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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.

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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.

T0 review reviewed 2026-08-02 challenge →

load-bearing objection 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. the 3 major comments →

arxiv 2602.15452 v2 pith:HZBXX56I submitted 2026-02-17 quant-ph

Nonlocality without entanglement in exclusion of quantum states

Satyaki Manna , Anandamay Das Bhowmik This is my paper
classification quant-ph MSC 81P5081P45 PACS 03.67.-a
keywords quantum state exclusionantidistinguishabilitynonlocality without entanglementLOCCproduct statesx-antidistinguishabilityminimal number of statesmultipartite quantum information
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

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.

Core claim

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

What carries the argument

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

Load-bearing premise

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.

What would settle it

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.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • 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.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • 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.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 5 minor

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.

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 (3)
  1. [Definition 6, Theorem 2, Theorem 4] 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
  2. [Theorem 3] 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.
  3. [Theorem 2 and Theorem 4] 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.
minor comments (5)
  1. [Abstract] Typo: 'antidistinguiahbaility' should be 'antidistinguishability'.
  2. [Reference [16]] Reference [16] lacks the journal name: it should be J. Phys. A: Math. Theor. 51, 365303 (2018).
  3. [Eq. (13)] 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.
  4. [Eq. (12)] 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.
  5. [Appendices B and C] 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.

Circularity Check

0 steps flagged

No significant circularity: central claims rest on independent conditions and external results; self-citations are numerous but not load-bearing.

full rationale

Walking the derivation chain, the paper's central results do not reduce to their inputs by construction. Global antidistinguishability in Theorem 4 is verified through the independent Caves-Fuchs-Schack necessary and sufficient conditions (Eqs. 3-4), not derived from the LOCC conclusion. The LOCC negative results use Theorem 2's argument about local reduced-state sets; although Definition 6's one-pass, each-round-must-eliminate model is nonstandard and is a legitimate correctness/scope concern, it is not circular reasoning: the theorem is not assumed as its own premise. The SDP verifications in Appendices A-C are independent computational checks, not fitted parameters renamed as predictions. The main examples rely on external results (PBR, Webb et al., Walgate-Hardy, Johnston et al.) rather than on the authors' own prior work. There is heavy self-citation (Refs. [6,17,18,19,29,32,41,42]), but none of these citations is load-bearing for the main proofs; they are contextual or peripheral. Therefore no circular step meets the evidentiary bar, and the appropriate score is in the 0-2 range. The nonstandard LOCC definition should be discussed as a correctness/scope risk, not as circularity.

Axiom & Free-Parameter Ledger

2 free parameters · 5 axioms · 0 invented entities

No fitted constants in the usual sense; the family parameters epsilon and r_i are chosen by hand. No new physical entities are introduced. The most consequential assumption is the nonstandard one-pass LOCC model, which underpins all negative results.

free parameters (2)
  • epsilon in Eq. (12) = range (7/20, 1/2] for Prop. 1; <=1/3 for Prop. 2
    Controls Bob's local four states; chosen by hand to satisfy antidistinguishability ranges, not fitted to data. The starter-dependence claim depends on this choice.
  • r_i in Eq. (13) = unspecified (only constrained by normalization of |a>)
    Defines the three-state nonlocality example; the proof requires the local pair {|0>, |a>} to be non-orthogonal, but no explicit values are given, leaving the example under-specified.
axioms (5)
  • standard math Caves-Fuchs-Schack necessary and sufficient conditions (Eq. (4)) for antidistinguishability of three pairwise non-orthogonal pure states.
    Used in Theorems 4, 6, and 7 to certify global antidistinguishability by overlap inequalities; cited from Ref. [12] and not re-derived.
  • domain assumption Ref. [22]: the four states in Eq. (14) are globally strongly 2-antidistinguishable when cos 2theta <= sqrt(2)-1.
    Load-bearing for Theorem 5's global side; the paper does not reproduce the entangled six-outcome measurement.
  • domain assumption Ref. [33] (PBR): the four two-qubit product states in Eq. (14) at 2theta=pi/4 are antidistinguishable.
    Load-bearing for Theorem 6's global side; cited rather than derived.
  • domain assumption Ref. [14] sufficient condition for antidistinguishability of four states, used in Proposition 1.
    Used to assert Bob can eliminate one state at each outcome; no statement of the condition is given.
  • ad hoc to paper The LOCC protocol is one-pass sequential (each party measures once, fixed order) and every branch must eliminate a state.
    Definition 6 imposes this; it is not standard full LOCC and is load-bearing for all negative results.

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Cite this review

Pith. "Pith review of Nonlocality without entanglement in exclusion of quantum states." pith.science (2026). https://pith.science/paper/HZBXX56I

@misc{pith2026260215452,
  author       = {Pith},
  title        = {Pith review of: Nonlocality without entanglement in exclusion of quantum states},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HZBXX56I}},
  note         = {Machine review of arXiv:2602.15452}
}
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abstract

We study the task of quantum state exclusion, focusing on antidistinguishability and its generalization to $x$-antidistinguishability, under global measurements and local operations with classical communication (LOCC). We also introduce weak and strong notions of antidistinguiahbaility ($x$-antidistinguishability) depending on whether all states or all $x$-tuples are exhaustively eliminated. Our results reveal striking differences between state exclusion and the more familiar task of state discrimination. In particular, we show that LOCC antidistinguishability of multipartite product states is symmetric with respect to the initiating party but this symmetry breaks down for higher-order $x$-antidistinguishability. Most notably, we establish a manifestation of \emph{nonlocality without entanglement} in the context of state exclusion: we prove that three bipartite product states can be globally antidistinguishable while failing to be LOCC antidistinguishable, demonstrating that three is the minimal number of states required for this phenomenon. We further extend this separation to $2$-antidistinguishability and present example exhibiting the same type of nonlocality. At last, we provide an antidistinguishable tripartite product states that are not LOCC antidistinguishable across any bipartition, which ensures the phenomenon of \emph{genuine nonlocality without entanglement} in this framework.

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Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Local state antimarking : Nonlocality without entanglement

    quant-ph 2026-05 unverdicted novelty 7.0

    Certain sequences of product states allow global but not local identification of excluded sequences via the new LSAM task, showing nonlocality without entanglement.

  2. Local Marking of Locally Implementable Unitary Operations

    quant-ph 2026-04 unverdicted novelty 7.0

    There exist sets of globally distinguishable tripartite product unitaries that cannot be locally marked with LOCC, providing a stronger manifestation of nonlocality without entanglement.

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This paper was first reviewed by deepseek-v4-flash on August 2, 2026.