Pith. sign in

REVIEW 2 major objections 3 minor 60 references

Cluster-State Witnesses of Finite-Speed Hidden Influences

T0 review · 2 major / 3 minor · reviewed 2026-08-08 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Linear cluster states yield two facet-defining witnesses, $S_4 \le 6$ and $S_5 \le 10$, against all finite-speed hidden-influence theories that respect no-signaling and measurement independence.

desk verdict New cluster-state witnesses for finite-speed hidden-influence models with much larger violation margins, but the load-bearing Farkas certificates are not in the paper. read the letter →

arxiv 2608.05271 v1 pith:LZQT2IIK submitted 2026-08-05 quant-ph

Weikang Li , Mengyao Hu , Dong-Ling Deng , Valerio Scarani This is my paper · ORCID
classification quant-ph PACS 03.65.Ud03.67.-a
keywords finite-speedhiddeninfluencesclusterstatesBellnonlocalityno-signalingconditionallocalityprojectedpolytopesFarkascertificatesquantumwitnesses
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Bell experiments rule out local hidden causes but leave room for hidden influences that travel faster than light at a finite speed in a preferred frame. This paper turns that loophole into a testable constraint: when two late parties lie outside each other's hidden-influence cone, their correlations must be Bell-local once the early-side events are fixed. The authors construct a four-qubit witness $S_4\le 6$ with quantum value $4+2\sqrt{2}$, and a five-qubit witness $S_5\le 10$ with quantum value $6+4\sqrt{2}$, both built from linear-cluster states and evaluated from marginal data containing at most one late party. They certify that both inequalities are facet-defining faces of the projected hidden-influence polytopes, giving substantially better noise tolerance than earlier finite-speed hidden-influence witnesses. If correct, any finite-speed hidden-influence model satisfying operational no-signaling, conditional late-pair locality, and measurement independence is falsified by these cluster correlations.

What carries the argument

The load-bearing object is the hidden-influence causality set $\mathcal{HIC}_E = \mathrm{NS} \cap \mathrm{CL}(BC|E)$: the intersection of the full no-signaling polytope with the set of distributions for which the $BC$ marginal is Bell-local after conditioning on every non-null early-side input--output event. Its image under the no-BC projection, which deletes every correlator containing both $B$ and $C$, is the polytope $\mathcal{P}^{\mathrm{no-BC}}_E$ over which the witnesses are optimized. The proof machinery is linear-programming duality: each witness functional is written as $\alpha^T t$ over nonnegative hidden-influence weights $t$ constrained by $Nt=r$ (normalization plus no-signaling), and an integer dual vector $\eta$ with $N^T\eta \ge \alpha$ and $r^T\eta = B$ certifies the bound $S \le B$. Facet-definingness is then verified by exact rational rank computations and relative-interior feasibility on the zero-slack face. The explicit witnesses combine a distributed CHSH block on the $B$ side with stabilizer-lock blocks on the $C$ side, with relative weights fixed by the supporting facet of a two- or three-dimensional block projection.

What would settle it

Maximize $S_4$ over the feasible set $\{t \ge 0 : Nt = r\}$ using an independent linear-programming solver; if any feasible weight vector yields $S_4 > 6$ (or, in the five-qubit case, $S_5 > 10$), the paper's Farkas certificate is wrong. The claim stands only if every such optimization returns exactly 6 (or 10), and an experimental implementation that observes $S_4 = 4+2\sqrt{2} > 6$ from a linear-cluster state in the prescribed $B \sim C$ timing would confirm the claimed violation.

