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Noise-Robust Self-Testing: Detecting Non-Locality in Noisy Non-Local Inputs

T0 review · 3 major / 2 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read Convincingness, a p-value for rejecting a local explanation of a game's wins, gives the most nuanced ranking of noise-robustness among self-tests, and CHSH ranks highest on equal resources.

desk verdict A useful but overreaching comparison framework; the convincingness measure is sound, but the gapped score is an in-sample fit and Lemma 2 is false as stated. read the letter →

arxiv 2505.13537 v1 pith:TRV3R6LC submitted 2025-05-18 quant-ph cs.ITmath.IT

Romi Lifshitz This is my paper · ORCID
classification quant-phcs.ITmath.IT MSC 81P4081P6862F03 PACS 03.65.Ud03.67.-a
keywords noise-robustnessself-testingnon-localgamesconvincingnessgappedscorenoise-toleranceCHSHgamedepolarizingnoise
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

Non-local games are used to certify entanglement in untrusted devices, but real noise means ideal winning states are never available and there has been no agreed way to say which self-test is more robust than another. The paper proposes three comparative measures — noise-tolerance, convincingness, and an analytic gapped score — and argues that convincingness, an upper-tailed p-value for rejecting a local hidden-variable explanation of the observed win rate, is the most nuanced. Under the tested depolarizing noise model, the CHSH game is found to be the most noise-robust when all games get the same number of noisy EPR pairs, while optimized 2-CHSH variants can beat CHSH only when given roughly ten times more resources. If correct, the framework turns noise-robustness into a computable, comparable quantity that an experimentalist can match to a noise model and a resource budget.

What carries the argument

The load-bearing object is the gapped expression, $\Delta_G(\eta) = \omega^\eta_G - \omega^c_G = c_1\eta^2 + c_2\eta^4 + d - \omega^c_G$, which gives each game's score gap under depolarizing noise as a polynomial in the visibility $\eta$, plus the gapped score $\kappa_G = \left(\frac{c_1+c_2}{|d-\omega^c_G|}\right)^2 \frac{N_{\mathrm{res}}}{-\ln\alpha}$ built from its coefficients. This score tracks the convincingness p-value, $C_G \sim \exp(-N_{\mathrm{res}}\Delta_G^2)$, which measures how unlikely the observed win rate is under a local model, and it ranks games by the visibility at which their convincingness curves cross the significance threshold $\alpha$. The machinery works by reducing an incomparable pair of statistics (different dimensions, different score scales) to a normalized, resource-aware number per game.

What would settle it

Recompute the gapped expressions and significance crossings using a global 4-qubit depolarizing channel, $\varepsilon(\rho) = \eta^4\rho + (1-\eta^4)\frac{I_{16}}{16}$, in place of the tensor-product channel; if any 2-CHSH variant or the Magic Square Game crosses the threshold at a lower visibility than CHSH under this channel, the reported ranking is an artifact of the channel-extension choice. A second check is to repeat the comparison under dephasing or amplitude-damping noise and test whether $\kappa_G$ still predicts the crossing order.

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Extended reading notes

Core claim

The central claim is that noise-robustness of a self-test can be defined operationally: a game $G_1$ is more noise-robust than $G_2$ if it becomes significantly convincing of non-locality at lower visibilities (Def. VII.42), which in stable resource regimes is equivalent to comparing a single closed-form number, the gapped score (Def. VII.43). The paper reports that convincingness provides the most nuanced comparison of the tested measures, that the gapped score reliably predicts the order in which games cross the significance threshold once a few thousand noisy resources are available, and that under equal resource budgets CHSH outranks the 2-CHSH game, the Magic Square Game, and optimized 2-CHSH configurations, whereas with a roughly tenfold resource advantage the best optimized 2-CHSH variants surpass CHSH's significance crossing.

Load-bearing premise

The rankings assume that noise on a four-qubit system is just two independent two-qubit noise processes acting on each EPR pair separately; if the noise instead hits all four qubits collectively, the computed scores and the claimed ordering of the games could change.

Editorial extensions

If this is right

  • Given equal numbers of noisy EPR pairs, CHSH certifies non-locality at the lowest visibility among the tested games under depolarizing noise.
  • The gapped score $\kappa_G$ gives a closed-form ranking that matches the exact convincingness crossing order for stable resource regimes (roughly $N_{\mathrm{res}} \geq 2000$).
  • Optimized 2-CHSH games, which are worse than CHSH at equal resources, overtake CHSH's significance crossing when given about ten times more noisy resources.
  • Noise-tolerance rankings coincide with convincingness rankings in the asymptotic resource limit, so noise-tolerance is the coarser measure of the two.
  • The framework extends to other noise models by deriving the gapped expression for the new channel and re-computing $\kappa_G$.

