Verifying full quantum network nonlocality in arbitrary configurations by nonlinear Bell-like inequalities

Jinchuan Hou; Kan He; Mingxing Luo; Shuyuan Yang

REVIEW 1 major objections 4 minor 34 references

Verifying full quantum network nonlocality in arbitrary configurations by nonlinear Bell-like inequalities

T0 review · 1 major / 4 minor · reviewed 2026-08-12 · deepseek-v4-flash

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

Pith's one-line read This paper claims that full quantum network nonlocality can be certified in any network topology by violating a single nonlinear Bell-like inequality after enlarging the network with auxiliary local sources and parties.

desk verdict Clever auxiliary-source construction, but Theorem 1 hinges on a false factorization step, so the central claim is unproven as written. read the letter →

arxiv 2608.10972 v1 pith:XW6OMVO7 submitted 2026-08-11 quant-ph

Shuyuan Yang , Jinchuan Hou , Kan He , Mingxing Luo This is my paper · ORCID

classification quant-ph MSC 81P40 PACS 03.65.Ud03.67.-a

keywords fullquantumnetworknonlocalityBell-likeinequalitiesnetworkshierarchicalindependentpartiesWernerstatesSLSQPoptimization

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

The paper claims that full quantum network nonlocality—the property that every source in a network must be nonlocal—can be certified with a single Bell-like inequality, regardless of network topology. The method enlarges the original network with a carefully counted number of auxiliary local sources and parties, then tests the enlarged network with one nonlinear inequality. If that inequality is violated, the enlarged network can contain at most a known number of local sources; because exactly that many local sources were intentionally inserted, all original sources must be nonlocal. This would replace the current practice of decomposing an arbitrary network into many star subnetworks and testing each separately.

What carries the argument

The central objects are independent parties (spatially separated parties sharing no common source), the independence number $h$ of the network, and the topological parameter $w$: the minimum number of local sources that forces some independent party to receive only local sources. The paper defines $N(n,m)=w-1$ from the source-sharing sets, adds that many auxiliary local sources and parties, and builds a nonlinear inequality whose left-hand side is an $h$-th-root sum of two correlation products $I$ and $J$ built from binary observables $A^\pm_{x_i}$. The bound $|I|^{1/h}+|J|^{1/h}\le 2^{(h-1)/(2h)}$ is tight enough to certify that a violating network has at most $w-1$ local sources.

What would settle it

Take the triangular-network construction of Example 1 and set all five sources in the enlarged network to local Werner states with $p_i=1/3$, then apply the same SLSQP optimization to inequality (2.7): if the left-hand side exceeds $2^{1/3}$, the claim that violation forces at most two local sources is false, and the central criterion collapses.

Watch

Extended reading notes

Core claim

The central claim is that full quantum network nonlocality of an arbitrary network $\Xi(n,m)$ can be certified by a single nonlinear Bell-like inequality, provided the network is first expanded to $\Xi_{\mathrm{new}}(n,m)$ by adding $N(n,m)$ auxiliary local sources and corresponding parties to a chosen non-independent party. With $h$ the independence number of the original network and $\Gamma$ a maximum independent set, the enlarged network has $h+N(n,m)$ independent parties and the test reads $|I_{\mathrm{gen}}|^{1/(h+N(n,m))}+|J_{\mathrm{gen}}|^{1/(h+N(n,m))}\le 2^{(h+N(n,m)-1)/(2(h+N(n,m)))}$. A violation means the enlarged network contains at most $w-1=N(n,m)$ local sources; since $N(n,m)$ local sources were deliberately inserted, every original source must be nonlocal. The authors present this as a constructive, topology-independent replacement for decomposing networks into star-shaped pieces.

Load-bearing premise

The argument hinges on assuming in Eq. (2.2) that one party's measurement statistics can be pulled out as a product from the rest of the network's statistics, and this is not guaranteed when that party shares a local source with the other parties; if that step fails, the derived inequality bound and the full-network-nonlocality certification do not follow.