Watch

Extended reading notes

Core claim

The paper establishes that the projected no-BC hidden-influence polytopes for linear-cluster states admit compact, facet-defining witnesses. For the four-qubit cluster state $|\mathrm{LC}_4\rangle$, it proves $S_4 \le 6$ over $\mathcal{P}^{\mathrm{no-BC}}_{AD}$, with quantum value $S_4^Q = 4+2\sqrt{2} \approx 6.8284$. For the five-qubit cluster state $|\mathrm{LC}_5\rangle$, it proves $S_5 \le 10$ over $\mathcal{P}^{\mathrm{no-BC}}_{ADE}$, with quantum value $S_5^Q = 6+4\sqrt{2} \approx 11.6569$. Both witnesses contain no term with both late parties $B$ and $C$, both bounds are attained by explicit hidden-influence distributions, and exact rational arithmetic shows that the exposed faces have codimension one in the projected polytopes: dimension 43 of 44 for LC4 and 133 of 134 for LC5. The ideal white-noise visibilities are $\nu_4^* = 6/(4+2\sqrt{2}) \approx 0.8787$ and $\nu_5^* = 10/(6+4\sqrt{2}) \approx 0.8579$, compared with 0.9526 for the optimized earlier witness, so linear-cluster states are presented as certifiable and experimentally friendly resources for finite-speed hidden-influence tests.

Load-bearing premise

The entire certification rests on the assumption that every finite-speed hidden-influence model is exactly characterized by the intersection of operational no-signaling with conditional Bell locality of the two late parties after conditioning on every non-null early input-output event, together with measurement independence and no postselection; if any of these fails, the bounds $S_4 \le 6$ and $S_5 \le 10$ do not apply to the broader model class.

Editorial extensions

If this is right

  • If the paper is right, any finite-speed hidden-influence model that keeps operational no-signaling and conditional $BC$ locality is experimentally falsified whenever a linear-cluster state produces $S_4 > 6$ or $S_5 > 10$ in the specified spacetime geometry.
  • Because the certified bounds coincide with the fully local bounds, these witnesses isolate the specific nonlocality that finite-speed influences cannot generate: nonlocal correlations that survive conditioning on all early events.
  • The improved ideal white-noise thresholds, 0.8787 and 0.8579 versus the earlier 0.9526, bring a finite-speed hidden-influence test substantially closer to what current quantum devices can reach.
  • Since both inequalities are facet-defining, no strictly weaker linear inequality in the same no-BC coordinate space can expose the same face; the bounds are tight for their projected polytopes.
  • The five-qubit witness can be run in the same four-site spacetime layout as the earlier proposal by treating $D$ and $E$ as a single four-outcome measurement device.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The same stabilizer-block plus projected-polytope recipe could in principle be iterated to larger linear cluster states, but the paper gives no scaling law; computing the next witness and its visibility would test whether the advantage grows or saturates.
  • Under realistic readout errors the comparison may flip: LC4 uses only two- and three-body correlators, while LC5 contains four-body terms that attenuate faster with per-qubit readout flips, so LC4 may be the more robust experimental target despite its higher ideal white-noise threshold.
  • A successful loophole-conscious implementation would not only rule out finite-speed influences; it would operationalize the known result that, within this model class, preserving the observed correlations forces faster-than-light signaling between users, because the polytope constraint is exactly what enforces no-signaling.
  • The four completion terms in $S_5$ vanish on the cluster state yet determine whether the inequality is a facet, so similar degenerate terms may be systematically necessary in stabilizer-based no-BC witnesses; their role in other graph states is a natural follow-up question.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 3 minor

Summary. The manuscript proposes two linear-cluster-state witnesses for finite-speed hidden-influence models. The theoretical framework is a projected-polytope separation problem: define the hidden-influence set as HICE = NS ∩ CL(BC|E), project away all correlations containing both late parties, and certify linear inequalities over this projection by LP duality. The reported results are an LC4 witness with S4 ≤ 6 and quantum value 4+2√2, and an LC5 witness with S5 ≤ 10 and quantum value 6+4√2. The authors further claim, via integer Farkas certificates and exact rational rank/relative-interior computations, that both inequalities are facet-defining for the relevant projected polytopes, with projected dimensions 44 and 134 and face dimensions 43 and 133. The paper includes explicit primal HIC points, an explicit five-site spacetime arrangement, and white-noise visibility estimates of 0.8787 and 0.8579, presented as improvements over the earlier Bancal et al. witness.

