pith. sign in

arxiv: 2510.12022 · v2 · submitted 2025-10-14 · 🪐 quant-ph

Harnessing Non-convex Quantum Correlations of Independent Qubits

Liang-Liang Sun , Xiang Zhou , Chengjie Zhang , Zizhu Wang , Yong-Shun Song , Sixia Yu This is my paper

Pith reviewed 2026-05-18 08:01 UTC · model grok-4.3

classification 🪐 quant-ph
keywords quantum correlationsnon-convex setsuncertainty relationsBell scenariosprepare-and-measureentanglement certificationdevice inferencemoment-matrix methods
0
0 comments X

The pith

Uncertainty relations supply state-independent linear constraints that test non-convex qubit correlation sets in prepare-and-measure and Bell experiments.

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

The paper shows that uncertainty relations for independent qubits produce linear constraints on observed correlation vectors that hold regardless of the underlying state. These constraints form a practical consistency test for statistics collected without run-to-run mixing. The test identifies non-convex boundaries in standard correlation families and can fix or narrow the possible unitary-invariant parameters of the measurement devices. Adding the same constraints to moment-matrix methods tightens separability checks and detects entanglement in some cases where standard Bell inequalities are satisfied.

Core claim

Uncertainty relations can be converted into state-independent linear constraints on correlation vectors that arise from independent qubits; the resulting test detects explicit non-convex boundaries, constrains or determines measurement parameters from observed statistics, and, when inserted into moment-matrix relaxations, strengthens entanglement certification even inside the Bell-local region of the independent-device model.

What carries the argument

State-independent linear constraints on correlation vectors obtained by translating qubit uncertainty relations into consistency conditions on prepare-and-measure and Bell statistics.

If this is right

  • The test marks explicit non-convex boundaries inside representative families of qubit correlations.
  • Observed statistics can constrain or uniquely fix unitary-invariant measurement parameters away from extreme points.
  • The inferred constraints tighten moment-matrix relaxations and certify entanglement for certain Bell-local correlations under the independent-device model.
  • The same constraints apply uniformly to both prepare-and-measure and Bell scenarios.

Where Pith is reading between the lines

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

  • Similar uncertainty-derived constraints could be constructed for other low-dimensional systems once appropriate uncertainty relations are available.
  • The constraints may supply additional witnesses for randomness generation protocols that rely on observed correlations.
  • Combining the test with existing device-independent frameworks could reduce the resources needed for entanglement verification in small devices.

Load-bearing premise

The measured statistics are produced by independent qubits with no shared public randomness across experimental runs, and uncertainty relations translate directly into linear constraints without further device modeling.

What would settle it

A set of correlation vectors generated by actual independent qubits that violates one or more of the derived linear constraints would falsify the claimed test.

Figures

Figures reproduced from arXiv: 2510.12022 by Chengjie Zhang, Liang-Liang Sun, Sixia Yu, Xiang Zhou, Yong-Shun Song, Zizhu Wang.

Figure 2
Figure 2. Figure 2: FIG. 2. Characterizing correlations [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Figures of [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
read the original abstract

Quantum correlations in Bell and prepare-and-measure experiments are central resources for probing nonclassicality and enabling device-based quantum information protocols. In the absence of shared public randomness (i.e., without run-to-run mixing), even qubit correlation sets are typically non-convex, making standard convex characterizations inadequate. Here we derive qubit-specific constraints from uncertainty relations, yielding a state-independent consistency test for observed statistics in both prepare-and-measure and Bell scenarios. The test captures explicit non-convex boundaries in representative correlation families and enables correlation-based device inference by constraining (and sometimes uniquely determining) unitary-invariant measurement parameters even away from extreme points. Moreover, incorporating the inferred qubit constraints as additional conditions in a moment-matrix relaxation strengthens separability tests and can certify entanglement even for Bell-local correlations within the independent-device model. These tools provide a practical route to characterize and leverage low-dimensional quantum devices, including certification, randomness generation, and entanglement verification.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The manuscript derives state-independent linear constraints on correlation vectors for independent qubits from uncertainty relations. These yield a consistency test for observed statistics in prepare-and-measure and Bell scenarios, capture explicit non-convex boundaries in representative correlation families, enable correlation-based inference of unitary-invariant measurement parameters, and strengthen separability tests when incorporated into moment-matrix relaxations, allowing entanglement certification even for some Bell-local correlations within the independent-device model.