Reading between the lines

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

  • The tensor-product channel extension is the step that all rankings inherit: a global 4-qubit depolarizing model, or a dephasing model, could reorder the crossings, so the framework's main empirical claim should be re-tested under those channels.
  • The $\kappa_G$ score compresses each game's noise behaviour into four numbers $(c_1, c_2, d, \omega^c_G)$, so noise-robustness rankings could be tabulated per noise model as a lookup table — a practical step the paper leaves implicit.
  • The tenfold resource penalty for 2-CHSH-OPT hints at a resource-theoretic cost of parallel repetition; a rigorous lower bound on the resource amplification needed for parallel-repetition self-tests to match CHSH's crossing would settle whether this penalty is fundamental or an artifact of the specific optimization.
  • The finite-resource flip at lenient thresholds suggests significance levels could be tuned per application; a systematic scan over $\alpha$ and $N_{\mathrm{res}}$ could yield decision charts for choosing a self-test, going beyond the single-threshold analysis reported.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 2 minor

Summary. The paper introduces three measures of noise-robustness for non-local games used as self-tests: noise-tolerance, convincingness (an upper-tailed p-value against the local bound), and the gapped score, an analytic approximation to convincingness. Under a depolarizing-noise model with a tensor-product extension from 2 to 4 qubits, the author computes scores for CHSH, 2-CHSH, several optimized 2-CHSH configurations, and the Magic Square Game, for resource counts from 10^3 to 10^6. The main claims are that convincingness is the most nuanced ranking measure, that the gapped score reliably recovers the significance-crossing order in stable resource regimes, and that CHSH is most noise-robust under equal resources while some 2-CHSH variants can surpass it with substantially more resources. The paper also proposes formal definitions of noise-robustness based on these scores.

Significance. The paper addresses a genuine gap: comparing self-tests of different dimensions and input-output sizes under noise. The p-value-based convincingness is an operationally meaningful normalization, and the explicit treatment of finite resources is a useful contribution. If the gapped score's reliability could be established by out-of-sample tests or by a derivation, Definition VII.43 would give a simple analytic method for ranking self-tests. The computational study is fairly extensive, and the paper is unusually honest about noise-model dependence and open questions. However, the analytic claims need repair before the framework can be accepted.

major comments (3)
  1. [V.B (Def. V.41, Obs. 5, Def. VII.43)] The gapped score is validated only in-sample. The text reports that multiple candidate scores were explored and that Def. V.41 was selected because it best reproduced the observed crossing order in Fig. 8; it is then evaluated on the same eleven games and configurations used for that selection. No held-out games, new noise models, or unseen resource counts are used, and no parameter-free derivation from the tail bound exp(-Nres(omega_eta_G - omega_c_G)^2) establishes the specific functional form ((c1+c2)^2 / |d - omega_c|^2) * (Nres / -ln alpha). Since Definition VII.43 defines noise-robustness through kappa_G and Observation 5 is the only evidence for its reliability, an out-of-sample prediction or an analytic derivation is needed before the analytic definition can be accepted.
  2. [V (Lemma 2) and VI (Theorem VI.6)] Lemma 2 asserts that Delta_G(eta) is strictly increasing for any game G, but Table 1 and App. XIV list the 2-CHSH-OPT configurations for eta' = 0.83 and 0.84 with Delta_G = 0; these configurations have constant raw score 0.53125, so strict monotonicity fails as stated. The proof's assertion that the winning state always scores above the maximally mixed state is not justified for the 4-qubit tensor-product channel and is false for those degenerate configurations. Theorem VI.6, which invokes Lemma 2 to conclude eta*_G < eta_dagger_G for every finite Nres, is therefore not proven as stated; the theorem also steps from an asymptotic equivalence CG ~ exp(-Nres Delta^2) to an exact equality at finite Nres. Please restrict the lemma and theorem to configurations with strictly positive gap and provide the explicit 4-qubit derivative computation.
  3. [III.B (Def. III.36, Algorithm 1, Figs. 4-6)] The convincingness definition and its implementation describe different statistics. Definition III.36 and Eq. (14) define C_G as the deterministic binomial tail evaluated at k = round(n*omega_v_G). Algorithm 1 first samples k ~ Binomial(n, omega_v_G), and the figure captions say the p-value was averaged over random seeds. If k is used, the plotted convincingness is a random variable and the significance crossings eta_dagger_G in Table 2 are not fixed game properties unless variances or error bars are reported; if k is not used and the tail is evaluated at round(n*omega_v_G), the random-seed averaging is superfluous and should be removed. This distinction matters because Table 2 and Observations 1-5 compare significance crossings, so the quantity being plotted must be unambiguous.
minor comments (2)
  1. [V.A, Eq. (24)] Equation (24) gives omega_eta^{2-CHSH, eta'=1} = 0.10937 eta^4 + 0.30936 eta^2(1-eta^2) + 0.21875(1-eta^2)^2, which does not match the corresponding raw expression in App. XIV (0.63748 eta^4 + 0.74686 eta^2(1-eta^2) + 0.21875(1-eta^2)^2) nor the coefficients in Table 1; please correct the typo.
  2. [Def. II.13 and abstract] The 4-qubit depolarizing channel is defined as a tensor product of independent 2-qubit channels, and all cross-game rankings are conditional on this extension. The paper states this in Sec. VI, but the abstract and conclusion should carry the qualifier so that readers do not interpret the equal-resource ranking as noise-model-independent.