Significance. If the computational certificates are valid, this is a significant step for experimental tests of finite-speed hidden influences: the witnesses use compact graph states, two-setting X–Z measurements, and substantially better ideal white-noise thresholds than the previous 0.9526 benchmark. The authors also give credit-worthy exact data: explicit feasible HIC distributions, exact rational projected dimensions, positive relative-interior solutions with ε = 1/176 and ε = 1/416, and a clear discussion of the no-BC projection. The main reservation is not methodological circularity but verifiability: the central bounds and facet claims rest on Farkas certificates and rank computations that are only summarized, not shipped.

major comments (2)
  1. [Supplemental Material, Secs. IV–V; main text Eq. (4); Table S1] The load-bearing claims S4 ≤ 6, S5 ≤ 10, and facet dimensions 43/133 are not independently verifiable because the actual Farkas certificate vectors η, the zero-slack index sets J, and the verifier code are not included. The supplement reports statistics (||η||₁ = 70/362, 22/98 nonzero entries, zero-slack counts 176/888) and states that substitution into Eq. (S62) proves the bounds, but no certificate is displayed and the Data/Code Availability statement defers release until publication. The explicit primal points prove tightness at specific distributions and the rank/relative-interior checks prove facet tightness only once J is known. Since an error in the LP encoding or in the certificate would invalidate the central claim, the revision must include the full machine-readable certificates and an independent verifier, or the headline claims should be explicitly downgraded to unverified computational assertions.
  2. [Main text Eq. (1); Supplement I A; main text p. 2] The paper's scope statement is stronger than its model class. The main text says the criteria falsify 'all models with finite v', but Eq. (1) defines HICE as NS ∩ CL(BC|E), and Supplement I A explicitly states that these conditions are necessary but 'do not characterize all finite-speed theories'. A finite-v model whose correlations fall outside NS ∩ CL(BC|E), for example one permitting operational signaling that no user can exploit, or one with measurement dependence, is not constrained by the certified inequalities. The theorem should be stated with explicit quantification over P ∈ Π^{no-BC}(NS ∩ CL(BC|E)), and the abstract and introduction should be reworded so that 'finite-speed hidden-influence model' is understood as 'a model satisfying the assumptions listed in Sec. I of the supplement'.
minor comments (3)
  1. [Table I and main text discussion of LC5] The 'tightness' column reports (44,43) and (134,133) without a label for the second entry; the caption should state that the first number is the projected affine dimension and the second is the active-face dimension.
  2. [Supplemental Material, Sec. II C, Eq. (S47)] The distributions P1–P3 are given in bit notation with a shared fair bit ξ; the claim that b becomes independent of w after summing over ξ in P1 is correct but would be easier to check if the summation step were written out explicitly.
  3. [Main text, 'substantially larger margins' and Supplement VIII B] The statement that the new witnesses give 'substantially larger margins than previous finite-speed hidden-influence witnesses' refers to ideal white-noise visibility; the readout-error analysis in Sec. VIII B correctly warns that LC5's four-body terms may offset its lower ν*. The main-text sentence should carry that qualification.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found: the S4≤6 and S5≤10 bounds are certified by Farkas duality against the HIC polytope, with the block-weight choices constituting legitimate witness design rather than assumption of the conclusion.