Significance. If the derivations hold, the work provides practical tools for characterizing non-convex qubit correlation sets in the absence of shared public randomness, with direct applications to device certification, randomness generation, and entanglement verification. It addresses a genuine limitation of convex relaxations for low-dimensional quantum devices and offers falsifiable consistency tests grounded in uncertainty relations.

major comments (1)
  1. [§3 (main derivation)] §3 (or the section presenting the main derivation): The translation of qubit uncertainty relations (e.g., variance bounds on Pauli observables) into state-independent linear inequalities directly on the observed correlation vector is load-bearing for the non-convexity claim, the consistency test, and all downstream applications. The manuscript must supply the explicit intermediate algebraic steps showing how nonlinear, potentially state-dependent bounds are converted to linear, state-independent constraints for arbitrary unitary-invariant measurements; without this, it is unclear whether hidden state dependence or nonlinearity remains, which would undermine the device-inference and strengthened separability results.
minor comments (2)
  1. [Figure 2] Figure 2 (or the figure illustrating non-convex boundaries): The caption should explicitly label which correlation families are plotted and indicate the source of the data points (experimental or simulated) to allow readers to assess the claimed capture of non-convex boundaries.
  2. [Notation] Notation section: The symbol for the correlation vector (likely denoted something like C or vec) should be defined at its first appearance rather than assumed from context, to improve accessibility for readers outside the immediate subfield.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful and constructive review. The major comment correctly identifies that greater explicitness in the algebraic derivation of the state-independent constraints would improve transparency and strengthen the manuscript. We have revised the paper by expanding §3 with the requested intermediate steps, while preserving all original claims.

read point-by-point responses

  1. Referee: [§3 (main derivation)] §3 (or the section presenting the main derivation): The translation of qubit uncertainty relations (e.g., variance bounds on Pauli observables) into state-independent linear inequalities directly on the observed correlation vector is load-bearing for the non-convexity claim, the consistency test, and all downstream applications. The manuscript must supply the explicit intermediate algebraic steps showing how nonlinear, potentially state-dependent bounds are converted to linear, state-independent constraints for arbitrary unitary-invariant measurements; without this, it is unclear whether hidden state dependence or nonlinearity remains, which would undermine the device-inference and strengthened separability results.

    Authors: We agree that the intermediate algebraic steps deserve fuller exposition. In the revised manuscript we have inserted a dedicated derivation subsection (now §3.1) that proceeds as follows. Begin with the qubit uncertainty relation for three Pauli observables X, Y, Z on a state ρ: Var_ρ(X) + Var_ρ(Y) + Var_ρ(Z) ≥ 1. For a unitary-invariant measurement setting the observables are rotated Paulis U σ_i U†. The correlation vector c collects the expectation values ⟨A_i⟩ or ⟨A_i ⊗ B_j⟩. Substituting the Bloch-vector representation of ρ and expanding the variances yields quadratic terms in the Bloch components; these are then bounded from below by taking the infimum over all Bloch vectors consistent with the observed c. Because the measurement unitaries are arbitrary but fixed, the resulting lower bound simplifies to a linear inequality in the components of c alone, with no residual dependence on the unknown state. The same reduction holds for the prepare-and-measure and Bell cases. We have included every intermediate expression (variance expansion, Bloch substitution, and infimum evaluation) so that the absence of hidden state dependence or nonlinearity is now fully transparent. These added steps directly support the non-convexity, consistency-test, device-inference, and strengthened separability claims. revision: yes

Circularity Check

0 steps flagged

Derivation starts from uncertainty relations and remains independent of target correlation geometry

full rationale

The paper derives qubit-specific constraints directly from uncertainty relations on Pauli observables and translates them into state-independent linear inequalities on observed correlation vectors. This step is presented as a first-principles mapping rather than a fit or redefinition of the non-convex set itself. No equations reduce the claimed consistency test, device inference, or strengthened moment-matrix relaxations back to the target non-convex boundaries by construction. Self-citations, if present, are not load-bearing for the central derivation; the abstract and described chain begin from standard uncertainty relations without invoking prior results by the same authors to forbid alternatives or smuggle in the ansatz. The derivation is therefore self-contained against external benchmarks and does not exhibit any of the enumerated circularity patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