Circularity Check

0 steps flagged · score 1.0 of 10

No circular derivation: convincingness is a direct p-value and the gapped score is an explicit analytic proxy; its in-sample validation is a methodological weakness, not a circular step.

full rationale

The paper's main derivation chain is self-contained. Convincingness is defined directly as an upper-tailed binomial p-value (Def. III.36, Eq. 14), and the simplified exponential form follows from a standard Hoeffding bound (Theorem III.4), so the measure is not defined in terms of the conclusions it is used to draw. The gapped expressions are computed from the score operators under an explicitly stated tensor-product depolarizing channel (Theorem V.5, Eqns. 23-26), and the gapped score of Def. V.41 is a fixed closed-form function of those coefficients rather than a value fitted to the observed significance crossings. The reliability claim in Observation 5 is empirical and in-sample: the text states that the authors 'searched for a score which reflects' the crossing intuition and that 'out of the existing ratio and gap-inspired scores explored, Def. V.41 best captures the desired behaviour,' then evaluated the same games used for that model selection. This is a legitimate methodological concern about out-of-sample validation, but it is not a circular derivation because the score's formula is not equivalent to the crossing order by construction and no parameter is fitted to the crossing data. There is no load-bearing self-citation, no imported uniqueness theorem, and no renaming of an input as a prediction. The tensor-product channel extension is an explicit scope condition of the comparison rather than a hidden input smuggled into the output.

Assumptions & free parameters 2 free parameters · 4 assumptions · 1 invented entities

The central claim rests on a modest set of assumptions: the Bernoulli null hypothesis, the tensor-product depolarizing channel extension, the unproven strict monotonicity of Delta_G, and the ad hoc form of the gapped score. The free parameters are a conventional significance threshold and the chosen functional form of the gapped score. No new physical entities are introduced.

free parameters (2)
  • Significance threshold alpha = 0.05
    Set by convention; all significance crossings and gapped scores depend on this choice. The paper notes that alpha = 0.5 would change rankings (Observation 3).
  • Gapped score functional form = kappa_G = ((c1+c2)/|d-omega_cG|)^2 * N_res / (-ln alpha)
    The numerator c1+c2, denominator |d-omega_cG|, and quadratic power were chosen after comparing several candidate formulas to match observed crossing order (Sec. V.B); this is an ad hoc modeling choice rather than a derived quantity.
assumptions (4)
  • domain assumption The local-bound hypothesis is Bernoulli(omega_cG) for the null model of locality
    Used in Def. III.36 and Algorithm 1; assumes that the maximum classical score is the right null distribution for a p-value test. Standard but not the only possible choice.
  • domain assumption The 4-qubit depolarizing channel is the tensor product epsilon_2 tensor epsilon_2
    Def. II.13; this is the channel extension that makes CHSH and MSG/2-CHSH comparisons meaningful. All rankings depend on it.
  • domain assumption For any game and its winning state, Tr(SG rho_win) > Tr(SG I/4)
    Used in the proof of Lemma 2 to claim Delta_G(eta) is strictly increasing; stated without proof and contradicted by the paper's own eta' = 0.83 and 0.84 configurations where Delta_G = 0.
  • ad hoc to paper The gapped score formula is a valid proxy for significance crossing order in stable resource regimes
    Def. V.41; supported only by the same experiments used to select the formula; not derived from first principles.
invented entities (1)
  • Gapped score kappa_G
    purpose: Analytic single-number proxy for the convincingness-based ordering of games
    It is validated only on the five games and configurations in this paper; no external benchmark or prediction beyond the in-sample crossing orders. It has no falsifiable handle outside the paper.

