pith. sign in

arxiv: 2607.01193 · v1 · pith:IID32LJPnew · submitted 2026-07-01 · 🪐 quant-ph

Non-signaling assistance in prepare-and-measure scenarios with classical communication

Jos\'e Nogueira , Carlos Vieira , Lucas E. A. Porto , Lucas Pollyceno , Rafael Rabelo , Otfried G\"uhne This is my paper

Pith reviewed 2026-07-02 11:28 UTC · model grok-4.3

classification 🪐 quant-ph
keywords non-signaling assistanceprepare-and-measure scenariosadaptive strategiesclassical communicationquantum simulationqudit transmissionnon-local correlations
0
0 comments X

The pith

Non-adaptive non-signaling assistance with a classical dit simulates the transmission of a qudit in prepare-and-measure scenarios.

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

The paper gives explicit characterizations of all behaviors achievable in prepare-and-measure scenarios when the receiver is assisted by non-signaling correlations, distinguishing the non-adaptive case from the adaptive case. These characterizations establish that non-adaptive assistance already reaches the full power of quantum communication using a message of the same dimension. The results also show that any extra power from adaptive non-signaling assistance appears only in scenarios where the receiver has no choice of measurement. This separates the simulation of quantum communication from the adaptive advantages seen in entanglement-assisted quantum protocols.

Core claim

In prepare-and-measure scenarios, the set of behaviors realizable with non-adaptive non-signaling assistance and a classical message of dimension d coincides with the set realizable by quantum communication of dimension d. Adaptive non-signaling assistance yields a strict advantage only in scenarios where the receiver performs a single fixed measurement, with no multi-setting advantages possible.

What carries the argument

The sets of behaviors realizable with non-adaptive and adaptive non-signaling assistance, characterized for arbitrary prepare-and-measure scenarios.

If this is right

  • Quantum prepare-and-measure behaviors achievable with a qudit message are also achievable with a classical dit plus non-signaling correlations without any adaptation.
  • Adaptive non-signaling assistance cannot produce advantages that require multiple measurement choices at the receiver.
  • The scenarios admitting a strict adaptive non-signaling advantage are fully classified as those with a single receiver measurement.

Where Pith is reading between the lines

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

  • Non-local correlations without signaling can substitute for quantum messages in a range of communication tasks.
  • The absence of multi-setting adaptive advantages under non-signaling assistance highlights a structural difference from entanglement-assisted quantum protocols.
  • Similar characterizations may apply to other resource theories that combine classical communication with non-local resources.

Load-bearing premise

The standard definition of non-signaling assistance applies uniformly across all prepare-and-measure scenarios.

What would settle it

A concrete prepare-and-measure behavior that can be achieved with a quantum message of dimension d but cannot be achieved with a classical message of dimension d plus non-adaptive non-signaling assistance.

Figures

Figures reproduced from arXiv: 2607.01193 by Carlos Vieira, Jos\'e Nogueira, Lucas E. A. Porto, Lucas Pollyceno, Otfried G\"uhne, Rafael Rabelo.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic of a prepare-and-measure scenario. Alice en [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Schematic representation of a prepare-and-measure sce [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Schematic representation of a prepare-and-measure sce [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
read the original abstract

Extracting the full power of non-local correlations in prepare-and-measure (PM) scenarios requires precise control over the timing and structure of the receiver's measurements. Indeed, recent developments in entanglement-assisted classical communication scenarios have shown that adaptive strategies-where the receiver uses the transmitted message to guide their measurement choice-can outperform standard non-adaptive protocols. Moving beyond quantum theory, however, the ultimate limits of such advantages remain largely unexplored. In this work, we thoroughly study adaptive and non-adaptive non-signaling (NS) assistance in PM scenarios with classical communication. We provide simple characterizations of the sets of behaviors that can be realized using both non-adaptive and adaptive NS assistance in arbitrary PM scenarios. As a consequence, we show that non-adaptive NS assistance is already strong enough to reproduce quantum communication with the same message dimension: the transmission of a qudit can be simulated by a classical dit assisted non-adaptively by NS correlations. We then compare adaptive and non-adaptive NS assistance. We prove that any adaptive NS advantage can be traced back to scenarios in which the receiver has no measurement choice, ruling out the genuinely multi-setting advantages found in entanglement-assisted quantum protocols. Finally, we identify all PM scenarios where adaptive NS strategies provide a strict advantage over non-adaptive ones.