Editorial extensions

If this is right

A single violation of one Bell-like inequality would certify full quantum network nonlocality for arbitrary network topologies, eliminating the need for repeated star-subnetwork tests.
For chain, cyclic, and tree-shaped networks, the construction specifies exactly how many auxiliary local sources and parties to add, so the test is directly implementable.
Numerical examples with Werner states of visibility around 0.9–0.96 and auxiliary local sources at $p=1/3$ violate the relevant inequalities, indicating a concrete experimental route.
If the criterion holds, it provides an efficient fault-detection tool for large quantum networks: one inequality would reveal whether any source has degenerated into a classical source.
The inequality parameter depends only on network topology, so for any given network the test can be precomputed from its source-sharing structure.

Reading between the lines

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

Beyond the paper's examples, the same expansion strategy could likely certify higher-level hierarchical network nonlocality by inserting $w-l$ auxiliary local sources and testing the corresponding $l$-level inequality; the authors only treat the $l=1$ full-nonlocality case.
The auxiliary-source count $N(n,m)$ depends on the chosen maximum independent set, so minimizing the overhead over valid choices is an open optimization problem the paper does not address.
Because the auxiliary sources are local classical resources, the added experimental cost is classical rather than quantum; whether the single-inequality search remains practical for much larger networks would require studying the scaling of the SLSQP optimization, which the paper does not do.

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.

Desk Editor's Note

read the letter

Colleague, here's my read of Yang et al. The idea is genuinely appealing: instead of decomposing a network into stars to certify full quantum network nonlocality, add auxiliary local sources and parties, then certify l-QNN with a single inequality. If it worked, it would remove a real experimental obstacle, and the construction is concrete—explicit N(n,m), explicit inequalities for chains, cycles, trees, and general networks. The paper is worth reading for that.

The problem is the proof of Theorem 1. Eq. (2.2) factorizes the independent party A_t from the rest of the network: |⟨A_t^+ B0⟩| ≤ |⟨A_t^+⟩| |⟨B0⟩| (and similarly with A_t^-). That step is false. 'Independent' here only means A_t shares no source with the other parties in Γ; it can share a local hidden variable with parties in Γ̄, which correlates A_t with B0. The stress-test counterexample works: in a triangle with h=1, a classical bit λ shared between A_t and a Γ̄ party, with A_xt = B0 = λ, gives |⟨A_t^+ B0⟩|=1 while |⟨A_t^+⟩||⟨B0⟩|=0. So Eq. (2.2) is not justified, and since the (h-1)-party reduction from Ref. [24] enters through that step, the w-QNL inequality (2.1) is not established. Corollary 5 and the examples inherit the gap.

Two more issues. Eq. (2.6) for w is asserted without proof; it may be true, but it's load-bearing because w sets the number of auxiliary sources and the inequality threshold. And the numerical violations are SLSQP maxima without global optimality certificates, with no code or explicit coefficients, so they are suggestive but not reproducible. That said, the failure is in the proof, not in the concept. The auxiliary-source reduction is new, and the examples show the intended logic clearly.

My take: this is a promising start that needs a real proof fix. I'd send it to a referee rather than desk reject—the construction deserves scrutiny, and a referee might see a way to salvage the inequality or at least document the gap for the authors. But as it stands, the central claim is unsupported.

Referee Report

1 major / 4 minor

Summary. The manuscript proposes a method to certify full quantum network nonlocality (FQNN) in arbitrary quantum networks by adding auxiliary local sources and parties, and then testing a single nonlinear Bell-like inequality on the enlarged network. The central theoretical result is Theorem 1, which asserts an l-QNL inequality for arbitrary networks, and Corollary 5, which uses this inequality to certify FQNN. The paper illustrates the method on triangular, chain, cyclic, and tree-shaped networks, using Werner states and SLSQP optimization to exhibit violations.