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Cite this review

Pith. "Pith review of Noise-Robust Self-Testing: Detecting Non-Locality in Noisy Non-Local Inputs." pith.science (2026). https://pith.science/paper/TRV3R6LC

@misc{pith2026250513537,
  author       = {Pith},
  title        = {Pith review of: Noise-Robust Self-Testing: Detecting Non-Locality in Noisy Non-Local Inputs},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TRV3R6LC}},
  note         = {Machine review of arXiv:2505.13537}
}
read the original abstract

Non-local games test for non-locality and entanglement in quantum systems and are used in self-tests for certifying quantum states in untrusted devices. However, these protocols are tailored to ideal states, so realistic noise prevents maximal violations and leaves many partially non-local states undetected. Selecting self-tests based on their 'robustness' to noise can tailor protocols to specific applications, but current literature lacks a standardized measure of noise-robustness. Creating such a measure is challenging as there is no operational measure for comparing tests of different dimensionalities and input-output settings. We propose and study three comparative measures: noise-tolerance, convincingness, and an analytic approximation of convincingness called the gapped score. Our computational experiments and analytic framework demonstrate that convincingness provides the most nuanced measure for noise-robustness. We then show that the CHSH game has the highest noise-robustness compared to more complex games (2-CHSH variants and the Magic Square Game) when given equal resources, while with unequal resources, some 2-CHSH variants can outperform CHSH at a high resource cost. This work provides the first systematic and operational framework for comparing noise-robustness in self-testing protocols, laying a foundation for theoretical advances in understanding noise-robustness of self-tests and practical improvements in quantum resource utilization.

Figures

Figures reproduced from arXiv: 2505.13537 by the authors.

Figure 1
Figure 1. The CHSH game has 2 inputs and 2 outputs while the 2-CHSH game has 4 inputs and 4 outputs. What is [PITH_FULL_IMAGE:figures/full_fig_p012_1.png] view at source ↗
Figure 2
Figure 2. Optimization axes for non-local games, illustrat [PITH_FULL_IMAGE:figures/full_fig_p016_2.png] view at source ↗
Figure 3
Figure 3. Experiments for evaluating noise-robustness with a comparative score. Illustrating two ways to look at how a game can be robust to noise: robust across a region, or robust for a particular noise type. Green axes are varied and Red axes are fixed. 3a (left): Fixing known (i.e., optimal) weights, coefficients, and measurements while varying the visibility η of the input state ρη. 3b (right): Optimizing the coefficient… view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: Convincingness Behaviour Analysis for Finite Resources (low Nres). The convincingness curves were computed for the CHSH, MSG, 2-CHSH, and 2-CHSH-OPT games using the methods proposed in Sec. IV.. Each point on a curve was computed assuming Nres η-noisy EPR pairs are ava…
Figure 5
Figure 5. Figure 5: Convincingness Behaviour Analysis for Near-Infinite Resources (high Nres). The convincingness was computed the same way as in [PITH_FULL_IMAGE:figures/full_fig_p026_5.png]
Figure 6
Figure 6. Figure 6: Convincingness Behaviour Analysis for Near-Infinite, Unequal Resources Between CHSH and 2-CHSH-OPT Configurations. The right figure is a zoom-in of the left figure. We took the most convincing 2- CHSH-OPT games, and permitted them to have much more noisy resources (man…
Figure 7
Figure 7. Figure 7: Order of Crossings (1 − η † G) for Games at Different Nres. With these observations in mind, we compare the crossing orders of experiments conducted for unstable (Nres = 500, 1000) and stable (Nres = 2000) resource regions to the values of all candidate predictors in …
Figure 8
Figure 8. Figure 8: Comparing Candidate Predictors of Crossing Order. The figures show the true crossings attained at Nres = 500, 1000, or 2000 across all experiments versus the gapped score (right) and all other candidate metrics (left). Some scaling was applied to metrics in order to ma…
Figure 9
Figure 9. Figure 9: Noise-Tolerance Analysis. Left: The horizontal dotted and filled lines represent the local and quantum bounds, respectively, for the curve of that colour. The vertical dotted lines indicate the intersection of the local bound with the curves, indicating the noise-toler…

