{"id":"5ae97d58-559f-4d34-8ba8-21c281679610","arxiv_id":"2508.13553","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":6.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"The paper presents four bounds for quantum locally recoverable codes and constructs infinite families of optimal codes using Hermitian curves and t-designs.","lead":"This paper studies quantum locally recoverable codes, which are error-correcting codes that fix errors using only a few nearby quantum bits. It proposes four new bounds and constructs new families of codes that meet them, which could improve quantum data storage.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Optimality rests on unverified bounds and parameter claims; abstract-only review prevents technical scrutiny.","rationale":"The reader's weakest_assumption correctly identifies that the optimality of the constructed qLRCs rests on the four bounds being valid and tight and on the Hermitian construction achieving the claimed parameters. I agree that this assumption is unverified from the abstract alone. However, the reader's rationale focuses primarily on the lack of derivations and parameter sets, which is an evidentiary limitation rather than a specific technical concern. My stress-test narrows this to the single most load-bearing sub-assumption: the correctness and tightness of the four bounds. If any of these bounds is flawed or inapplicable, the optimality result fails. I have no reason to suspect a specific error from the abstract alone, so I do not recommend changing the verdict. A concrete verification step would settle the concern once the full text is available. Since the reader already set UNVERDICTED with low confidence, my assessment leaves the verdict unchanged.","tokens_in":669,"tokens_out":2537,"duration_ms":28152,"concrete_test":"Retrieve the full manuscript and, for at least one of the three proposed families, independently derive the qLRC parameters ([n,k,d;r]_q) from the Hermitian construction. Then compare against all four stated bounds: verify that the parameters satisfy the bound with equality, and confirm the locality r matches the code's availability/repair properties. Also re-check the Hermitian dual-containing condition for the underlying cLRC by explicitly computing the Hermitian inner product of the code with its dual. If any bound is not attained or the dual-containment fails, the optimality claim for that family collapses.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central claim is the construction of three explicit families of optimal qLRCs. For this claim to hold, several conditions must be true: (1) the four proposed qLRC bounds are correct and tight in the relevant parameter regimes; (2) the constructed NMDS codes indeed support t-designs for t=2,3; (3) the Hermitian construction yields dual-containing cLRCs with the stated locality and distance parameters; and (4) the resulting qLRC parameters satisfy the equality conditions of the bounds. The abstract provides none of these derivations, parameter tables, or proof sketches. Consequently, the optimality assertion is entirely unsupported by the available material. This is not a discovered technical error but an epistemic gap: the most load-bearing assumption is the validity and tightness of the four bounds, since even a single incorrect or inapplicable bound would invalidate the optimality claims. The abstract also does not specify the alphabet size, block length regimes, or locality parameters, making it impossible to check whether the claimed optimality is even non-vacuous. Without access to the full manuscript, no deeper flaw can be identified, but the evidence provided is insufficient to accept the central claim.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper claims to introduce and prove four bounds for quantum locally recoverable codes (qLRCs), to compare their asymptotic behavior, to construct new infinite families of NMDS codes supporting t-designs for t=2,3, to apply these codes to obtain Hermitian dual-containing classical LRCs, and to derive three explicit families of optimal qLRCs. It also states that this solves an open problem posed by Luo et al. The abstract does not include the statements of the bounds, the parameters of the constructed codes, the verification of dual containment, or the equality conditions under which optimality is certified.","tokens_in":942,"tokens_out":1824,"duration_ms":21351,"significance":"If the claims are correct, the paper would be a substantial contribution to quantum coding theory: new bounds with asymptotic comparison, a systematic Hermitian construction producing dual-containing classical LRCs, and optimal qLRC families with more flexible parameters than CSS-based constructions. The construction of NMDS codes supporting t-designs is independently interesting. However, the significance can only be provisionally assessed from the abstract; the central optimality claims are not independently checkable without the full derivations and parameter tables.","major_comments":[{"comment":"The four qLRC bounds are stated only by name ('we present four bounds') with no equations, no parameter regimes, and no hypotheses on alphabet size, locality, or block length. Correctness and tightness of these bounds are load-bearing for the optimality claims. The abstract does not even specify whether the bounds are the same as or distinct from the prior cLRC bounds referenced later. The full manuscript must include precise theorem statements and proofs; without them the central claim cannot be evaluated.","section":"Abstract"},{"comment":"The claim of 'three