Significance. If Theorem 1 were correct, the paper would provide a significant advance: a single-inequality test for FQNN in arbitrary network topologies, improving on existing star-specific or decomposition-based methods. The constructive idea of adding auxiliary local sources to increase the independence number is appealing, and the paper contains explicit constructions for several network families. However, the central proof contains a load-bearing error in Eq. (2.2), and the paper does not provide a valid derivation of the main inequality. Consequently, the claimed FQNN certification criterion and all numerical demonstrations that rely on it are not established. The significance is therefore contingent on a substantial repair of the proof.

major comments (1)

[Section II, Eq. (2.2), proof of Theorem 1] The proof also states, immediately after Eq. (2.2), that removing the independent party A_t leaves a network that is (h−1)-independent. This is not true in general. For example, in the triangular network with h=1, removing the independent party A1 leaves parties A2 and A3 connected by a source, so the remaining network has independence number 1, not 0. In the 4-cycle with Γ={1,3}, removing vertex 1 leaves a path on vertices 2,3,4, which has independence number 2, not h−1=1. Therefore the appeal to Ref. [24] for an (h−1)-independent network is not valid when the remaining network has a larger independence number.

minor comments (4)

[Section II, Eq. (2.6)] The closed-form expression for w is asserted without proof. Since w appears in the right-hand side of Ineq. (2.1) and in the number of auxiliary sources to be added, this formula is load-bearing for the examples and Corollary 5. A derivation or an explicit reference is needed.
[Examples 1–5] The numerical results report SLSQP maxima (e.g., |I1|^{1/3}+|J1|^{1/3}=1.357 in Example 1) without providing the optimized measurement coefficients or a global optimality certificate. While a single explicit violating assignment would be sufficient to demonstrate a violation, as written the reader cannot verify the reported values. The statement in Example 1 that SLSQP 'can always' find suitable measurements is an unsupported heuristic claim.
[Section II, repeated paragraph] The paragraph beginning 'Based on the preceding analysis, we first introduce an l-QNL inequality...' appears twice verbatim in the text; one occurrence should be removed.
[Eq. (2.9)] There is a typographical error in Eq. (2.9): 'α11_{r1,r2}=0' should likely be 'α11_{r1,r2}', and the equation is missing the summation structure present in Eq. (2.8).

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the FQNN certification is a valid conditional inference, not a definitional reduction; the main flagged issue is the unjustified factorization in Eq. (2.2), a correctness gap rather than circularity.

full rationale

The FQNN certification argument is conditional: if the enlarged network Ξnew violates inequality (3.18), then by the contrapositive of Theorem 1 the enlarged network has at most w−1 = N(n,m) local sources; since N(n,m) auxiliary local sources were explicitly inserted, all original sources must be nonlocal. This is a genuine inference, not an equivalence by construction. Inequality (2.1) is a Bell-like bound on w-QNL correlations, not a definition of FQNN, so Corollary 5 does not define the target property into the inequality. The numerical examples use SLSQP to exhibit measurement settings that violate the inequalities for Werner states; they are existence demonstrations, not fitted parameters renamed as predictions. The main self-citation is Ref. [24] (coauthor Ming-Xing Luo), which supplies the (h−1)-independent network bound used in the proof of Theorem 1; it is load-bearing but is a published external PRL and is not a uniqueness theorem or ansatz, so it does not by itself make the derivation circular. A separate concern is that Eq. (2.2) factorizes |⟨A_t^+ B0⟩| ≤ |⟨A_t^+⟩| |⟨B0⟩| using only the statement 'A_t is independent'; this is not justified because A_t may share local sources with parties in Γ̄, so this is a major correctness gap in the proof, but it is not a circular reduction of the result to its inputs. Overall the paper contains minor self-citation and an unproven factorization step, but no step of the claimed derivation is equivalent to its inputs by construction; score 2 reflects the self-citation and the proof gap without treating them as circularity.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The central criterion borrows its bound from Ref. 24, relies on an unproved combinatorial formula for w, and uses hand-picked Werner visibilities and unverified SLSQP optima for the existence demonstrations.