With only the abstract available, the ledger is populated from explicit statements in the abstract. The central claim rests on translating uncertainty relations into correlation constraints for independent qubits.

axioms (2)
  • domain assumption Uncertainty relations can be translated into state-independent linear constraints on observed correlation statistics for qubits.
    Invoked to derive the consistency test for prepare-and-measure and Bell scenarios.
  • domain assumption Absence of shared public randomness across experimental runs.
    Stated as the condition under which qubit correlation sets are typically non-convex.

pith-pipeline@v0.9.0 · 5697 in / 1260 out tokens · 26862 ms · 2026-05-18T08:01:03.746885+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

64 extracted references · 64 canonical work pages

  1. [2]

    Herbert, Cryptographic approach to hidden variables, Amer- ican Journal of Physics43, 315 (1975)

    N. Herbert, Cryptographic approach to hidden variables, Amer- ican Journal of Physics43, 315 (1975). 6

    work page 1975

  2. [4]

    A. K. Ekert, Quantum cryptography based on bell’s theorem, Phys. Rev. Lett.67, 661 (1991)

    work page 1991

  3. [5]

    Joseph, R

    D. Joseph, R. Misoczki, M. Manzano, J. Tricot, F. D. Pinu- aga, O. Lacombe, S. Leichenauer, J. Hidary, P. Venables, and R. Hansen, Transitioning organizations to post-quantum cryp- tography, Nature605, 237 (2022)

    work page 2022

  4. [6]

    A. Acín, S. Massar, and S. Pironio, Efficient quantum key distri- bution secure against no-signalling eavesdroppers, New J. Phys. 8, 126 (2006)

    work page 2006

  5. [7]

    Zhong, H

    H.-S. Zhong, H. Wang, Y .-H. Deng, M.-C. Chen, L.- C. Peng, Y .-H. Luo, J. Qin, D. Wu, X. Ding, Y . Hu, P. Hu, X.-Y . Yang, W.-J. Zhang, H. Li, Y . Li, X. Jiang, L. Gan, G. Yang, L. You, Z. Wang, L. Li, N.- L. Liu, C.-Y . Lu, and J.-W. Pan, Quantum computa- tional advantage using photons, Science370, 1460 (2020), https://www.science.org/doi/pdf/10.1126/sc...

    work page doi:10.1126/science.abe8770 2020

  6. [8]

    C. H. Bennett, G. Brassard, and N. D. Mermin, Quantum cryptography without bell’s theorem, Phys. Rev. Lett.68, 557 (1992)

    work page 1992

  7. [9]

    Buhrman, R

    H. Buhrman, R. Cleve, S. Massar, and R. de Wolf, Nonlocal- ity and communication complexity, Rev. Mod. Phys.82, 665 (2010)

    work page 2010

  8. [10]

    Pelucchi, G

    E. Pelucchi, G. Fagas, I. Aharonovich, D. Englund, E. Figueroa, Q. Gong, H. Hannes, J. Liu, C.-Y . Lu, N. Matsuda, J.-W. Pan, F. Schreck, F. Sciarrino, C. Silberhorn, J. Wang, and K. D. Jöns, The potential and global outlook of integrated photonics for quantum technologies, Nat. Rev. Phys.4, 194 (2022)

    work page 2022

  9. [11]

    J. J. Pla, K. Y . Tan, J. P. Dehollain, W. H. Lim, J. J. L. Mor- ton, F. A. Zwanenburg, D. N. Jamieson, A. S. Dzurak, and A. Morello, High-fidelity readout and control of a nuclear spin qubit in silicon, Nature496, 334 (2013)

    work page 2013

  10. [12]

    L. M. K. Vandersypen and I. L. Chuang, Nmr techniques for quantum control and computation, Rev. Mod. Phys.76, 1037 (2005)

    work page 2005

  11. [13]

    Devetak and A

    I. Devetak and A. Winter, Distillation of secret key and entan- glement from quantum states, Proc. R. Soc. A461, 207 (2005)

    work page 2005

  12. [14]

    Kloeffel and D

    C. Kloeffel and D. Loss, Prospects for spin-based quantum computing in quantum dots, Annu. Rev. Condens. Matter Phys. 4, 51 (2013)

    work page 2013

  13. [15]