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

0 major / 0 minor

Summary. The manuscript provides simple characterizations of the sets of behaviors realizable with non-adaptive and adaptive non-signaling (NS) assistance in arbitrary prepare-and-measure (PM) scenarios with classical communication. It shows that non-adaptive NS assistance suffices to simulate the transmission of a qudit by a classical dit, proves that any adaptive NS advantage reduces to scenarios in which the receiver has no measurement choice, and identifies all PM scenarios admitting a strict adaptive advantage over non-adaptive strategies.

Significance. If the characterizations hold, the work supplies a general and explicit description of NS-assisted PM behaviors that directly yields the simulation of quantum communication by classical messages plus NS correlations. The demonstration that adaptive NS advantages are confined to no-choice cases distinguishes NS assistance from entanglement-assisted quantum protocols and supplies a complete classification of strict adaptive advantage. These results are grounded in standard non-signaling axioms and constitute a parameter-free, falsifiable framework for the field.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive summary, significance assessment, and recommendation to accept the manuscript. There are no major comments requiring response.

Circularity Check

0 steps flagged

No significant circularity; derivations follow from standard NS axioms

full rationale

The paper derives characterizations of achievable behaviors in PM scenarios directly from the standard definition of non-signaling assistance applied to classical communication channels. These characterizations are then used to prove the simulation result (qudit transmission via classical dit + non-adaptive NS) and the adaptive/non-adaptive comparison. No step reduces a claimed prediction or theorem to a fitted parameter, self-referential definition, or load-bearing self-citation; the central results are consequences of the NS no-signaling conditions and the prepare-and-measure structure without internal circular reduction. The work is self-contained against external benchmarks of NS theory.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The work rests on the standard non-signaling condition for assistance correlations and the classical communication model; no free parameters or new entities are introduced in the abstract.

axioms (1)
  • domain assumption Non-signaling conditions hold for the assistance correlations
    Invoked when defining the sets of behaviors realizable with NS assistance.

pith-pipeline@v0.9.1-grok · 5777 in / 1124 out tokens · 31636 ms · 2026-07-02T11:28:38.499468+00:00 · methodology

discussion (0)

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

Reference graph

Works this paper leans on

299 extracted references · 83 canonical work pages · 18 internal anchors

  1. [1]

    The most discriminable quantum states in the multicopy regime

    The most discriminable quantum states in the multicopy regime. 2026 , archivePrefix =. 2604.26927 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  2. [2]

    and Chatzikokolakis, Kostas and Palamidessi, Catuscia and Smith, Geoffrey , booktitle=

    Alvim, M'rio S. and Chatzikokolakis, Kostas and Palamidessi, Catuscia and Smith, Geoffrey , booktitle=. Measuring Information Leakage Using Generalized Gain Functions , year=

  3. [3]

    2020 , DOI =

    Alvim, M. 2020 , DOI =

    2020

  4. [4]

    Quantitative Notions of Leakage for One-try Attacks , journal =

    Christelle Braun and Konstantinos Chatzikokolakis and Catuscia Palamidessi , keywords =. Quantitative Notions of Leakage for One-try Attacks , journal =. 2009 , note =. doi:https://doi.org/10.1016/j.entcs.2009.07.085 , url =

    work page doi:10.1016/j.entcs.2009.07.085 2009

  5. [5]

    and Thomas, Joy A

    Cover, Thomas M. and Thomas, Joy A. , title =. 2006 , isbn =

    2006

  6. [6]