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  1. Exploring entanglement, Wigner negativity and Bell nonlocality for anisotropic two-qutrit states

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Reference graph

Works this paper leans on

55 extracted references · 47 canonical work pages · cited by 1 Pith paper

  1. [30]

    Bell nonlocality with a single shot.Quantum, 4:353, 2020

    Mateus Araújo, Flavien Hirsch, and Marco Túlio Quintino. Bell nonlocality with a single shot.Quantum, 4:353, 2020

    work page 2020

  2. [1]

    On the einstein podolsky rosen paradox.Physics Physique Fizika, 1(3):195, 1964

    John S Bell. On the einstein podolsky rosen paradox.Physics Physique Fizika, 1(3):195, 1964

    1964

  3. [2]

    Loophole-free bell inequality violation using electron spins separated by 1.3 kilometres.Nature, 526(7575):682–686, 2015

    Bas Hensen, Hannes Bernien, Anaïs E Dréau, Andreas Reiserer, Norbert Kalb, Machiel S Blok, Just Ruitenberg, Raymond FL Vermeulen, Raymond N Schouten, Carlos Abellán, et al. Loophole-free bell inequality violation using electron spins separated by 1.3 kilometres.Nature, 526(7575):682–686, 2015

    work page 2015

  4. [3]

    Strong loophole-free test of local realism

    Lynden K Shalm, Evan Meyer-Scott, Bradley G Christensen, Peter Bierhorst, Michael A Wayne, Martin J Stevens, Thomas Gerrits, Scott Glancy, Deny R Hamel, Michael S Allman, et al. Strong loophole-free test of local realism. Physical review letters, 115(25):250402, 2015

    work page 2015

  5. [4]

    Significant-loophole-free test of bell’s theorem with entangled photons.Physical review letters, 115(25):250401, 2015

    Marissa Giustina, Marijn AM Versteegh, Sören Wengerowsky, Johannes Handsteiner, Armin Hochrainer, Kevin Phe- lan, Fabian Steinlechner, Johannes Kofler, Jan-Åke Larsson, Carlos Abellán, et al. Significant-loophole-free test of bell’s theorem with entangled photons.Physical review letters, 115(25):250401, 2015

    work page 2015

  6. [5]

    Self-testing of quantum systems: a review.Quantum, 4:337, 2020

    Ivan Šupić and Joseph Bowles. Self-testing of quantum systems: a review.Quantum, 4:337, 2020

    work page 2020

  7. [6]

    Fully device independent quantum key distribution.Communications of the ACM, 62(4):133–133, 2019

    Umesh Vazirani and Thomas Vidick. Fully device independent quantum key distribution.Communications of the ACM, 62(4):133–133, 2019

    work page 2019

  8. [7]

    Simple and tight device-independent security proofs

    Rotem Arnon-Friedman, Renato Renner, and Thomas Vidick. Simple and tight device-independent security proofs. SIAM Journal on Computing, 48(1):181–225, 2019

    work page 2019

Show all 55 references
  1. [8]

    Satellite-based entanglement distribution over 1200 kilometers.Science, 356(6343):1140–1144, 2017

    Juan Yin, Yuan Cao, Yu-Huai Li, Sheng-Kai Liao, Liang Zhang, Ji-Gang Ren, Wen-Qi Cai, Wei-Yue Liu, Bo Li, Hui Dai, et al. Satellite-based entanglement distribution over 1200 kilometers.Science, 356(6343):1140–1144, 2017

    2017

  2. [9]

    Random numbers certified by bell’s theorem.Nature, 464(7291):1021–1024, 2010

    Stefano Pironio, Antonio Acín, Serge Massar, A Boyer de La Giroday, Dzmitry N Matsukevich, Peter Maunz, Steven Olmschenk, David Hayes, Le Luo, T Andrew Manning, et al. Random numbers certified by bell’s theorem.Nature, 464(7291):1021–1024, 2010

    2010

  3. [10]

    Experimental self-testing of entangled states.arXiv preprint arXiv:1803.10961, 2018

    Wen-Hao Zhang, Geng Chen, Xing-Xiang Peng, Xiao-Min Hu, Zhi-Bo Hou, Shang Yu, Xiang-Jun Ye, Zong-Quan Zou, Xiao-Ye Xu, Jian-Shun Tang, et al. Experimental self-testing of entangled states.arXiv preprint arXiv:1803.10961, 2018

    2018 arXiv

  4. [11]