free parameters (2)

Original-source Werner visibilities p_i = 0.90, 0.95, 0.96 in the examples
Chosen by hand to make the numerical violations work; not predicted by the theory.
SLSQP measurement coefficients = not reported
The numerical maxima rely on locally optimized measurements, but the coefficients are not given, so the demonstrations cannot be independently checked.

assumptions (4)

domain assumption Ref. 24 provides a bound of the form |...|^{1/(h-1)} + |...|^{1/(h-1)} <= sqrt(2) for any (h-1)-independent network.
Invoked in the proof of Theorem 1 without restating its hypotheses; it is an external theorem by one of the same authors.
ad hoc to paper For a chosen maximum independent set Γ, the value w from Eq. (2.6) is the minimal number of local sources that guarantees condition (P).
Combinatorial lemma asserted without proof; all FQNN conclusions depend on it.
domain assumption Auxiliary sources can be implemented as Werner states at p=1/3, which are local.
Standard local threshold for two-qubit Werner states; used to identify inserted sources as local.
ad hoc to paper SLSQP converges to a value above the bound, so a violation is certified.
The examples infer violation from local optimizer outputs without global optimality certificates.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Verifying full quantum network nonlocality in arbitrary configurations by nonlinear Bell-like inequalities." pith.science (2026). https://pith.science/paper/XW6OMVO7

@misc{pith2026260810972,
  author       = {Pith},
  title        = {Pith review of: Verifying full quantum network nonlocality in arbitrary configurations by nonlinear Bell-like inequalities},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XW6OMVO7}},
  note         = {Machine review of arXiv:2608.10972}
}

read the original abstract

Full quantum network nonlocality (FQNN) describes a scenario where all sources in a network are nonlocal. Existing criteria of FQNN can only be verified in star networks by violating a single Bell-like inequality. Here we propose a method that certifies FQNN in general quantum networks using only a single Bell-like inequality. We show that the topological obstacle to one-shot detection can be overcome by expanding the original network with a carefully chosen number of auxiliary local sources and parties. The correlations of the enlarged network are then tested with a single inequality; a violation implies that all original sources must be nonlocal. Our approach provides an efficient, experimentally friendly way to verify FQNN in any network topology.

Figures

Figures reproduced from arXiv: 2608.10972 by the authors.

**Figure 1.** The triangular quantum network consists of three sources and three parties: S1, S2, S3 and A1, A2, A3. The yellow circle represents the independent party. The source indicated by the red arrow is a local state, while (◦ · · · ◦) denotes a nonlocal state. (a) A triangular network comprising two nonlocal sources S1, S2 and one local source, where the local source is described by a hidden variable λ2. (b) A triangular … view at source ↗

**Figure 3.** (a) A cyclic network Ξ(n, n) composed of n parties and n sources. (b) The network Ξnew(n, n), which is formed by adding k auxiliary local sources and k auxiliary parties (AUX1, AUX2, . . . , AUXk) to a cyclic network Ξ(n, n). the parties with even indices are all independent. Thus, Γ = {2, 4, . . . , n}. Denote the remaining parties as Γ =¯ {1, 2, . . . , n}\Γ. If v ∈ Γ, then add ¯ n 2 auxiliary local sources and t… view at source ↗

**Figure 4.** The yellow circles in the figure represent independent parties. (a) A cyclic network Ξ(4, 4). (b) The network Ξnew(4, 4), which is formed by adding 2 auxiliary local sources and 2 auxiliary parties to a cyclic Ξ(4, 4). Corollary 3. The network Ξ(n, n) is FQNN if there are suitable measurements in Ξ new(n, n) such that the generated correlations violate the inequality |Icyce| 1 n + |Jcyce| 1 n ≤ 2 n−1 (3.14) 2n , whe… view at source ↗

Figures from the paper (3 more)