    The Quantum Reverse Shannon Theorem based on One-Shot Information Theory

    The Quantum Reverse Shannon Theorem Based on One-Shot Information Theory. Communications in Mathematical Physics , keywords =. doi:10.1007/s00220-011-1309-7 , archivePrefix =. 0912.3805 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1007/s00220-011-1309-7

  7. [7]

    Berta, Mario and Brandão, Fernando G. S. L. and Christandl, Matthias and Wehner, Stephanie , journal=. Entanglement Cost of Quantum Channels , year=. doi:10.1109/TIT.2013.2268533 , archivePrefix =. 1108.5357 , primaryClass =

    work page doi:10.1109/tit.2013.2268533 2013

  8. [8]

    No-Signalling-Assisted Zero-Error Capacity of Quantum Channels and an Information Theoretic Interpretation of the Lovász Number , year=

    Duan, Runyao and Winter, Andreas , journal=. No-Signalling-Assisted Zero-Error Capacity of Quantum Channels and an Information Theoretic Interpretation of the Lovász Number , year=. doi:10.1109/TIT.2015.2507979 , archivePrefix =. 1409.3426 , primaryClass =

    work page doi:10.1109/tit.2015.2507979 2015

  9. [9]

    On the quantum no-signalling assisted zero-error classical simulation cost of non-commutative bipartite graphs , year=

    Wang, Xin and Duan, Runyao , booktitle=. On the quantum no-signalling assisted zero-error classical simulation cost of non-commutative bipartite graphs , year=. doi:10.1109/ISIT.2016.7541698 , archivePrefix =. 1601.06855 , primaryClass =

    work page doi:10.1109/isit.2016.7541698 2016

  10. [10]

    IEEE Transactions on Information Theory , volume =

    Fang, Kun and Wang, Xin and Tomamichel, Marco and Berta, Mario , title =. IEEE Transactions on Information Theory , volume =. 2019 , doi =

    2019

  11. [11]

    arXiv e-prints , keywords =

    Quantum correlations in prepare-and-measure scenarios and their semi-device-independent applications. arXiv e-prints , keywords =. doi:10.48550/arXiv.2603.23604 , archivePrefix =. 2603.23604 , primaryClass =

    work page doi:10.48550/arxiv.2603.23604

  12. [12]

    Entanglement-assisted capacity of a quantum channel and the reverse Shannon theorem

    Entanglement-assisted capacity of a quantum channel and the reverse Shannon theorem. 2001 , archivePrefix =. quant-ph/0106052 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv 2001

  13. [13]

    The Communication Value of a Quantum Channel , year=

    Chitambar, Eric and George, Ian and Doolittle, Brian and Junge, Marius , journal=. The Communication Value of a Quantum Channel , year=

  14. [14]

    Local hidden--variable models for entangled quantum states

    Local hidden-variable models for entangled quantum states. Journal of Physics A Mathematical General , keywords =. doi:10.1088/1751-8113/47/42/424002 , archivePrefix =. 1405.7321 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/1751-8113/47/42/424002

  15. [15]

    Classical randomness in quantum measurements

    Classical randomness in quantum measurements. Journal of Physics A Mathematical General , keywords =. doi:10.1088/0305-4470/38/26/010 , archivePrefix =. quant-ph/0408115 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/0305-4470/38/26/010

  16. [16]

    Local Hidden Variable Models for Entangled Quantum States Using Finite Shared Randomness , author =. Phys. Rev. Lett. , volume =. 2015 , month =. doi:10.1103/PhysRevLett.114.120401 , url =

    work page doi:10.1103/physrevlett.114.120401 2015

  17. [17]

    Algorithmic construction of local models for entangled quantum states: Optimization for two-qubit states , author =. Phys. Rev. A , volume =. 2018 , month =. doi:10.1103/PhysRevA.98.022115 , url =

    work page doi:10.1103/physreva.98.022115 2018

  18. [18]

