{"id":"c08d579e-5b56-411f-8c67-c0e169183e01","arxiv_id":"2602.15452","paper_version":2,"verdict":"REJECT","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"high","formal_verification":"none","parameter_count":2,"one_line_summary":"Three bipartite product states are globally antidistinguishable yet not LOCC antidistinguishable under the paper's restricted one-pass LOCC model, giving a claimed minimal example of exclusion-based nonlocality.","lead":"This paper asks whether quantum state exclusion can be impossible with local measurements and classical communication even when a single global measurement succeeds. It reports three-state and four-state examples of this effect for antidistinguishability, plus a tripartite version that fails across every bipartition.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Central claim only proven for a nonstandard one-pass LOCC model; Theorem 2's inference is invalid under adaptive LOCC, so the three-state separation may not hold for standard LOCC.","rationale":"The reader's weakest assumption is correct and it is the load-bearing gap. The paper's own examples (e.g., Eq. 10) show that local filtering can change the reduced ensemble enough to enable antidistinguishment even when the original reduced sets are not antidistinguishable; that is precisely the mechanism standard LOCC could exploit, so the restricted model cannot support the unqualified LOCC claim. Independent support is limited: no machine-checked proofs or code, and the SDP appendices give only truncated numeric POVMs, not verifiable certificates. However, the examples are concretely specified and the restricted-model results may be correct and interesting. The verdict should remain REJECT as written, with a path to acceptance by either re-scoped claims ('one-pass LOCC') or a full-LOCC proof.","tokens_in":14329,"tokens_out":7082,"duration_ms":68432,"concrete_test":"Take the three product states of Eq. (13) with d=2: |0⟩|0⟩, |0⟩(1/2|0⟩+√3/2|1⟩), (1/2|0⟩+√3/2|1⟩)⊗2. Run a numerical search over two-round adaptive LOCC protocols: Alice's first POVM, Bob's POVM conditioned on Alice's outcome, and Alice's second POVM conditioned on both. If any such protocol excludes one state at every final outcome, then the claimed LOCC nonlocality fails under standard adaptive LOCC. If no two-round protocol exists, expand to three rounds to test whether the indefinite-round LOCC class can succeed. This directly probes whether the one-pass restriction in Definition 6 is load-bearing.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Definition 6 defines LOCC as a single left-to-right pass (Alice, then Bob, ...) in which each round must eliminate at least one state. This is not the standard LOCC model, which allows adaptive multi-round local measurements and classical feedback, including inconclusive branches that can be rescued later. The negative results (Theorems 4–7, and the symmetry Theorem 2) are all proved in this restricted model. In particular, Theorem 2's proof only analyzes a specific protocol family: parties use POVMs whose first N−1 elements each eliminate a state and whose last element eliminates none; if all parties hit their last element, the final party 'must' antidistinguish all N states on their subsystem. But success in standard LOCC does not require the final reduced states to be antidistinguishable—earlier (or later) adaptive measurements by the same party can change the ensemble, and the proof assumes the last party can always finish if the set is globally antidistinguishable, which is exactly what is at issue. Thus the central example (Theorem 4, Eq. 13) only demonstrates failure in this one-pass model, not LOCC as conventionally understood.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies quantum state exclusion, in particular antidistinguishability and x-antidistinguishability, under global measurements versus LOCC. It introduces weak and strong notions of (x-)antidistinguishability, claims a starter-symmetry for LOCC antidistinguishability of product states, and reports a starter-asymmetry for 2-antidistinguishability. The central advertised result is a nonlocality-without-entanglement phenomenon in state exclusion: three bipartite product states that are globally antidistinguishable but not LOCC antidistinguishable, with three claimed to be the minimal number. Further results extend the separation to 2-antidistinguishability and to a tripartite example claimed to be genuinely nonlocal in the exclusion sense.","tokens_in":14522,"tokens_out":12360,"duration_ms":121709,"significance":"If established for standard LOCC, the main result would indeed be a conceptually