full rationale

The derivation chain is self-contained relative to the stated model. The HIC set is defined in Eq. (1) as HICE = NS ∩ CL(BC|E), and the support bounds are proved by the Farkas certificate condition in Eq. (4): any η with N^T η ≥ α and r^T η = B certifies S ≤ B. The LC4 and LC5 functionals are built from cluster-state stabilizers with known expectation values; their quantum values 4+2√2 and 6+4√2 follow from stabilizer identities, not from the inequalities they are claimed to violate. The bounds 6 and 10 are obtained from dual feasibility and exact rational checks, not assumed. The block weights (1,2) for LC4 and (1,1,2) for LC5 are chosen by maximizing the cluster-state value relative to the certified HIC support function; optimizing a witness against a certified polytope is legitimate construction, not a fitted parameter renamed as a prediction. Tightness and facet claims use explicit primal HIC points (v1, v2 and w1, w2, w3) plus exact rank and relative-interior computations; these points do not presuppose the inequalities they saturate. Self-citations such as Bancal et al. [30], Barnea et al. [31], and earlier Scarani works provide context, benchmarks, and the model definition but are not the mathematical basis for the S4/S5 bounds; no uniqueness theorem is imported from the authors to force the choice. The main caveats are verification and completeness, not circularity: the integer Farkas certificates and verifiers are not included in the manuscript (Data and Code availability: 'The certificate files and verifiers will be released upon publication'), so the exact central bounds and facet dimensions 43 and 133 cannot be independently rechecked from the text alone. The paper also explicitly limits its claims: the visibilities are 'theory-level benchmarks rather than complete experimental thresholds', the facet results are 'two facets, not complete facet lists', and the model assumes measurement independence and no postselection (Supplement I D). These are honest scope limitations, not evidence that the derivation reduces to its inputs. No passage in the manuscript asserts or exhibits a step in which a claimed prediction is definitionally equal to an input quantity, and no load-bearing self-citation chain is present. Therefore the appropriate circularity score is 0.

Assumptions & free parameters 1 free parameters · 5 assumptions · 0 invented entities

No physical entities are invented; the hidden influence is the target model class from the prior literature, not a new postulated object. The only construction-level choices are the block weights, which are fixed by optimization, and the effective variables eA0 and eA1, which are deterministic functions of recorded outcomes.

free parameters (1)
  • Block weights (p,ℓ) for LC4 and (p,ℓ1,ℓ2) for LC5 = (1,2) and (1,1,2)
    Chosen to maximize the cluster-state value relative to the certified hidden-influence support function (Supplement II B-C). They are fixed witness coefficients, not fit to experimental data, and the support bounds are proven for the chosen weights.
assumptions (5)
  • domain assumption Measurement independence: experimenters' setting choices are independent of hidden variables and earlier outcomes.
    Stated in the introduction: 'under measurement independence, which we assume for the rest of the paper'. Without it, hidden-influence models can adjust predictions to the settings and the derived bounds do not apply.
  • domain assumption Operational no-signaling: the full probability table P(o_E,b,c|s_E,y,z) must satisfy no-signaling across parties, including the early side.
    This defines HICE = NS ∩ CL(BC|E), Eq. (1), and is enforced in Eq. (S4). If signaling is allowed, the HIC bound does not constrain the model.
  • domain assumption Conditional BC locality: for every non-null early input-output event, P(b,c|...) admits the local decomposition of Eq. (3).
    This is the defining physical content of the finite-speed model: B and C lie outside each other's v-cones, so once the early events are fixed they can only be correlated by common causes.
  • domain assumption The preferred-frame finite-speed causal structure and the explicit spacetime arrangements in Supplement I, including the LC5 collection-event construction, are realizable.
    The bounds are meaningful only for this model class; the LC5 proof uses Minkowski geometry and independent, free delay choices at the late parties.
  • standard math Linear programming duality and polyhedral facet theory, including the Farkas certificate argument and exact rational rank and relative-interior checks.
    Used to certify support bounds and the facet-defining property; these are standard results from Schrijver and Ziegler.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Cluster-State Witnesses of Finite-Speed Hidden Influences." pith.science (2026). https://pith.science/paper/LZQT2IIK

@misc{pith2026260805271,
  author       = {Pith},
  title        = {Pith review of: Cluster-State Witnesses of Finite-Speed Hidden Influences},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LZQT2IIK}},
  note         = {Machine review of arXiv:2608.05271}
}
abstract