    2004 , month =

    Daniel Collins and Nicolas Gisin , title =. 2004 , month =. doi:10.1088/0305-4470/37/5/021 , url =

    work page doi:10.1088/0305-4470/37/5/021 2004

  19. [19]

    Quantum , volume =

    Tavakoli, Armin and Zukowski, Marek and Brukner, Caslav , title =. Quantum , volume =. 2020 , month = sep, doi =

    2020

  20. [20]

    Physical Review Research , keywords =

    Improved local models and new Bell inequalities via Frank-Wolfe algorithms. Physical Review Research , keywords =. doi:10.1103/PhysRevResearch.5.043059 , archivePrefix =. 2302.04721 , primaryClass =

    work page doi:10.1103/physrevresearch.5.043059

  21. [21]

    Research on Hidden Variable Theories: a review of recent progresses

    Research on hidden variable theories: A review of recent progresses. Physics Reports , keywords =. doi:10.1016/j.physrep.2005.03.003 , archivePrefix =. quant-ph/0701071 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/j.physrep.2005.03.003 2005

  22. [22]

    PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association , author =

    Bell’s inequality, information transmission, and prism models , volume =. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association , author =. 1992 , pages =. doi:10.1086/psaprocbienmeetp.1992.1.192771 , number =

    work page doi:10.1086/psaprocbienmeetp.1992.1.192771 1992

  23. [23]

    Cost of Exactly Simulating Quantum Entanglement with Classical Communication. Phys. Rev. Lett. , keywords =. doi:10.1103/PhysRevLett.83.1874 , archivePrefix =. quant-ph/9901035 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevlett.83.1874

  24. [24]

    Towards Quantifying Non-Local Information Transfer: Finite-Bit Non-Locality

    Towards quantifying non-local information transfer: finite-bit non-locality. Physics Letters A , keywords =. doi:10.1016/S0375-9601(00)00315-7 , archivePrefix =. quant-ph/9902014 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/s0375-9601(00)00315-7

  25. [25]

    Minimum classical bit for remote preparation and measurement of a qubit. Phys. Rev. A , keywords =. doi:10.1103/PhysRevA.63.014302 , archivePrefix =. quant-ph/9907022 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physreva.63.014302

  26. [26]

    Classical simulation of quantum entanglement without local hidden variables. Phys. Rev. A , keywords =. doi:10.1103/PhysRevA.63.052305 , archivePrefix =. quant-ph/0009088 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physreva.63.052305

  27. [27]

    Classical Teleportation of a Quantum Bit. Phys. Rev. Lett. , keywords =. doi:10.1103/PhysRevLett.84.2521 , archivePrefix =. quant-ph/9906105 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevlett.84.2521

  28. [29]

    Classical Cost of Transmitting a Qubit. Phys. Rev. Lett. , keywords =. doi:10.1103/PhysRevLett.130.120801 , archivePrefix =. 2207.02244 , acin2006grothendieckprimaryClass =

    work page doi:10.1103/physrevlett.130.120801

  29. [30]

    New Journal of Physics , keywords =

    Interplays between classical and quantum entanglement-assisted communication scenarios. New Journal of Physics , keywords =. doi:10.1088/1367-2630/ad0526 , archivePrefix =. 2205.05171 , primaryClass =

    work page doi:10.1088/1367-2630/ad0526

  30. [31]

    2026 , archivePrefix =

    Bounding the classical cost of simulating quantum behaviors in the prepare-and-measure scenario. 2026 , archivePrefix =. 2603.01255 , primaryClass =

    work page arXiv 2026

  31. [32]

    Physical Review A , author =

    Quantum states with. Physical Review A , author =. 1989 , pages =. doi:10.1103/PhysRevA.40.4277 , number =

    work page doi:10.1103/physreva.40.4277 1989

  32. [33]

    Quantum , keywords =

    The minimal communication cost for simulating entangled qubits. Quantum , keywords =. doi:10.22331/q-2023-10-24-1149 , archivePrefix =. 2207.12457 , primaryClass =

    work page doi:10.22331/q-2023-10-24-1149 2023

  33. [34]