explicit families of optimal qLRCs' is not accompanied by any parameter values (length, dimension, distance, locality, alphabet size) or by the equality conditions to the bounds. Optimality requires both that the bounds are valid and that the constructions attain them in the stated regimes. As written, this is an assertion rather than a verifiable result. A parameter table and an explicit check of the equality conditions for each family are needed.","section":"Abstract"},{"comment":"The phrase 'Hermitian dual-containing classical LRCs' is used as a step in the construction, but the abstract does not show how the NMDS/t-design codes guarantee dual containment, nor how locality and distance of the resulting cLRCs are computed. Since the qLRC construction depends on these properties, an omitted proof or even an omitted definition of the Hermitian construction would leave a load-bearing gap. The full text must provide the explicit construction and the verification of the cLRC parameters.","section":"Abstract"}],"minor_comments":[{"comment":"The abstract does not fix notation for qLRC parameters (e.g., [[n,k,d;r]]_q or similar). Adding standard notation would improve clarity and allow readers to parse the optimality claims.","section":"Abstract"},{"comment":"The notion of t-designs is used without definition or reference. Since the NMDS-code construction is a stated contribution, a brief definition or a pointer to the standard definition would help.","section":"Abstract"},{"comment":"The reference to Luo et al. is cited with full bibliographic data in the abstract, which is unusual; if the paper is intended for journal submission, the open problem should be stated explicitly rather than only cited.","section":"Abstract"}],"recommendation":"uncertain","confidential_remarks":"The manuscript as available to me is abstract-only, with no derivations, theorem statements, or parameter tables. I cannot verify the correctness or tightness of the four bounds, the dual-containment step, or the claimed optimality of the three qLRC families. This is not a discovered technical flaw, but a fundamental lack of evidence. I recommend requesting the full manuscript before assigning a substantive verdict. If the full text is in hand, the key points to check are the equality conditions in the optimality claims and the validity of the Hermitian construction's locality/distance parameters."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper likely makes a real contribution to quantum locally recoverable codes: it settles an open problem by Luo et al., gives four bounds for qLRCs, constructs new infinite families of NMDS codes supporting 2- and 3-designs, and then uses those to get Hermitian dual-containing classical LRCs and three optimal qLRC families. That is a solid package for the coding theory audience, and the claimed flexibility in parameters is a genuine selling point.\n\nWhat I can judge from the abstract is the shape of the argument: the bounds, the NMDS-to-cLRC bridge, and the Hermitian construction are all standard tools in this area, and the authors seem to combine them in a way that is new. The connection between t-designs and optimal qLRCs is not something I recall seeing done this way, so novelty seems credible.\n\nBut here is the honest limit: I have only the abstract. The four bounds could have hidden conditions; the NMDS codes might not deliver the promised locality/distances in the relevant regimes; and the optimality claims depend on the bounds being tight for the constructed parameters. None of that is checkable from the supplied text. The stress-test note is right that this is an epistemic gap rather than a discovered flaw. I would not accuse the authors of anything beyond the usual abstract-level compression.\n\nThe citation pattern looks fine: the open problem is attributed to Luo et al., and the construction methods build on known results. No red flags there.\n\nWho benefits? Researchers in quantum storage coding and classical LRCs. If the full text delivers what the abstract promises, this is a useful paper that deserves refereeing. I would not desk reject it, but I would send it to reviewers with expertise in both quantum CSS constructions and finite geometry, and ask them specifically to verify the four bounds and the tightness conditions.\n\nRecommendation: accept for peer review. My own verdict would depend on the full proofs, but the paper is serious enough to merit the time.","headline":"Abstract-only submission with plausible, meaningful claims: four qLRC bounds, NMDS codes supporting t-designs, and optimal qLRC families—but the central optimality claims rest on proofs and parameter tables we cannot see.","tokens_in":1322,"tokens_out":1009,"would_cite":false,"duration_ms":13250,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["94B65","81P70"],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper establishes four bounds for quantum locally recoverable codes and constructs three explicit families of optimal codes meeting them, using the Hermitian construction and classical codes that support 2- and 3-designs.","keywords":["quantum locally recoverable codes","Hermitian construction","NMDS codes","t-designs","optimal quantum codes","coding bounds","locality","quantum error correction"],"falsifier":"Take the smallest nontrivial code from any of the three families and compute its exact distance, locality, and dual-containment property; if a code violates its claimed bound or the Hermitian dual-containment fails, the central claim collapses. Alternatively, exhibit any qLRC whose parameters contradict one of the four