**Figure 5.** Figure 5: Ai1 , Ai2 , ..., Aih and Aj1 , Aj2 , ..., Ajn−h represent independent parties and non-independent parties, respectively, with the black lines indicating the sources shared among the parties. The schematic illustrates the newly formed network after adding N(n, m) additi…

**Figure 6.** Figure 6: (a) A network Ξ(4, 4) with the maximum independence number 2. (b) The new network Ξnew(4, 4) formed after adding two auxiliary local sources and two auxiliary parties. natural to assume its measurement strategy takes the specific form: Axr=0 = X 3 r1,r2,...,rt=0 α r0 …

**Figure 7.** Figure 7: (a) A network Ξ(7, 6) with the maximum independence number 5. (b) The new network Ξnew(7, 6) formed after adding one auxiliary local source and one auxiliary party. The additional party AUX1 is denoted as A8. By calculation, we can obtain N(4, 4) = 1 + 3 − 2 = 2. Sin…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

34 extracted references · 33 canonical work pages

[24]

Computationally efficient nonlinear bell inequalities for quantum networks.Phys

Ming-Xing Luo. Computationally efficient nonlinear bell inequalities for quantum networks.Phys. Rev. Lett., 120:140402, Apr 2018

work page 2018
[1]

Lago-Rivera, J

D. Lago-Rivera, J. V. Rakonjac, S. Grandi, et al. Long distance multiplexed quantum teleportation from a telecom photon to a solid-state qubit.Nature Communications, 14:1889, 2023

work page 2023
[2]

J. I. Cirac, A. K. Ekert, S. F. Huelga, and C. Macchiavello. Distributed quantum computation over noisy channels.Phys. Rev. A, 59:4249, 1999

work page 1999
[3]

Gisin and R

N. Gisin and R. Thew. Quantum communication.Nat. Photonics, 1:165–171, 2007

work page 2007
[4]

H. J. Kimble. The quantum internet.Nature, 453:1023–1030, 2008

2008
[5]

Scarani, Bechmann-Pasquinucci H., N

V. Scarani, Bechmann-Pasquinucci H., N. J. Cerf, M. Duˇ sek, N. L¨ utkenhaus, and M. Peev. The security of practical quantum key distribution.Rev. Mod. Phys., 81:1301, 2009

work page 2009
[6]

T. J. Proctor, P. A. Knott, and J. A. Dunningham. Multi-parameter estimation in networked quantum sensors.Phys. Rev. Lett., 120:080501, 2018

work page 2018
[7]

F. Xu, X. Ma, Q. Zhang, H. K. Lo, and J. W Pan. Secure quantum key distribution with realistic devices.Rev. Mod. Phys., 92:025002, 2020

work page 2020

Show all 34 references

[8]

Y. A. Chen, Q. Z. Zhang, T. Y. Chen, S. K. Liao, et al. An integrated space-to-ground quantum communication network over 4,600 kilometres.Nature, 589:214–219, 2021

2021
[9]

Zhang and Q

Z. Zhang and Q. Zhang. Distributed quantum sensing.Quantum Sci. Technol., 6:043001, 2021

2021
[10]

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

1969
[11]

Bell non- locality in networks.Reports on Progress in Physics, 85(5):056001, mar 2022

Armin Tavakoli, Alejandro Pozas-Kerstjens, Ming-Xing Luo, and Marc-Olivier Renou. Bell non- locality in networks.Reports on Progress in Physics, 85(5):056001, mar 2022

2022
[12]

Entanglement witnesses constructed by permutation pairs

Jin-Chuan Hou and Wen-Li Wang. Entanglement witnesses constructed by permutation pairs. Acta Math. Sci., 41:843–874, 2021

2021
[13]

Positive maps constructed from permutation pairs.Acta Math

Jin-Chuan Hou and Hai-Li Zhao. Positive maps constructed from permutation pairs.Acta Math. Sci., 39:148–164, 2019

2019
[14]

Branciard, N

C. Branciard, N. Gisin, and S. Pironio. Characterizing the nonlocal correlations created via en- tanglement swapping.Phys. Rev. Lett., 104:170401, Apr 2010