    Communication cost of simulating B ell correlations. Phys. Rev. Lett. , keywords =. doi:10.1103/PhysRevLett.91.187904 , archivePrefix =. quant-ph/0304076 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevlett.91.187904

  34. [35]

    Adaptive Advantage in Entanglement-Assisted Communications. Phys. Rev. Lett. , keywords =. doi:10.1103/PhysRevLett.129.120504 , archivePrefix =. 2203.05372 , primaryClass =

    work page doi:10.1103/physrevlett.129.120504

  35. [36]

    Physical Review Letters , author =

    Simulating positive-operator-valued measures with projective measurements , volume =. Physical Review Letters , author =. 2017 , pages =. doi:10.1103/PhysRevLett.119.190501 , number =

    work page doi:10.1103/physrevlett.119.190501 2017

  36. [37]

    PRX Quantum , keywords =

    General Method for Classicality Certification in the Prepare and Measure Scenario. PRX Quantum , keywords =. doi:10.1103/PRXQuantum.2.030311 , archivePrefix =. 2101.10459 , primaryClass =

    work page doi:10.1103/prxquantum.2.030311

  37. [38]

    Algorithmic Construction of Local Hidden Variable Models for Entangled Quantum States. Phys. Rev. Lett. , keywords =. doi:10.1103/PhysRevLett.117.190402 , archivePrefix =. 1512.00262 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevlett.117.190402

  38. [39]

    General Method for Constructing Local Hidden Variable Models for Entangled Quantum States. Phys. Rev. Lett. , keywords =. doi:10.1103/PhysRevLett.117.190401 , archivePrefix =. 1512.00277 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevlett.117.190401

  39. [40]

    Better local hidden variable models for two-qubit Werner states and an upper bound on the Grothendieck constant $K_G(3)$

    Better local hidden variable models for two-qubit W erner states and an upper bound on the G rothendieck constant K_G(3). Quantum , keywords =. doi:10.22331/q-2017-04-25-3 , archivePrefix =. 1609.06114 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.22331/q-2017-04-25-3 2017

  40. [41]

    arXiv e-prints , keywords =

    FrankWolfe.jl: a high-performance and flexible toolbox for Frank-Wolfe algorithms and Conditional Gradients. arXiv e-prints , keywords =

  41. [42]

    Randomness Amplification under Minimal Fundamental Assumptions on the Devices , author =. Phys. Rev. Lett. , volume =. 2016 , month =. doi:10.1103/PhysRevLett.117.230501 , url =

    work page doi:10.1103/physrevlett.117.230501 2016

  42. [43]

    arXiv preprint arXiv:2304.09643 , year=

    Finite Device-Independent Extraction of a Block Min-Entropy Source against Quantum Adversaries , author=. arXiv preprint arXiv:2304.09643 , year=

    work page arXiv

  43. [44]

    arXiv preprint arXiv:2108.08819 , year=

    No-signaling-proof randomness extraction from public weak sources , author=. arXiv preprint arXiv:2108.08819 , year=

    work page arXiv

  44. [45]

    , journal =

    Eberhard, Philippe H. , journal =. Background level and counter efficiencies required for a loophole-free. 1993 , month =. doi:10.1103/PhysRevA.47.R747 , url =

    work page doi:10.1103/physreva.47.r747 1993

  45. [46]

    Simulating quantum correlations as a distributed sampling problem , author =. Phys. Rev. A , volume =. 2005 , month =. doi:10.1103/PhysRevA.72.062314 , url =

    work page doi:10.1103/physreva.72.062314 2005

  46. [47]

    Manik Banik and M. D. Rajjak Gazi and Subhadipa Das and Ashutosh Rai and Samir Kunkri , title =. 2012 , month =. doi:10.1088/1751-8113/45/20/205301 , url =

    work page doi:10.1088/1751-8113/45/20/205301 2012

  47. [48]

