable text: the bottleneck is the file, not the science—yet the monotone-in-dimension claim needs a careful check before it is believed.","tokens_in":18706,"tokens_out":2111,"would_cite":false,"duration_ms":21547,"reading_group":"maybe","serious_thinker":"unclear","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"High-dimensional entanglement in any bipartite pure state can be certified efficiently under local operations and classical communication, and the sample cost for a fixed degree of entanglement falls monotonically as local dimension grows.","keywords":["high-dimensional entanglement","entanglement certification","LOCC","Schmidt rank","sample complexity","two-qubit states","separable operations","quantum resource certification"],"falsifier":"Use the proposed LOCC protocol to certify a fixed Schmidt rank $r$ on states $|\\psi_d\\rangle = \\sum_{i=1}^r \\sqrt{\\lambda_i}\\,|i_A i_B\\rangle$ embedded in $d\\times d$ dimensions for $d=2,3,4,\\dots$ while holding the Schmidt coefficients $\\lambda_i$ fixed; if the number of copies required does not decrease monotonically in $d$, the central claim fails. For the two-qubit result, check whether the constructed optimal separable measurement for a target state above the claimed entanglement threshold can be decomposed into LOCC; a state above threshold whose optimal strategy provably requires a non-","tokens_in":17793,"feed_emoji":"⚛️","tokens_out":9336,"duration_ms":89934,"temperature":0.7,"pith_summary":"The paper sets out to make high-dimensional entanglement certification practical for bipartite pure states when the experimenter is limited to local operations and classical communication (LOCC). It claims a simple, general framework that certifies a given degree of high-dimensional entanglement in every such state, and shows that the number of samples needed for a fixed degree of entanglement decreases as the local dimension grows. If the claim holds, larger Hilbert spaces make certifying entanglement cheaper rather than harder. The paper also constructs an optimal two-qubit certification strategy using separable operations, and shows this strategy is realizable by LOCC when the target state is highly entangled. The same core concept is intended to extend to certifying other quantum resources under restricted operations.","feed_headline":"Certifying entanglement gets cheaper as dimension grows","feed_subtitle":"With local measurements and classical communication, a fixed degree of entanglement needs fewer samples as dimensions grow.","key_machinery":"The central object is a certificate for high-dimensional entanglement that is estimable under restricted operations such as LOCC. The certificate is designed around the Schmidt structure of the pure target state, so that its outcome statistics reveal the entanglement dimension without global measurements. In the two-qubit setting the machinery becomes an optimal separable-operation strategy, together with a LOCC implementation for sufficiently entangled target states. The framework's versatility claim rests on this certificate concept being independent of the specific state family and of the choice of restricted operation set.","core_discovery":"The paper's central claim is that for every bipartite pure state, the degree of high-dimensional entanglement—its Schmidt rank, the number of nonzero coefficients in the Schmidt decomposition—can be certified under LOCC through a framework whose sample efficiency improves with local dimension. Fix a degree of entanglement and increase the local dimensions while keeping the target state pure; the copies required for certification decrease monotonically. In the two-qubit case, the paper identifies an optimal certification strategy within separable operations, with a LOCC realization whenever the target state has sufficiently high entanglement. The framework's core object is a certificate built","pith_inferences":["The monotone sample-cost decrease is framed for pure states; a likely consequence not shown in the paper is that the advantage weakens or disappears under noise, since mixed-state Schmidt rank is replaced by a more complicated entanglement dimension.","The same certificate logic could plausibly be exported to other resource theories with a discrete rank-like measure, such as Wigner negativity or non-Gaussianity, whenever the allowed operations are restricted.","A direct experimental test of the monotonicity would be to certify the same Schmidt rank in photonic orbital-angular-momentum or time-bin states of increasing dimension and compare copy counts."],"forward_implications":["High-dimensional entanglement in bipartite pure states can be certified using only local operations and classical communication, removing the need for global measurements in practical verification.","For a fixed degree of entanglement, certification becomes cheaper as the local dimension grows, so higher-dimensional systems are not inherently harder to verify.","The two-qubit result gives an optimal entanglement certification strategy under separable operations, with LOCC realizability for highly entangled targets.","Because the core certificate concept is general, the same approach can be adapted to certify other quantum resources under restricted operations.","The sample-cost monotonicity provides a concrete prediction for experiments: larger local dimensions should require fewer copies to certify the same Schmidt rank."],"supporting_citations":[],"fun_headline_variants":["Need fewer samples to certify entanglement in higher dimensions","Entanglement certification cost falls as dimension grows","Higher-dim entanglement needs fewer samples to certify","Sample cost drops as dimension rises for entanglement cert"],"cache_read_input_tokens":2816,"weakest_assumption_plain":"The load-bearing assumption is that the target state is exactly pure, so that a fixed degree of high-dimensional entanglement can be identified with a fixed Schmidt rank and probed by the paper's LOCC certificate; for mixed states, the claimed monotone sample-cost behavior is not established.","fun_headline_variants_meta":{"raw":{"variants":["Need fewer samples to certify entanglement in higher dimensions","Entanglement certification cost falls as dimension grows","Higher-dim entanglement needs fewer samples to certify","Sample cost drops as dimension rises for entanglement cert"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000469,"raw_usage":{"total_tokens":2119,"prompt_tokens":635,"completion_tokens":1484,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":379,"completion_tokens_details":{"reasoning_tokens":1427}},"tokens_in":379,"tokens_out":1484,"duration_ms":11254,"temperature":1.0,"reasoning_tokens":1427,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-05T23:18:02.973496+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Use the proposed LOCC protocol to certify a fixed Schmidt rank $r$ on states $|\\psi_d\\rangle = \\sum_{i=1}^r \\sqrt{\\lambda_i}\\,|i_A i_B\\rangle$ embedded in $d\\times d$ dimensions for $d=2,3,4,\\dots$ while holding the Schmidt coefficients $\\lambda_i$ fixed; if the number of copies required does not decrease monotonically in $d$, the central claim fails. For the two-qubit result, check whether the constructed optimal separable measurement for a target state above the claimed entanglement threshold can be decomposed into LOCC; a state above threshold whose optimal strategy provably requires a non-","supporting_citations":[],"review_version":1}