Bell experiments rule out local common-cause explanations of quantum correlations, yet they do not exclude hidden influences that travel faster than light while still having a finite speed in a preferred frame. Multipartite spacetime arrangements turn this possibility into a constraint: two late parties that are outside each other's hidden-influence cones must remain Bell-local once the earlier events are fixed. Here, we formulate this constraint as a projected-polytope separation problem for cluster-state correlations, using only marginal data containing at most one late party. From linear cluster states, we construct a four-qubit witness with the bound $S_4\le 6$ and quantum value $4+2\sqrt2$, and a five-qubit witness with $S_5\le 10$ and quantum value $6+4\sqrt2$. We certify that the exposed faces are facets of the corresponding projected hidden-influence polytopes. These results identify linear-cluster graph states as certifiable and experimentally friendly resources for finite-speed hidden-influence tests.

Figures

Figures reproduced from arXiv: 2608.05271 by the authors.

Figure 1
Figure 1. FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

60 extracted references · 51 canonical work pages

  1. [1]

    Einstein, B

    A. Einstein, B. Podolsky, and N. Rosen, Can quantum- mechanical description of physical reality be considered com- plete?, Phys. Rev.47, 777 (1935)

    1935

  2. [2]

    J. S. Bell, On the Einstein Podolsky Rosen paradox, Physics Physique Fizika1, 195 (1964)

    1964

  3. [3]

    J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, Pro- posed experiment to test local hidden-variable theories, Phys. Rev. Lett.23, 880 (1969)

    1969

  4. [5]

    Brunner, D

    N. Brunner, D. Cavalcanti, S. Pironio, V . Scarani, and S. Wehner, Bell nonlocality, Rev. Mod. Phys.86, 419 (2014)

    2014

  5. [6]

    S. J. Freedman and J. F. Clauser, Experimental test of local hidden-variable theories, Phys. Rev. Lett.28, 938 (1972)

    1972

  6. [7]

    Aspect, J

    A. Aspect, J. Dalibard, and G. Roger, Experimental test of Bell’s inequalities using time-varying analyzers, Phys. Rev. Lett.49, 1804 (1982)

    1982

  7. [8]

    Tittel, J

    W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, Violation of Bell inequalities by photons more than 10 km apart, Phys. Rev. Lett.81, 3563 (1998)

    work page 1998

  8. [9]

    Weihs, T

    G. Weihs, T. Jennewein, C. Simon, H. Weinfurter, and A. Zeilinger, Violation of Bell’s inequality under strict Einstein locality conditions, Phys. Rev. Lett.81, 5039 (1998)

    work page 1998

Show all 60 references
  1. [10]

    M. A. Rowe, D. Kielpinski, V . Meyer, C. A. Sackett, W. M. Itano, C. Monroe, and D. J. Wineland, Experimental violation of a Bell’s inequality with efficient detection, Nature409, 791 (2001)

    2001

  2. [11]

    Scheidl, R

    T. Scheidl, R. Ursin, J. Kofler, S. Ramelow, X.-S. Ma, T. Herbst, L. Ratschbacher, A. Fedrizzi, N. K. Langford, T. Jennewein, and A. Zeilinger, Violation of local realism with freedom of choice, Proc. Natl. Acad. Sci. U.S.A.107, 19708 (2010)

    2010

  3. [12]

    Handsteiner, A

    J. Handsteiner, A. S. Friedman, D. Rauch,et al., Cosmic Bell test: Measurement settings from Milky Way stars, Phys. Rev. Lett.118, 060401 (2017)

    2017

  4. [13]

    Hensen, H

    B. Hensen, H. Bernien, A. E. Dr ´eau,et al., Loophole-free Bell inequality violation using electron spins separated by 1.3 kilo- metres, Nature526, 682 (2015)

    2015

  5. [14]

    Giustina, M

    M. Giustina, M. A. M. Versteegh, S. Wengerowsky,et al., Significant-loophole-free test of Bell’s theorem with entangled photons, Phys. Rev. Lett.115, 250401 (2015)

    2015

  6. [15]

    L. K. Shalm, E. Meyer-Scott, B. G. Christensen,et al., Strong Loophole-Free Test of Local Realism, Phys. Rev. Lett.115, 250402 (2015)