    Koh, Dax Enshan and Hall, Michael J. W. and Setiawan and Pope, James E. and Marletto, Chiara and Kay, Alastair and Scarani, Valerio and Ekert, Artur , journal =. Effects of Reduced Measurement Independence on. 2012 , month =. doi:10.1103/PhysRevLett.109.160404 , url =

    work page doi:10.1103/physrevlett.109.160404 2012

  48. [49]

    Bell tests with min-entropy sources , author =. Phys. Rev. A , volume =. 2013 , month =. doi:10.1103/PhysRevA.87.062121 , url =

    work page doi:10.1103/physreva.87.062121 2013

  49. [50]

    and Kay, Alastair , journal =

    Pope, James E. and Kay, Alastair , journal =. Limited measurement dependence in multiple runs of a. 2013 , month =. doi:10.1103/PhysRevA.88.032110 , url =

    work page doi:10.1103/physreva.88.032110 2013

  50. [51]

    Bell Inequalities with Auxiliary Communication , author =. Phys. Rev. Lett. , volume =. 2003 , month =. doi:10.1103/PhysRevLett.90.157904 , url =

    work page doi:10.1103/physrevlett.90.157904 2003

  51. [52]

    Regev, Oded and Toner, Ben , title =. SIAM J. Comput. , volume =. 2010 , doi =

    2010

  52. [53]

    Lower bound on the communication cost of simulating bipartite quantum correlations , author =. Phys. Rev. A , volume =. 2009 , month =. doi:10.1103/PhysRevA.80.062316 , url =

    work page doi:10.1103/physreva.80.062316 2009

  53. [54]

    Quantifying the Nonlocality of

    Branciard, Cyril and Gisin, Nicolas , journal =. Quantifying the Nonlocality of. 2011 , month =. doi:10.1103/PhysRevLett.107.020401 , url =

    work page doi:10.1103/physrevlett.107.020401 2011

  54. [55]

    Bell inequalities with communication assistance , author =. Phys. Rev. A , volume =. 2014 , month =. doi:10.1103/PhysRevA.89.042108 , url =

    work page doi:10.1103/physreva.89.042108 2014

  55. [56]

    Europhys

    Physics and theology , author=. Europhys. News , volume=

  56. [57]

    Costa de Beauregard, Olivier , year=. M\'. Comptes Rendus Acad\'

  57. [58]

    2023 , eprint=

    Corrected Bell and Noncontextuality Inequalities for Realistic Experiments , author=. 2023 , eprint=

    2023

  58. [59]

    arXiv e-prints , keywords =

    Better bounds on Grothendieck constants of finite orders. arXiv e-prints , keywords =

  59. [60]

    arXiv e-prints , keywords =

    Conditional Gradient Methods. arXiv e-prints , keywords =

  60. [61]

    , title =

    Steiner, M. , title =. Phys. Lett. A , year=

  61. [62]

    Bell's Theorem without Inequalities and without Probabilities for Two Observers , author =. Phys. Rev. Lett. , volume =. 2001 , month =. doi:10.1103/PhysRevLett.86.1911 , url =

    work page doi:10.1103/physrevlett.86.1911 2001

  62. [63]

    Cabello, Ad\'an , journal =. ``. 2001 , month =. doi:10.1103/PhysRevLett.87.010403 , url =

    work page doi:10.1103/physrevlett.87.010403 2001

  63. [64]

    Theoretical Computer Science , author =

    Strict hierarchy among. Theoretical Computer Science , author =. 2013 , pages =. doi:10.1016/j.tcs.2012.12.011 , urldate =

    work page doi:10.1016/j.tcs.2012.12.011 2013

  64. [65]

    Science , author =

    Quantum advantage with shallow circuits , volume =. Science , author =. 2018 , pages =. doi:10.1126/science.aar3106 , number =

    work page doi:10.1126/science.aar3106 2018

  65. [66]