    Robust self-testing of multiparticle entanglement.Physical Review Letters, 127(23):230503, 2021

    Dian Wu, Qi Zhao, Xue-Mei Gu, Han-Sen Zhong, You Zhou, Li-Chao Peng, Jian Qin, Yi-Han Luo, Kai Chen, Li Li, et al. Robust self-testing of multiparticle entanglement.Physical Review Letters, 127(23):230503, 2021

    2021

  5. [12]

    Self-testing of a single quantum system from theory to experiment.npj Quantum Information, 9(1):103, 2023

    Xiao-Min Hu, Yi Xie, Atul Singh Arora, Ming-Zhong Ai, Kishor Bharti, Jie Zhang, Wei Wu, Ping-Xing Chen, Jin- Ming Cui, Bi-Heng Liu, et al. Self-testing of a single quantum system from theory to experiment.npj Quantum Information, 9(1):103, 2023

    2023

  6. [13]

    Experimental comparison of tomography and self-testing in certifying entanglement.Physical Review A, 100(2):022305, 2019

    Koon Tong Goh, Chithrabhanu Perumangatt, Zhi Xian Lee, Alexander Ling, and Valerio Scarani. Experimental comparison of tomography and self-testing in certifying entanglement.Physical Review A, 100(2):022305, 2019

    2019

  7. [14]

    Proposed experiment to test local hidden- variable theories.Physical review letters, 23(15):880, 1969

    John F Clauser, Michael A Horne, Abner Shimony, and Richard A Holt. Proposed experiment to test local hidden- variable theories.Physical review letters, 23(15):880, 1969

    1969

  8. [15]

    Analysing nonlocality robustness in multiqubit systems under noisy conditions and weak measurements.Quantum Information Processing, 17:1–33, 2018

    Parvinder Singh and Atul Kumar. Analysing nonlocality robustness in multiqubit systems under noisy conditions and weak measurements.Quantum Information Processing, 17:1–33, 2018

    2018

  9. [16]

    Enhancing pseudo-telepathy in the magic square game

    Łukasz Pawela, Piotr Gawron, Zbigniew Puchała, and Jan Sładkowski. Enhancing pseudo-telepathy in the magic square game. PloS one, 8(6):e64694, 2013

    2013

  10. [17]

    Open-system dynamics of entanglement: a key issues review

    Leandro Aolita, Fernando De Melo, and Luiz Davidovich. Open-system dynamics of entanglement: a key issues review. Reports on Progress in Physics, 78(4):042001, 2015. 37

    2015

  11. [18]

    Noise-tolerant testing of high entanglement of formation.arXiv preprint arXiv:1712.09368, 2017

    Rotem Arnon-Friedman and Henry Yuen. Noise-tolerant testing of high entanglement of formation.arXiv preprint arXiv:1712.09368, 2017

    2017 arXiv

  12. [19]

    Detecting nonlocality of noisy multipartite states with the chsh inequality.arXiv preprint arXiv:1311.4678, 2013

    Rafael Chaves, Antonio Acín, Leandro Aolita, and Daniel Cavalcanti. Detecting nonlocality of noisy multipartite states with the chsh inequality.arXiv preprint arXiv:1311.4678, 2013

    2013 arXiv

  13. [20]

    Bounding the persistency of the nonlocality of w states

    Péter Diviánszky, Réka Trencsényi, Erika Bene, and Tamás Vértesi. Bounding the persistency of the nonlocality of w states. Physical Review A, 93(4):042113, 2016

    2016

  14. [21]

    Symmetrized persistency of bell correlations for dicke states and ghz-based mixtures: Studying the limits of monogamy.arXiv preprint arXiv:2102.08141, 2021

    Marcin Wieśniak. Symmetrized persistency of bell correlations for dicke states and ghz-based mixtures: Studying the limits of monogamy.arXiv preprint arXiv:2102.08141, 2021

    2021 arXiv

  15. [22]

    Highly noise resistant multipartite quantum correlations

    Wieslaw Laskowski, Tamas Vertesi, and Marcin Wiesniak. Highly noise resistant multipartite quantum correlations. arXiv preprint arXiv:1412.8745, 2014

    2014 arXiv

  16. [23]

    Decoherence effects on the nonlocality of symmetric states

    Adel Sohbi, Isabelle Zaquine, Eleni Diamanti, and Damian Markham. Decoherence effects on the nonlocality of symmetric states. Physical Review A, 91(2):022101, 2015

    2015

  17. [24]