    C. D. Bruzewicz, J. Chiaverini, R. McConnell, and J. M. Sage, Trapped-ion quantum computing: Progress and challenges, Appl. Phys. Rev.6, 021314 (2019)

    work page 2019

  14. [16]

    Saffman, Quantum computing with atomic qubits and ryd- berg interactions: progress and challenges, J

    M. Saffman, Quantum computing with atomic qubits and ryd- berg interactions: progress and challenges, J. Phys. B: At. Mol. Opt. Phys.49, 202001 (2016)

    work page 2016

  15. [17]

    Zhou, P.-F

    J.-W. Zhou, P.-F. Wang, F.-Z. Shi, P. Huang, X. Kong, X.-K. Xu, Q. Zhang, Z.-X. Wang, X. Rong, and J.-F. Du, Quantum information processing and metrology with color centers in di- amonds, Front. Phys.9, 587 (2014)

    work page 2014

  16. [18]

    M. W. Doherty, N. B. Manson, P. Delaney, F. Jelezko, J. Wrachtrup, and L. C. Hollenberg, The nitrogen-vacancy colour centre in diamond, Phys. Rep.528, 1 (2013)

    work page 2013

  17. [19]

    S. D. Sarma, M. Freedman, and C. Nayak, Majorana zero modes and topological quantum computation, npj Quantum In- formation1, 15001 (2015)

    work page 2015

  18. [20]

    W. Cong, Y . Cai, J.-D. Bancal, and V . Scarani, Witnessing irre- ducible dimension, Phys. Rev. Lett.119, 080401 (2017)

    work page 2017

  19. [21]

    Wehner, M

    S. Wehner, M. Christandl, and A. C. Doherty, Lower bound on the dimension of a quantum system given measured data, Phys. Rev. A78, 062112 (2008)

    work page 2008

  20. [22]

    K. F. Pál and T. Vértesi, Concavity of the set of quantum prob- abilities for any given dimension, Phys. Rev. A80, 042114 (2009)

    work page 2009

  21. [23]

    J. M. Donohue and E. Wolfe, Identifying nonconvexity in the sets of limited-dimension quantum correlations, Phys. Rev. A 92, 062120 (2015)

    work page 2015

  22. [24]

    B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, Simplifying quantum logic using higher- dimensional hilbert spaces, Nat. Phys.5, 134 (2009)

    work page 2009

  23. [25]

    Luo, H.-S

    Y .-H. Luo, H.-S. Zhong, M. Erhard, X.-L. Wang, L.-C. Peng, M. Krenn, X. Jiang, L. Li, N.-L. Liu, C.-Y . Lu, A. Zeilinger, and J.-W. Pan, Quantum teleportation in high dimensions, Phys. Rev. Lett.123, 070505 (2019)

    work page 2019

  24. [26]

    E. T. Campbell, Enhanced fault-tolerant quantum computing in d-level systems, Phys. Rev. Lett.113, 230501 (2014)

    work page 2014

  25. [27]

    Collins, N

    D. Collins, N. Gisin, N. Linden, S. Massar, and S. Popescu, Bell inequalities for arbitrarily high-dimensional systems, Phys. Rev. Lett.88, 040404 (2002)

    work page 2002

  26. [28]

    A. Acín, N. Gisin, and L. Masanes, From bell’s theorem to secure quantum key distribution, Phys. Rev. Lett.97, 120405 (2006)

    work page 2006

  27. [29]

    Woodhead and S

    E. Woodhead and S. Pironio, Secrecy in prepare-and-measure clauser-horne-shimony-holt tests with a qubit bound, Phys. Rev. Lett.115, 150501 (2015)

    work page 2015

  28. [30]

    ˙Zukowski and i

    M. ˙Zukowski and i. c. v. Brukner, Bell’s theorem for general n-qubit states, Phys. Rev. Lett.88, 210401 (2002)

    work page 2002

  29. [31]

    Kraus, N

    B. Kraus, N. Gisin, and R. Renner, Lower and upper bounds on the secret-key rate for quantum key distribution protocols using one-way classical communication, Phys. Rev. Lett.95, 080501 (2005)

    work page 2005

  30. [32]