    2021 , pages =

    Communications of the ACM , author =. 2021 , pages =. doi:10.1145/3485628 , number =

    work page doi:10.1145/3485628 2021

  66. [67]

    Bounding the set of quantum correlations , volume =. Phys. Rev. Lett. , author =. 2007 , pages =. doi:10.1103/PhysRevLett.98.010401 , number =

    work page doi:10.1103/physrevlett.98.010401 2007

  67. [68]

    A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations , volume =. New. J. Phys. , author =. 2008 , pages =. doi:10.1088/1367-2630/10/7/073013 , number =

    work page doi:10.1088/1367-2630/10/7/073013 2008

  68. [69]

    Violation of all two-party facet

    Ramanathan, Ravishankar , journal =. Violation of all two-party facet. 2021 , month =. doi:10.1103/PhysRevResearch.3.033100 , url =

    work page doi:10.1103/physrevresearch.3.033100 2021

  69. [70]

    and Ramanathan, Ravishankar and Cabello, Ad\'an , notitle=

    Liu, Yuan and Chung, Ho Yiu and Zambrini Cruzeiro, Emmanuel and Gonzales-Ureta, Junior R. and Ramanathan, Ravishankar and Cabello, Ad\'an , notitle=. 2023 , archiveprefix =. 2310.10600 , primaryclass =

    work page arXiv 2023

  70. [71]

    2309.05735 , archivePrefix=

    Zhen-Peng Xu and Debashis Saha and Kishor Bharti and Ad\'an Cabello , year=. 2309.05735 , archivePrefix=

    work page arXiv

  71. [72]

    Minimum quantum resources for strong non-locality

    Samson Abramsky and Barbosa, Rui Soares and Giovanni Car \`u and De Silva , Nadish and Kohei Kishida and Shane Mansfield. Minimum quantum resources for strong non-locality. 12th Conference on the Theory of Quantum Computation, Communication, and Cryptography, TQC 2017. 2018. doi:10.4230/LIPIcs.TQC.2017.9

    work page doi:10.4230/lipics.tqc.2017.9 2017

  72. [73]

    and Shi, Yaoyun , journal=

    Jain, Rahul and Miller, Carl A. and Shi, Yaoyun , journal=. Parallel Device-Independent Quantum Key Distribution , year=

  73. [74]

    Vidick, Thomas , doi=

  74. [75]

    and Barrett, M

    Leibfried, D. and Barrett, M. D. and Schaetz, T. and Britton, J. and Chiaverini, J. and Itano, W. M. and Jost, J. D. and Langer, C. and Wineland, D. J. , title=. Science , volume=. 2004 , doi=

    2004

  75. [76]

    and Riebe, Mark and Häffner, Hartmut and Hänsel, Wolfgang and Benhelm, Jan and Lancaster, Gavin P

    Roos, Christian F. and Riebe, Mark and Häffner, Hartmut and Hänsel, Wolfgang and Benhelm, Jan and Lancaster, Gavin P. T. and Becher, Christoph and Schmidt-Kaler, Ferdinand and Blatt, Rainer , title=. Science , volume=. 2004 , doi=

    2004

  76. [77]

    Bell's Inequalities and Quantum Communication Complexity , author =. Phys. Rev. Lett. , volume =. 2004 , month =. doi:10.1103/PhysRevLett.92.127901 , url =

    work page doi:10.1103/physrevlett.92.127901 2004

  77. [78]

    2023 , archiveprefix =

    Liu, Yuan and Chung, Ho Yiu and Ramanathan, Ravishankar , notitle=. 2023 , archiveprefix =. 2309.06304 , primaryclass =

    work page arXiv 2023

  78. [79]

    Cleve, R. and. Proceedings. 19th IEEE Annual Conference on Computational Complexity , title =. 2004 , pages =

    2004

  79. [80]

    Ball, Philip , title =. Sci. Am. (On line news) , year =

  80. [81]

    Science (On line news) , year =

    Cho, Adrian , title =. Science (On line news) , year =

Showing first 80 references.