interesting exclusion-based analogue of nonlocality without entanglement. The paper contains explicit constructions, uses independent known criteria for the global claims (CFS, PBR, Webb et al., Johnston et al.), and provides numerical SDP data in appendices. The problem is that the central negative claims are proved only for a restricted, nonstandard LOCC model; as a result the advertised phenomenon is not established for LOCC in its usual meaning. The paper also has a significant gap in the proof of the starter-asymmetry claim. Therefore the significance of the results depends on an unproven strengthening or on a substantial reframing of the claims.","major_comments":[{"comment":"Definition 6 defines LOCC as a one-pass sequential protocol in which each party measures once in a fixed order and each round must eliminate at least one state. This is not the standard LOCC model, which allows adaptive multi-round measurements, classical feedback, and inconclusive branches. Theorem 2's conclusion that 'at least one party necessarily possesses an antidistinguishable set of states' is proven only inside this restricted model. Under standard LOCC, a party may perform a filtering measurement that eliminates no state but changes the reduced ensemble for a later round, so the last-party argument in Theorem 2 is invalid for standard LOCC. Since Theorems 4, 5, 6, and 7 all rely on Theorem 2 for their impossibility claims, the central separation — e.g., the three states in Eq. (13) are not LOCC antidistinguishable — is not established for the usual meaning of LOCC. The paper mus","section":"Definition 6, Theorem 2, Theorem 4"},{"comment":"The Bob-starter impossibility is not proved. The argument considers only one particular POVM of the form {c1|0><0|, c2|1><1|, c3|+><+|, c4|-><-|}; showing that two of its outcomes lead to failure, and that setting c2=c3=0 makes the measurement invalid, does not rule out other Bob measurements. A starter-asymmetry claim requires an optimization over all of Bob's POVMs or a general no-go argument. The SDP in Appendix A only establishes that Alice's reduced set is antidistinguishable; it does not prove Bob's impossibility.","section":"Theorem 3"},{"comment":"Even within the paper's one-pass model, Theorem 2's inference from 'the last party must antidistinguish all N states' to 'whichever party starts the protocol' does not follow. Definition 6 requires every round to eliminate a state, so a party without an antidistinguishable set cannot simply pass to a later party who has one. Moreover, Theorem 4's assertion that the local reduced sets in Eq. (13) are 'evidently' not antidistinguishable is too terse: with duplicate reduced states the argument must explicitly account for the labeling of identical states. These gaps could be repaired locally, but they reinforce that the central nonlocality claim depends on a model and an inference that are not standard.","section":"Theorem 2 and Theorem 4"}],"minor_comments":[{"comment":"Typo: 'antidistinguiahbaility' should be 'antidistinguishability'.","section":"Abstract"},{"comment":"Reference [16] lacks the journal name: it should be J. Phys. A: Math. Theor. 51, 365303 (2018).","section":"Reference [16]"},{"comment":"The vector |a> = (1/2)|0> + sum_i r_i |zeta_i> must be normalized; the condition sum_i |r_i|^2 = 3/4 should be stated explicitly, together with d >= 2.","section":"Eq. (13)"},{"comment":"The nested square-root expressions in Bob's states are hard to read; the range of epsilon should be stated before the displayed equation, not only in the proposition.","section":"Eq. (12)"},{"comment":"The appendix headings are inconsistent: Appendix B is titled 'Theorem 1 and Lemma 2' although the relevant statement is Proposition 1, and Appendix C is titled 'Theorem 3' but concerns Proposition 3. The numerical POVM matrices would be more useful with code or higher-precision data.","section":"Appendices B and C"}],"recommendation":"reject","confidential_remarks":"The central issue is not a matter of presentation: the paper's 'LOCC' is a one-pass sequential class, and the advertised nonlocality-without-entanglement result is therefore not about standard LOCC. Reframing to the weaker model would change the main claim substantially. The editor may also wish to check the novelty overlap with the authors' own elimination-paradigm work, Ref. [6], and ensure that the numerical SDP results are reproducible."