2010
[15]

Bilocal versus nonbilocal cor- relations in entanglement-swapping experiments.Phys

Cyril Branciard, Denis Rosset, Nicolas Gisin, and Stefano Pironio. Bilocal versus nonbilocal cor- relations in entanglement-swapping experiments.Phys. Rev. A, 85:032119, Mar 2012

2012
[16]

Mukherjee, B

K. Mukherjee, B. Paul, and D. Sarkar. Correlations inn-local scenario.Quantum Inf Process, 14:2025–2042, June 2015. VERIFYING FULL QUANTUM NETWORK NONLOCALITY IN ARBITRARY CONFIGURATIONS BY NONLINEAR BELL-LIKE INEQUALITIES 19

2025
[17]

Maximal qubit violation ofn-local inequalities in a quantum network.Phys

Amit Kundu, Mostak Kamal Molla, Indrani Chattopadhyay, and Debasis Sarkar. Maximal qubit violation ofn-local inequalities in a quantum network.Phys. Rev. A, 102:052222, Nov 2020

2020
[18]

Nonlocal correlations in the star-network configuration.Phys

Armin Tavakoli, Paul Skrzypczyk, Daniel Cavalcanti, and Antonio Ac ´ ın. Nonlocal correlations in the star-network configuration.Phys. Rev. A, 90:062109, Dec 2014

2014
[19]

Genuine quantum nonlocality in the triangle network.Phys

Marc-Olivier Renou, Elisa B¨ aumer, Sadra Boreiri, Nicolas Brunner, Nicolas Gisin, and Salman Beigi. Genuine quantum nonlocality in the triangle network.Phys. Rev. Lett., 123:140401, Sep 2019

2019
[20]

Jing, X.J

B. Jing, X.J. Wang, Y. Yu, P.F. Sun, Y. Jiang, S.J. Yang, W.H. Jiang, X.Y. Luo, J. Zhang, X. Jiang, X.H. Bao, and J.W. Pan. Entanglement of three quantum memories via interference of three single photons.Nature Photonics, 13:210–213, March 2019

2019
[21]

Nonlocal correlations in the tree-tensor-network con- figuration.Phys

Lihua Yang, Xiaofei Qi, and Jinchuan Hou. Nonlocal correlations in the tree-tensor-network con- figuration.Phys. Rev. A, 104:042405, Oct 2021

2021
[22]

Polynomial bell inequalities.Phys

Rafael Chaves. Polynomial bell inequalities.Phys. Rev. Lett., 116:010402, Jan 2016

2016
[23]

Bell-type inequalities for arbitrary noncyclic networks.Phys

Armin Tavakoli. Bell-type inequalities for arbitrary noncyclic networks.Phys. Rev. A, 93:030101, Mar 2016

2016
[25]

Full network nonlocality.Phys

Alejandro Pozas-Kerstjens, Nicolas Gisin, and Armin Tavakoli. Full network nonlocality.Phys. Rev. Lett., 128:010403, Jan 2022

2022
[26]

Lee and Matty J

Ciar´ an M. Lee and Matty J. Hoban. Towards device-independent information processing on general quantum networks.Phys. Rev. Lett., 120:020504, Jan 2018

2018
[27]

Quantum random number generators

Miguel Herrero-Collantes and Juan Carlos Garcia-Escartin. Quantum random number generators. Rev. Mod. Phys., 89:015004, Feb 2017

2017
[28]

Piveteau E

A. Piveteau E. H ˚ akansson, S. Muhammad, and M. Bourennane. Experimental demonstration of full network nonlocality in the bilocal scenario.Arxiv, 2022

2022
[29]

Entanglement swapping and quantum correlations via symmetric joint measurements.Phys

Cen-Xiao Huang, Xiao-Min Hu, Yu Guo, Chao Zhang, Bi-Heng Liu, Yun-Feng Huang, Chuan-Feng Li, Guang-Can Guo, Nicolas Gisin, Cyril Branciard, and Armin Tavakoli. Entanglement swapping and quantum correlations via symmetric joint measurements.Phys. Rev. Lett., 129:030502, Jul 2022