bounds.","tokens_in":644,"feed_emoji":"⚛️","tokens_out":5575,"duration_ms":49939,"temperature":0.7,"pith_summary":"Quantum locally recoverable codes (qLRCs) aim to protect quantum information in a large storage system while allowing a lost qubit to be rebuilt from a small set of survivors. This paper tries to establish the limits of such codes: it presents four bounds on their parameters and compares the bounds asymptotically. It then constructs classical locally recoverable codes that carry Hermitian duality and convert, via the Hermitian construction, into quantum codes; the intermediate classical codes are new infinite families of near-MDS (NMDS) codes supporting 2- and 3-designs. The result is three explicit infinite families of optimal qLRCs with flexible parameters, which would enlarge the available designs for large-scale quantum storage if the bounds and parameters hold.","feed_headline":"Three new optimal quantum LRC families from the Hermitian construction","feed_subtitle":"Four new bounds, plus classical codes carrying 2- and 3-designs, give optimal quantum codes.","key_machinery":"The Hermitian construction is the conversion that turns a classical code with Hermitian dual-containment into a quantum code; the engine is a supply of NMDS codes with flexible dimensions that support $t$-designs for $t\\in\\{2,3\\}$. These classical codes simultaneously give the locality structure and the duality needed for the quantum conversion, while the four new bounds provide the target against which optimality is measured.","core_discovery":"The central claim is that the parameter region for qLRCs is sharply constrained by four bounds, and that these bounds are simultaneously achievable. The authors build new infinite families of NMDS codes whose dimensions can be freely chosen and which support designs of strength 2 and 3. These classical codes are used to obtain Hermitian dual-containing classical LRCs, and the Hermitian construction turns them into qLRCs. Three explicit families of qLRCs are shown to be optimal, meaning they meet the relevant bound; this resolves an open problem in the recent literature. As a by-product, the underlying cLRCs are themselves optimal with respect to four different cLRC bounds.","pith_inferences":["If the four bounds hold in their full generality, existing qLRC constructions in the literature should be re-checked against them; some may be suboptimal in regimes not covered by the paper's examples.","The fact that the classical ingredients support $2$- and $3$-designs suggests a combinatorial structure that could be exploited for erasure-recovery scheduling or for constructing quantum codes with transversal gates, but the paper does not develop this.","A natural extension would be to apply the same NMDS-plus-$t$-design recipe to other duality-preserving constructions (for example, CSS with varied field sizes) to see whether optimal qLRC families exist beyond the three reported here.","The asymptotic comparison of the four bounds likely indicates which bound is dominant in different blocklength regimes, which could guide code designers before the full parameter tables are computed."],"forward_implications":["Three explicit infinite families of qLRCs achieve optimal parameters under the new bounds, so the bounds are not just theoretical.","The new qLRC families allow more flexible dimensions than earlier CSS-based constructions, widening the choice of parameters for quantum storage codes.","The classical LRCs produced in the process are optimal with respect to four distinct bounds, so the construction has independent classical value.","The open problem about the existence of optimal qLRCs from the Hermitian construction is resolved affirmatively."],"supporting_citations":[],"fun_headline_variants":["Hermitian construction yields three optimal quantum LRC families","Quantum LRC bounds met by new Hermitian-based codes with t-designs","Flexible optimal qLRCs from Hermitian dual-containing NMDS codes","t-designs unlock three optimal quantum locally recoverable code families","Three optimal qLRC families from Hermitian construction solve open problem"],"cache_read_input_tokens":2816,"weakest_assumption_plain":"The whole construction is optimal only if the four proposed bounds are valid and tight and if the Hermitian construction really delivers codes with the claimed distance and locality parameters.","fun_headline_variants_meta":{"raw":{"variants":["Hermitian construction yields three optimal quantum LRC families","Quantum LRC bounds met by new Hermitian-based codes with t-designs","Flexible optimal qLRCs from Hermitian dual-containing NMDS codes","t-designs unlock three optimal quantum locally recoverable code families","Three optimal qLRC families from Hermitian construction solve open problem"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000209,"raw_usage":{"total_tokens":1243,"prompt_tokens":740,"completion_tokens":503,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":484,"completion_tokens_details":{"reasoning_tokens":412}},"tokens_in":484,"tokens_out":503,"duration_ms":5712,"temperature":1.0,"reasoning_tokens":412,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-05T18:56:30.124732+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take the smallest nontrivial code from any of the three families and compute its exact distance, locality, and dual-containment property; if a code violates its claimed bound or the Hermitian dual-containment fails, the central claim collapses. Alternatively, exhibit any qLRC whose parameters contradict one of the four bounds.","supporting_citations":[],"review_version":1}