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague, the punchline: the paper's central claim—three bipartite product states can be globally antidistinguishable but not LOCC antidistinguishable—is not actually proved for standard LOCC. Definition 6 defines LOCC as a single left-to-right pass where each round must eliminate a state. That is a restricted model, not the usual adaptive LOCC. The impossibility proofs, especially Theorem 2, only analyze protocols of that form. In standard LOCC, the last party does not necessarily face an antidistinguishable set after earlier rounds, and later adaptive measurements can change the ensemble. So the abstract's unqualified \"LOCC\" is unsupported. The example may still be nonlocal under full LOCC—I suspect it is, because the local reduced sets contain two non-orthogonal states and a no-elimination branch seems unavoidable—but the paper does not show that.\n\nWhat is genuinely new: the three-state construction is concrete and satisfies the global antidistinguishability conditions; the starter asymmetry for 2-antidistinguishability is a real observation; and the tripartite genuine-exclusion example is a reasonable extension. The paper correctly uses the Caves-Fuchs-Schack conditions and the PBR result, with no fitted parameters; the claims are checked against independent known results. That is real evidence.\n\nSoft spots beyond the LOCC model: Theorem 3's proof is thin—the claim that Bob's remaining set is 2-antidistinguishable is not fully justified, and the SDP appendices give numerical matrices without certificates or code, so the numerical claims are hard to verify. There is heavy self-citation and overlap with the authors' earlier elimination-paradigm paper [6], which makes the novelty more incremental than the abstract suggests, but that is not a fatal problem.\n\nWho this is for: people working on LOCC and state exclusion. The examples are worth knowing even if the main theorem is not fully proved. I would send this to a serious referee, because the counterexample is plausible and the minimality question is worthwhile. The referee should push the authors to either prove the separation for standard LOCC or explicitly rescope to one-pass LOCC. As written, I would not cite it for the LOCC claim.","headline":"The paper's advertised LOCC separation is only proved for a nonstandard one-pass version of LOCC, so the central claim as stated does not hold up.","tokens_in":15113,"tokens_out":11773,"would_cite":false,"duration_ms":104774,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["81P50","81P45"],"pacs":["03.67.-a"],"model":"deepseek-v4-flash","headline":"The paper establishes that three bipartite product states can be globally antidistinguishable while failing to be LOCC antidistinguishable, making three the minimal number for nonlocality in state exclusion.","keywords":["quantum state exclusion","antidistinguishability","nonlocality without entanglement","LOCC","product states","x-antidistinguishability","minimal number of states","multipartite quantum information"],"falsifier":"Run the three states of Eq. (13) through a standard adaptive LOCC protocol—where parties may each measure multiple times, with classical feedback and no requirement that every round eliminate a state—and check whether all three states are excluded in every run; if yes, the central three-state separation is false.","tokens_in":14090,"feed_emoji":"⚛️","tokens_out":6162,"duration_ms":60830,"temperature":0.7,"pith_summary":"The paper is trying to establish that quantum state exclusion—not just discrimination—can exhibit nonlocality without entanglement. It defines LOCC antidistinguishability and proves that three bipartite product states can be globally antidistinguishable while no one-pass LOCC protocol can exclude even one. Since two states cannot show the effect, three is shown to be minimal. The same separation is extended to eliminating two states at once and to tripartite states that are locally non-excludable across every bipartition. A sympathetic reading is that exclusion provides a new, sharper arena in which local operations fall short of global ones.","feed_headline":"Three states suffice for exclusion-based nonlocality","feed_subtitle":"A three-state set of separable bipartite states is globally antidistinguishable yet resists local exclusion—the minimal instance.","key_machinery":"Three ingredients carry the argument. First, a closed-form necessary-and-sufficient condition for three pure states to be antidistinguishable, used to certify the global side of the construction. Second, a reduction theorem for the paper's one-pass LOCC model—each round must eliminate at least one state and the protocol runs until all parties are exhausted—which states that for multipartite product states a successful LOCC protocol requires at least one party to hold an antidistinguishable