    Noise effects in quantum magic squares game.International Journal of Quantum Information, 6(supp01):667–673, 2008

    Piotr Gawron, Jarosław Miszczak, and Jan Sładkowski. Noise effects in quantum magic squares game.International Journal of Quantum Information, 6(supp01):667–673, 2008

    2008

  18. [25]

    Unbounded violation of tripartite bell inequalities.Communications in Mathematical Physics, 279:455–486, 2008

    David Pérez-García, Michael M Wolf, Carlos Palazuelos, Ignacio Villanueva, and Marius Junge. Unbounded violation of tripartite bell inequalities.Communications in Mathematical Physics, 279:455–486, 2008

    2008

  19. [26]

    Survey on nonlocal games and operator space theory.Journal of Mathematical Physics, 57(1), 2016

    Carlos Palazuelos and Thomas Vidick. Survey on nonlocal games and operator space theory.Journal of Mathematical Physics, 57(1), 2016

    2016

  20. [27]

    Quantum generalizations of bell’s inequality.Letters in Mathematical Physics, 4:93–100, 1980

    Boris S Cirel’son. Quantum generalizations of bell’s inequality.Letters in Mathematical Physics, 4:93–100, 1980

    1980

  21. [28]

    Quantum nonlocality as an axiom.Foundations of Physics, 24(3):379–385, 1994

    Sandu Popescu and Daniel Rohrlich. Quantum nonlocality as an axiom.Foundations of Physics, 24(3):379–385, 1994

    1994

  22. [29]

    Bellnonlocality

    NicolasBrunner, DanielCavalcanti, StefanoPironio, ValerioScarani, andStephanieWehner. Bellnonlocality. Reviews of modern physics, 86(2):419–478, 2014

    2014

  23. [31]

    Nielsen and Isaac L

    Michael A. Nielsen and Isaac L. Chuang. Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, 2010

    2010

  24. [32]

    Duxbury Pacific Grove, CA, 2002

    George Casella and Roger L Berger.Statistical inference, volume 2. Duxbury Pacific Grove, CA, 2002

    2002

  25. [33]

    V. Scarani. Bell Nonlocality. Oxford Graduate Texts. Oxford University Press, 2019

    2019

  26. [34]

    Lecture 6: Nonlocal games and Tsirelson’s theorem, 2020

    John Watrous. Lecture 6: Nonlocal games and Tsirelson’s theorem, 2020. Advanced Topics in Quantum Information Theory, CS 798/QIC 890, University of Waterloo

    2020

  27. [35]

    Lecture 14: Nonlocal games, 2018

    Scott Aaronson. Lecture 14: Nonlocal games, 2018. Introduction to Quantum Information Science, Fall 2018, University of Texas at Austin

    2018

  28. [36]

    B. S. Cirel’son. Quantum generalizations of bell’s inequality.Letters in Mathematical Physics, 4(2):93–100, 1980

    1980

  29. [37]

    Quantum nonlocality, bell inequalities, and the memory loophole.Phys

    Jonathan Barrett, Daniel Collins, Lucien Hardy, Adrian Kent, and Sandu Popescu. Quantum nonlocality, bell inequalities, and the memory loophole.Phys. Rev. A, 66:042111, Oct 2002

    2002

  30. [38]

    István Márton, Erika Bene, and Tamás Vértesi. Bounding the detection efficiency threshold in bell tests using multiple copies of the maximally entangled two-qubit state carried by a single pair of particles.Physical Review A, 107(2):022205, 2023. 38

    2023

  31. [39]

    Matlab version: 9.13.0 (r2022b), 2022

    The MathWorks Inc. Matlab version: 9.13.0 (r2022b), 2022

    2022

  32. [40]

    Centrum voor Wiskunde en Informatica Ams- terdam, 1995

    Guido Van Rossum and Fred L Drake Jr.Python reference manual. Centrum voor Wiskunde en Informatica Ams- terdam, 1995

    1995

  33. [41]

    Johansson, P.D

    J.R. Johansson, P.D. Nation, and Franco Nori. Qutip: An open-source python framework for the dynamics of open quantum systems. Computer Physics Communications, 183(8):1760–1772, August 2012

    2012

  34. [42]

    Security of quantum key distribution.International Journal of Quantum Information, 6(01):1–127, 2008

    Renato Renner. Security of quantum key distribution.International Journal of Quantum Information, 6(01):1–127, 2008

    2008

  35. [43]