    2015

  7. [16]

    Rosenfeld, D

    W. Rosenfeld, D. Burchardt, R. Garthoff, K. Redeker, N. Or- tegel, M. Rau, and H. Weinfurter, Event-ready Bell test using entangled atoms simultaneously closing detection and locality loopholes, Phys. Rev. Lett.119, 010402 (2017)

    2017

  8. [17]

    Storz, J

    S. Storz, J. Sch ¨ar, A. Kulikov,et al., Loophole-free Bell in- equality violation with superconducting circuits, Nature617, 265 (2023)

    2023

  9. [18]

    M.-H. Li, C. Wu, Y . Zhang,et al., Test of Local Realism into the Past without Detection and Locality Loopholes, Phys. Rev. Lett.121, 080404 (2018)

    2018

  10. [19]

    P. H. Eberhard, A realistic model for quantum theory with a locality property, inQuantum Theory and Pictures of Reality, edited by W. Schommers (Springer, Berlin, Heidelberg, 1989) pp. 169–215. 6

    1989

  11. [20]

    Scarani, W

    V . Scarani, W. Tittel, H. Zbinden, and N. Gisin, The speed of quantum information and the preferred frame: Analysis of ex- perimental data, Phys. Lett. A276, 1 (2000)

    2000

  12. [21]

    Suarez and V

    A. Suarez and V . Scarani, Does entanglement depend on the timing of the impacts at the beam-splitters?, Phys. Lett. A232, 9 (1997)

    1997

  13. [22]

    Zbinden, J

    H. Zbinden, J. Brendel, N. Gisin, and W. Tittel, Experimental test of nonlocal quantum correlation in relativistic configura- tions, Phys. Rev. A63, 022111 (2001)

    2001

  14. [23]

    Stefanov, H

    A. Stefanov, H. Zbinden, N. Gisin, and A. Suarez, Quantum correlations with spacelike separated beam splitters in motion: Experimental test of multisimultaneity, Phys. Rev. Lett.88, 120404 (2002)

    2002

  15. [24]

    Salart, A

    D. Salart, A. Baas, C. Branciard, N. Gisin, and H. Zbinden, Testing the speed of ‘spooky action at a distance’, Nature454, 861 (2008)

    2008

  16. [25]

    Cocciaro, S

    B. Cocciaro, S. Faetti, and L. Fronzoni, A lower bound for the velocity of quantum communications in the preferred frame, Phys. Lett. A375, 379 (2011)

    2011

  17. [26]

    J. Yin, Y . Cao, H.-L. Yong, J.-G. Ren, H. Liang, S.-K. Liao, F. Zhou, C. Liu, Y .-P. Wu, G.-S. Pan, L. Li, N.-L. Liu, Q. Zhang, C.-Z. Peng, and J.-W. Pan, Lower bound on the speed of nonlo- cal correlations without locality and measurement choice loop- holes, Phys. Rev. Lett....

    2013

  18. [27]

    Cocciaro, S

    B. Cocciaro, S. Faetti, and L. Fronzoni, Improved lower bound on superluminal quantum communication, Phys. Rev. A97, 052124 (2018)

    2018

  19. [28]

    Scarani and N

    V . Scarani and N. Gisin, Superluminal influences, hidden vari- ables, and signaling, Phys. Lett. A295, 167 (2002)

    2002

  20. [29]

    Scarani and N

    V . Scarani and N. Gisin, Superluminal hidden communication as the underlying mechanism for quantum correlations: Con- straining models, Braz. J. Phys.35, 328 (2005)

    2005

  21. [32]

    [28, 29]

    The protocol for actual signaling is obvious in the configura- tions of Refs. [28, 29]. In Ref. [30] there is a four-partite con- figuration withE= (A, D), in which signaling is enabled from AtoD. It has been argued that signaling correlations may be allowed if the spacetime c...