set of local states ab initio (Theorem 2); this converts LOCC success into a purely local condition. Third, the explicit state families (Eq. 13 for plain antidistinguishability, Eq. 14 for 2-antidistinguis","core_discovery":"The paper's central claim is that there exist sets of product states whose global information is enough to rule out at least one state, yet no local protocol with classical communication (LOCC) can achieve the same exclusion. The concrete instance is a family of three bipartite product states whose pairwise overlap pattern satisfies the necessary and sufficient three-state antidistinguishability inequalities, while every party's local sub-states fail those same inequalities. On the paper's model, a successful LOCC protocol for product-state exclusion forces at least one party to already possess an antidistinguishable subset from the start (Theorem 2), so failing local antidistinguishability","pith_inferences":["If standard adaptive LOCC is allowed—multi-round measurements, classical feedback, and no requirement that every round eliminate a state—the reduction theorem no longer holds, so the three-state examples might become locally excludable; the claimed nonlocality is proven for a narrower, one-pass operational model.","Exclusion appears to expose nonlocality with far fewer resources than discrimination: for product-state discrimination, nonlocal sets typically require many states, while exclusion does it with three; if this survives more general LOCC models, exclusion could be a sharper test of local inaccessibility.","A testable extension would be to implement the Eq. (13)-type states with qudits (for example, photonic information in two bases) and compare a global measurement against one-way LOCC protocols, looking for a gap in exclusion rates.","The local inaccessibility of antidistinguishability could feed into communication-complexity or cryptographic settings where the goal is to prove that separated parties cannot even rule out states; whether the advantage persists under less-restricted LOCC remains open."],"forward_implications":["Three is minimal: no two-state set can exhibit exclusion-based nonlocality, so any such phenomenon needs at least three states.","Four states achieve the same separation for eliminating two states at once (2-antidistinguishability): global protocols can exclude two states, local ones cannot.","Genuine multipartite nonlocality: three tripartite product states are globally antidistinguishable but fail LOCC antidistinguishability across every bipartition.","Starter symmetry is a special feature of single-state exclusion: for product states the initiating party does not matter, but for 2-antidistinguishability it does.","Strong vs weak: the paper distinguishes settings where all states or all x-tuples must be exhausted; strong global exclusion can hold where strong LOCC exclusion fails."],"fun_headline_variants":["Three product states: global exclusion beats local","State exclusion's nonlocality: minimal three-state set","Three states prove exclusion nonlocality","No local exclusion for three separable states","Exclusion nonlocality needs just three states"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The results rely on a one-pass LOCC model in which each measurement round must eliminate at least one state and parties cannot adaptively repeat measurements after receiving feedback; if standard multi-round adaptive LOCC is allowed, the proof that a party must already hold an antidistinguishable set breaks down.","fun_headline_variants_meta":{"raw":{"variants":["Three product states: global exclusion beats local","State exclusion's nonlocality: minimal three-state set","Three states prove exclusion nonlocality","No local exclusion for three separable states","Exclusion nonlocality needs just three states"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000499,"raw_usage":{"total_tokens":2287,"prompt_tokens":761,"completion_tokens":1526,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":505,"completion_tokens_details":{"reasoning_tokens":1458}},"tokens_in":505,"tokens_out":1526,"duration_ms":12105,"temperature":1.0,"reasoning_tokens":1458,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-02T22:53:56.574394+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the three states of Eq. (13) through a standard adaptive LOCC protocol—where parties may each measure multiple times, with classical feedback and no requirement that every round eliminate a state—and check whether all three states are excluded in every run; if yes, the central three-state separation is false.","supporting_citations":[],"review_version":1}