    Quantum random number generators.Reviews of Modern Physics, 89(1):015004, 2017

    Miguel Herrero-Collantes and Juan Carlos Garcia-Escartin. Quantum random number generators.Reviews of Modern Physics, 89(1):015004, 2017

    2017

  36. [44]

    Concentrating partial entan- glement by local operations.Physical Review A, 53(4):2046, 1996

    Charles H Bennett, Herbert J Bernstein, Sandu Popescu, and Benjamin Schumacher. Concentrating partial entan- glement by local operations.Physical Review A, 53(4):2046, 1996

    1996

  37. [45]

    Purification of noisy entanglement and faithful teleportation via noisy channels.Physical review letters, 76(5):722, 1996

    Charles H Bennett, Gilles Brassard, Sandu Popescu, Benjamin Schumacher, John A Smolin, and William K Wootters. Purification of noisy entanglement and faithful teleportation via noisy channels.Physical review letters, 76(5):722, 1996

    1996

  38. [46]

    Quantum entanglement.Reviews of modern physics, 81(2):865–942, 2009

    Ryszard Horodecki, Paweł Horodecki, Michał Horodecki, and Karol Horodecki. Quantum entanglement.Reviews of modern physics, 81(2):865–942, 2009

    2009

  39. [47]

    Device-independent secret-key-rate analysis for quantum repeaters

    Timo Holz, Hermann Kampermann, and Dagmar Bruß. Device-independent secret-key-rate analysis for quantum repeaters. Physical Review A, 97(1):012337, 2018

    2018

  40. [48]

    Experimental quantum key distribution certified by bell’s theorem

    David P Nadlinger, Peter Drmota, Bethan C Nichol, Gabriel Araneda, Dougal Main, Raghavendra Srinivas, David M Lucas, Christopher J Ballance, Kirill Ivanov, EY-Z Tan, et al. Experimental quantum key distribution certified by bell’s theorem. Nature, 607(7920):682–686, 2022

    2022

  41. [49]

    A device-independent quantum key distribution system for distant users.Nature, 607(7920):687–691, 2022

    Wei Zhang, Tim van Leent, Kai Redeker, Robert Garthoff, René Schwonnek, Florian Fertig, Sebastian Eppelt, Wenjamin Rosenfeld, Valerio Scarani, Charles C-W Lim, et al. A device-independent quantum key distribution system for distant users.Nature, 607(7920):687–691, 2022

    2022

  42. [50]

    Maximal randomness from partially entangled states.Physical Review Research, 2(4):042028, 2020

    Erik Woodhead, Jędrzej Kaniewski, Boris Bourdoncle, Alexia Salavrakos, Joseph Bowles, Antonio Acín, and Remigiusz Augusiak. Maximal randomness from partially entangled states.Physical Review Research, 2(4):042028, 2020

    2020

  43. [51]

    Quantum resource theories.Reviews of modern physics, 91(2):025001, 2019

    Eric Chitambar and Gilad Gour. Quantum resource theories.Reviews of modern physics, 91(2):025001, 2019

    2019

  44. [52]

    A mathematical theory of resources.Information and Compu- tation, 250:59–86, 2016

    Bob Coecke, Tobias Fritz, and Robert W Spekkens. A mathematical theory of resources.Information and Compu- tation, 250:59–86, 2016

    2016

  45. [53]

    Quantifying bell: The resource theory of nonclassicality of common-cause boxes.Quantum, 4:280, 2020

    Elie Wolfe, David Schmid, Ana Belén Sainz, Ravi Kunjwal, and Robert W Spekkens. Quantifying bell: The resource theory of nonclassicality of common-cause boxes.Quantum, 4:280, 2020

    2020

  46. [54]

    Magic-Square box

    Beata Zjawin, David Schmid, Matty J Hoban, and Ana Belén Sainz. Quantifying epr: the resource theory of nonclassicality of common-cause assemblages.Quantum, 7:926, 2023. 39 XIII. (APPENDIX) 2-CHSH-OPT Score Derivation Tr(Pη ¯BT η′) = Tr   1 16   16X a,b=1 Tr(ρin(Aa⊗Bb))|ea...

    2023

  47. [55]

    In particular, there is at least one deterministic wiring, call itΛdet, with Λdet(M) =T

    By the uniqueness statement in (i), this forces every such deterministic wiring to output the Tsirelson boxT . In particular, there is at least one deterministic wiring, call itΛdet, with Λdet(M) =T . (iv) Deterministic wirings preserve rationality. A deterministic DI operatio...

Pith tools

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