  22. [33]

    Scarani, J.-D

    V . Scarani, J.-D. Bancal, A. Suarez, and N. Gisin, Strong con- straints on models that explain the violation of Bell inequali- ties with hidden superluminal influences, Found. Phys.44, 523 (2014)

    2014

  23. [34]

    Popescu and D

    S. Popescu and D. Rohrlich, Quantum nonlocality as an axiom, Found. Phys.24, 379 (1994)

    1994

  24. [35]

    Barrett, N

    J. Barrett, N. Linden, S. Massar, S. Pironio, S. Popescu, and D. Roberts, Nonlocal correlations as an information-theoretic resource, Phys. Rev. A71, 022101 (2005)

    2005

  25. [36]

    Coiteux-Roy, O

    X. Coiteux-Roy, O. Makuta, F. Curran, R. Augusiak, and M.-O. Renou, The genuinely multipartite nonlocality of graph states is model-dependent, npj Quant. Inf.11, 90 (2025)

    2025

  26. [37]

    Raussendorf and H

    R. Raussendorf and H. J. Briegel, A one-way quantum com- puter, Phys. Rev. Lett.86, 5188 (2001)

    2001

  27. [38]

    M. Hein, J. Eisert, and H. J. Briegel, Multiparty entanglement in graph states, Phys. Rev. A69, 062311 (2004)

    2004

  28. [39]

    G ¨uhne, G

    O. G ¨uhne, G. T ´oth, P. Hyllus, and H. J. Briegel, Bell inequali- ties for graph states, Phys. Rev. Lett.95, 120405 (2005)

    2005

  29. [40]

    Enrico Fermi

    M. Hein, W. D ¨ur, J. Eisert, R. Raussendorf, M. Van den Nest, and H. J. Briegel, Entanglement in graph states and its appli- cations, inQuantum Computers, Algorithms and Chaos, Pro- ceedings of the International School of Physics “Enrico Fermi”, V ol. 162, edited by G. Casati...

    2006

  30. [41]

    N. D. Mermin, Extreme quantum entanglement in a superposi- tion of macroscopically distinct states, Phys. Rev. Lett.65, 1838 (1990)

    1990

  31. [42]

    Svetlichny, Distinguishing three-body from two-body non- separability by a Bell-type inequality, Phys

    G. Svetlichny, Distinguishing three-body from two-body non- separability by a Bell-type inequality, Phys. Rev. D35, 3066 (1987)

    1987

  32. [43]

    R. F. Werner and M. M. Wolf, All-multipartite Bell-correlation inequalities for two dichotomic observables per site, Phys. Rev. A64, 032112 (2001)

    2001

  33. [44]

    ´Sliwa, Symmetries of the Bell correlation inequalities, Phys

    C. ´Sliwa, Symmetries of the Bell correlation inequalities, Phys. Lett. A317, 165 (2003)

    2003

  34. [45]

    Coretti, E

    S. Coretti, E. H ¨anggi, and S. Wolf, Nonlocality is transitive, Phys. Rev. Lett.107, 100402 (2011)

    2011

  35. [46]

    Schrijver,Theory of Linear and Integer Programming, Wiley-Interscience Series in Discrete Mathematics and Opti- mization (John Wiley & Sons, Chichester, 1986)

    A. Schrijver,Theory of Linear and Integer Programming, Wiley-Interscience Series in Discrete Mathematics and Opti- mization (John Wiley & Sons, Chichester, 1986)

    1986

  36. [47]

    G. M. Ziegler,Lectures on Polytopes, Graduate Texts in Math- ematics, V ol. 152 (Springer, New York, 1995)

    1995

  37. [48]

    Pironio, Lifting Bell inequalities, J

    S. Pironio, Lifting Bell inequalities, J. Math. Phys.46, 062112 (2005)

    2005

  38. [49]

    T ´oth, O

    G. T ´oth, O. G¨uhne, and H. J. Briegel, Two-setting Bell inequal- ities for graph states, Phys. Rev. A73, 022303 (2006)

    2006

  39. [50]