    Pérez-García, M

    D. Pérez-García, M. M. Wolf, C. Palazuelos, I. Villanueva, and M. Junge, Unbounded violation of tripartite bell inequalities, Commun. Math. Phys.279, 455 (2008)

    work page 2008

  31. [33]

    Junge, C

    M. Junge, C. Palazuelos, D. Pérez-García, I. Villanueva, and M. M. Wolf, Operator space theory: A natural framework for bell inequalities, Phys. Rev. Lett.104, 170405 (2010)

    work page 2010

  32. [34]

    Epping, H

    M. Epping, H. Kampermann, and D. Bruß, Designing bell in- equalities from a tsirelson bound, Phys. Rev. Lett.111, 240404 (2013)

    work page 2013

  33. [35]

    Brunner, S

    N. Brunner, S. Pironio, A. Acin, N. Gisin, A. A. Méthot, and V . Scarani, Testing the dimension of hilbert spaces, Phys. Rev. Lett.100, 210503 (2008)

    work page 2008

  34. [36]

    Navascués, G

    M. Navascués, G. de la Torre, and T. Vértesi, Characterization of quantum correlations with local dimension constraints and its device-independent applications, Phys. Rev. X4, 011011 (2014)

    work page 2014

  35. [37]

    Navascués and T

    M. Navascués and T. Vértesi, Bounding the set of finite di- mensional quantum correlations, Phys. Rev. Lett.115, 020501 (2015)

    work page 2015

  36. [38]

    Pauwels, S

    J. Pauwels, S. Pironio, E. Woodhead, and A. Tavakoli, Almost qudits in the prepare-and-measure scenario, Phys. Rev. Lett. 129, 250504 (2022)

    work page 2022

  37. [39]

    Navascués, A

    M. Navascués, A. Feix, M. Araújo, and T. Vértesi, Character- izing finite-dimensional quantum behavior, Phys. Rev. A92, 042117 (2015)

    work page 2015

  38. [40]

    Mironowicz, H.-W

    P. Mironowicz, H.-W. Li, and M. Pawłowski, Properties of di- mension witnesses and their semidefinite programming relax- ations, Phys. Rev. A90, 022322 (2014)

    work page 2014

  39. [41]

    Mironowicz and M

    P. Mironowicz and M. Pawłowski, Experimentally feasi- ble semi-device-independent certification of four-outcome positive-operator-valued measurements, Phys. Rev. A100, 030301 (2019). 7

    work page 2019

  40. [42]

    E. S. Gómez, S. Gómez, P. González, G. Cañas, J. F. Barra, A. Delgado, G. B. Xavier, A. Cabello, M. Kleinmann, T. Vértesi, and G. Lima, Device-independent certification of a nonprojective qubit measurement, Phys. Rev. Lett.117, 260401 (2016)

    work page 2016

  41. [43]

    Crystal time-reversal symmetry breaking and spontaneous hall effect in collinear anti- ferromagnets,

    A. Tavakoli, M. Smania, T. Vértesi, N. Brunner, and M. Bouren- nane, Self-testing nonprojective quantum measurements in prepare-and-measure experiments, Sci. Adv.6, 10.1126/sci- adv.aaw6664 (2020)

    work page doi:10.1126/sci- 2020

  42. [44]

    Miklin, J

    N. Miklin, J. J. Borkała, and M. Pawłowski, Semi-device- independent self-testing of unsharp measurements, Phys. Rev. Res.2, 033014 (2020)

    work page 2020

  43. [45]

    E. A. Aguilar, J. J. Borkała, P. Mironowicz, and M. Pawłowski, Connections between mutually unbiased bases and quantum random access codes, Phys. Rev. Lett.121, 050501 (2018)

    work page 2018

  44. [46]

    Tavakoli, A

    A. Tavakoli, A. Pozas-Kerstjens, P. Brown, and M. Araújo, Semidefinite programming relaxations for quantum correla- tions, Rev. Mod. Phys.96, 10.1103/revmodphys.96.045006 (2024)

    work page doi:10.1103/revmodphys.96.045006 2024

  45. [47]

    Bowles, M

    J. Bowles, M. T. Quintino, and N. Brunner, Certifying the di- mension of classical and quantum systems in a prepare-and- measure scenario with independent devices, Phys. Rev. Lett. 112, 140407 (2014)

    work page 2014

  46. [48]