2022
[30]

Experimental full network nonlocality with independent sources and strict locality con- straints.Phys

Xue-Mei Gu, Liang Huang, Alejandro Pozas-Kerstjens, Yang-Fan Jiang, Dian Wu, Bing Bai, Qi- Chao Sun, Ming-Cheng Chen, Jun Zhang, Sixia Yu, Qiang Zhang, Chao-Yang Lu, and Jian-Wei Pan. Experimental full network nonlocality with independent sources and strict locality con- strai...

2023
[31]

N.-N. Wang, A. Pozas-Kerstjens, C. Zhang, B.-H. Liu, Y.-F. Huang, C.-F. Li, G.-C. Guo, N. Gisin, and A. Tavakoli. Certification of non-classicality in all links of a photonic star network without assuming quantum mechanics.Nature Communications, 14:2153, April 2023

2023
[32]

Hierarchical certification of nonclas- sical network correlations.Phys

Ming-Xing Luo, Xue Yang, and Alejandro Pozas-Kerstjens. Hierarchical certification of nonclas- sical network correlations.Phys. Rev. A, 110:022617, Aug 2024

2024
[33]

Verifying hierarchic multipartite and network nonlocalities with a unified method.Advanced Quantum Technologies, page 202400021, 2024

Ming-Xing Luo and Shao-Ming Fei. Verifying hierarchic multipartite and network nonlocalities with a unified method.Advanced Quantum Technologies, page 202400021, 2024. Article number 202400021

2024
[34]

Verifying hierarchical network nonlocality in general quantum networks.Chinese Physics B, 33(7):070304, jun 2024

Shu-Yuan Yang, Jin-Chuan Hou, and Kan He. Verifying hierarchical network nonlocality in general quantum networks.Chinese Physics B, 33(7):070304, jun 2024. 20 SHUYUAN YANG, JINCHUAN HOU, KAN HE ∗, MINGXING LUO∗ (Shuyuan Yang)School of Mathematics, North University of China, Ta...

2024

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.

[1] [24]

Computationally efficient nonlinear bell inequalities for quantum networks.Phys

Ming-Xing Luo. Computationally efficient nonlinear bell inequalities for quantum networks.Phys. Rev. Lett., 120:140402, Apr 2018

work page 2018

[2] [1]

Lago-Rivera, J

D. Lago-Rivera, J. V. Rakonjac, S. Grandi, et al. Long distance multiplexed quantum teleportation from a telecom photon to a solid-state qubit.Nature Communications, 14:1889, 2023

work page 2023

[3] [2]

J. I. Cirac, A. K. Ekert, S. F. Huelga, and C. Macchiavello. Distributed quantum computation over noisy channels.Phys. Rev. A, 59:4249, 1999

work page 1999

[4] [3]

Gisin and R

N. Gisin and R. Thew. Quantum communication.Nat. Photonics, 1:165–171, 2007

work page 2007

[5] [4]

H. J. Kimble. The quantum internet.Nature, 453:1023–1030, 2008

2008

[6] [5]

Scarani, Bechmann-Pasquinucci H., N

V. Scarani, Bechmann-Pasquinucci H., N. J. Cerf, M. Duˇ sek, N. L¨ utkenhaus, and M. Peev. The security of practical quantum key distribution.Rev. Mod. Phys., 81:1301, 2009

work page 2009

[7] [6]

T. J. Proctor, P. A. Knott, and J. A. Dunningham. Multi-parameter estimation in networked quantum sensors.Phys. Rev. Lett., 120:080501, 2018

work page 2018

[8] [7]

F. Xu, X. Ma, Q. Zhang, H. K. Lo, and J. W Pan. Secure quantum key distribution with realistic devices.Rev. Mod. Phys., 92:025002, 2020

work page 2020