    T ´oth and O

    G. T ´oth and O. G¨uhne, Detecting genuine multipartite entangle- ment with two local measurements, Phys. Rev. Lett.94, 060501 (2005)

    2005

  40. [51]

    T ´oth and O

    G. T ´oth and O. G¨uhne, Entanglement detection in the stabilizer formalism, Phys. Rev. A72, 022340 (2005)

    2005

  41. [52]

    McKague, Self-testing graph states, inTheory of Quan- tum Computation, Communication, and Cryptography, Lecture Notes in Computer Science, V ol

    M. McKague, Self-testing graph states, inTheory of Quan- tum Computation, Communication, and Cryptography, Lecture Notes in Computer Science, V ol. 6745, edited by D. Bacon, M. Martin-Delgado, and M. Roetteler (Springer, Berlin, Hei- delberg, 2014) pp. 104–120

    2014

  42. [53]

    Baccari, R

    F. Baccari, R. Augusiak, I. ˇSupi´c, J. Tura, and A. Ac´ın, Scalable Bell inequalities for qubit graph states and robust self-testing, Phys. Rev. Lett.124, 020402 (2020)

    2020

  43. [54]

    Horodecki and R

    P. Horodecki and R. Ramanathan, The relativistic causality ver- sus no-signaling paradigm for multi-party correlations, Nat. Commun.10, 1701 (2019)

    2019

  44. [55]

    distributed CHSH

    M. Weilenmann, Monogamy relations for relativistically causal correlations, Nat. Commun.16, 269 (2025). Supplemental Material: Cluster-State Witnesses of Finite-Speed Hidden Influences CONTENTS I. Finite-speed model, no-signaling, and the no-BCprojection 2 A. Spacetime assumpt...

    2025

  45. [56]

    containsBC

    Together, these identities generate all six terms ofS 4. D. Coefficient selection and witness The four identities form the blocksR 4 andL 4, with cluster-state point(R Q 4 , LQ 4 ) = (2 √ 2,2). Section II shows that the ratio of the cluster-state value to the HIC support is un...

  46. [57]

    Since eδ, t≥0, every such vectortis supported onK

    For any point inF ′ and any feasible weight vectortthat projects to it, 0 = 10−α ′T t= eδT t. Since eδ, t≥0, every such vectortis supported onK. Conversely, eδK = 0, so every feasible vector supported onKsaturates the inequality. The componentwise-positive vectort RI shows tha...

  47. [58]

    Bancal, S

    J.-D. Bancal, S. Pironio, A. Ac ´ın, Y .-C. Liang, V . Scarani, and N. Gisin, Quantum non-locality based on finite-speed causal influences leads to superluminal signalling, Nat. Phys.8, 867 (2012)

    2012

  48. [59]

    J. F. Clauser and M. A. Horne, Experimental consequences of objective local theories, Phys. Rev. D10, 526 (1974)

    1974

  49. [60]

    T. J. Barnea, J.-D. Bancal, Y .-C. Liang, and N. Gisin, Tripartite quantum state violating the hidden-influence constraints, Phys. Rev. A88, 022123 (2013)

    2013

  50. [61]

    Coiteux-Roy, O

    X. Coiteux-Roy, O. Makuta, F. Curran, R. Augusiak, and M.-O. Renou, The genuinely multipartite nonlocality of graph states is model- dependent, npj Quant. Inf.11, 90 (2025)

    2025

  51. [62]

    Schrijver,Theory of Linear and Integer Programming, Wiley-Interscience Series in Discrete Mathematics and Optimization (John Wiley & Sons, Chichester, 1986)

    A. Schrijver,Theory of Linear and Integer Programming, Wiley-Interscience Series in Discrete Mathematics and Optimization (John Wiley & Sons, Chichester, 1986)

    1986

  52. [63]

    G. M. Ziegler,Lectures on Polytopes, Graduate Texts in Mathematics, V ol. 152 (Springer, New York, 1995)

    1995

Pith tools

Reviewed August 8, 2026 · model on record in the stance chip above.