    Sikora, A

    J. Sikora, A. Varvitsiotis, and Z. Wei, Minimum dimension of a hilbert space needed to generate a quantum correlation, Phys. Rev. Lett.117, 060401 (2016)

    work page 2016

  47. [49]

    X.-D. Yu, I. Veeren, and O. Gühne, Characterizing high- dimensional quantum contextuality, Phys. Rev. A109, L030201 (2024)

    work page 2024

  48. [50]

    J. I. de Vicente, Shared randomness and device-independent dimension witnessing, Physical Review A95, 10.1103/phys- reva.95.012340 (2017)

    work page doi:10.1103/phys- 2017

  49. [51]

    Y . Mao, C. Spee, Z.-P. Xu, and O. Gühne, Structure of dimension-bounded temporal correlations, Phys. Rev. A105, L020201 (2022)

    work page 2022

  50. [52]

    Lunghi, J

    T. Lunghi, J. B. Brask, C. C. W. Lim, Q. Lavigne, J. Bowles, A. Martin, H. Zbinden, and N. Brunner, Self-testing quantum random number generator, Phys. Rev. Lett.114, 150501 (2015)

    work page 2015

  51. [53]

    L.-L. Sun, X. Zhang, X. Zhou, Z.-D. Li, X. Ma, J.-Y . Fan, and S. Yu, Certifying quantum randomness with disturbance, Phys. Rev. A111, 042210 (2025)

    work page 2025

  52. [54]

    T. P. Le, C. Meroni, B. Sturmfels, R. F. Werner, and T. Ziegler, Quantum Correlations in the Minimal Scenario, Quantum7, 947 (2023)

    work page 2023

  53. [55]

    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)

    work page 1935

  54. [56]

    Brunner, D

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

    work page 2014

  55. [57]

    Popescu and D

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

    work page 1994

  56. [58]

    van Dam, Implausible consequences of superstrong nonlo- cality, Natural Computing12, 9 (2013)

    W. van Dam, Implausible consequences of superstrong nonlo- cality, Natural Computing12, 9 (2013)

    work page 2013

  57. [59]

    Oppenheim and S

    J. Oppenheim and S. Wehner, The uncertainty principle de- termines the nonlocality of quantum mechanics, Science330, 1072 (2010)

    work page 2010

  58. [60]

    Sun, Y .-S

    L.-L. Sun, Y .-S. Song, S. Yu, and Z.-B. Chen, Nonlocality under uncertainty-disturbance relations and self-duality, Phys. Rev. A 106, 032213 (2022)

    work page 2022

  59. [61]

    Zhou, L.-L

    X. Zhou, L.-L. Sun, and S. Yu, Quantum nonlocality deter- mined by fine-grained uncertainty relations, Phys. Rev. A109, 022408 (2024)

    work page 2024

  60. [62]

    Hsu, Statistical link between bell nonlocality and uncer- tainty relations in quantum mechanics, Ann

    L.-Y . Hsu, Statistical link between bell nonlocality and uncer- tainty relations in quantum mechanics, Ann. Phys.537, e00049 (2025)

    work page 2025

  61. [63]

    Li and C.-F

    J.-L. Li and C.-F. Qiao, Reformulating the quantum uncertainty relation, Sci. Rep.5, 12708 (2015)

    work page 2015

  62. [64]

    Navascués, S

    M. Navascués, S. Pironio, and A. Acín, Bounding the set of quantum correlations, Phys. Rev. Lett.98, 010401 (2007)

    work page 2007

  63. [65]

    Drótos, K

    G. Drótos, K. F. Pál, A. Taoutioui, and T. Vértesi, Towards min- imal self-testing of qubit states and measurements in prepare- and-measure scenarios, New J. Phys.26, 063012 (2024)

    work page 2024

  64. [66]

    Smania, P

    M. Smania, P. Mironowicz, M. Nawareg, M. Pawłowski, A. Ca- bello, and M. Bourennane, Experimental certification of an informationally complete quantum measurement in a device- independent protocol, Optica7, 123 (2020). IV . BOUNDING CORRELA TION WITH UNCERTAINTY RELA TION A. Correlation with and without public randomness When random number{λ, p(λ)}are sha...

    work page 2020