Pith. sign in

REVIEW 3 major objections 5 minor 45 references

Finite-size security analysis for quantum protocols: A Python framework using the Entropy Accumulation Theorem with graphical interface

T0 review · 3 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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

Pith's one-line read The expdiqrng package claims to automate finite-size security analysis for quantum random number generation and quantum key distribution, constructing min-tradeoff functions via semidefinite programming and applying the Entropy…

desk verdict A genuinely useful EAT software framework whose security numbers rest on unverified floating-point dual SDP solutions—worth refereeing, but only after the authors certify their certificates. read the letter →

arxiv 2506.18888 v1 pith:JS6G34FL submitted 2025-06-23 quant-ph

Piotr Mironowicz , Mohamed Bourennane This is my paper · ORCID
classification quant-ph
keywords quantumcryptographyentropyaccumulationtheoremfinite-sizesecurityanalysismin-tradeofffunctionsemidefiniteprogrammingdevice-independentkeydistributionrandomnumbergenerationgraphicaluserinterface
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 presents an open-source Python package, expdiqrng, whose central claim is that finite-size security analysis for quantum random number generation and quantum key distribution -- including device-independent protocols that do not trust the hardware -- can be fully automated. Given a Bell expression, observed data, and a handful of protocol parameters, the package constructs a valid min-tradeoff function, an affine lower bound on the per-round conditional entropy, by solving semidefinite relaxations, and then feeds it into the Entropy Accumulation Theorem, a framework that turns per-round bounds into a total finite-size security guarantee. If the claim holds, experimentalists who would otherwise face a steep mathematical barrier can compute trustworthy randomness and key rates directly from raw experimental counts. The paper supports the claim with two end-to-end case studies, one based on the modified CHSH Bell expression and one on the standard CHSH scenario, and reports concrete finite-size rates in both.

What carries the argument

The load-bearing object is the min-tradeoff function, an affine map $f$ from observed per-round statistics to a lower bound on the conditional von Neumann entropy $H(A_iB_i|X_iY_iE)$ for any state consistent with those statistics. The package obtains $f$ by solving a semidefinite program -- an NPA-type hierarchy, a chain of relaxations approximating the quantum correlation set, or a quadrature-based relaxation for von Neumann entropy -- and reading the dual solution, so the function is a certificate rather than a heuristic fit. The EAT channel structure with the Markov condition lets this per-round bound accumulate over $n$ rounds into the smooth min-entropy bound $H^{\epsilon_s}_{\min}(A^nB^n|X^nY^nE) > nt - n(\epsilon_V+\epsilon_K) - \epsilon_\Omega$. The free parameter $\beta$ balances the variance and completeness penalties, and the package sweeps $\beta$, the test-round probability $\gamma$, and the data-chunk time to report the optimal secure rate.

What would settle it

Take a CHSH instance with very few rounds, say $n=3$, exhaustively search the quantum strategy space compatible with the observed correlations, compute the exact smooth min-entropy by direct enumeration, and check that the package's reported finite-size bound never exceeds that value; a single counterexample would show the automated certificate pipeline is unsound.

Watch

Extended reading notes

Core claim

The central claim is that a single software pipeline can take a raw click table from a QRNG or QKD experiment and return an EAT-based finite-size security bound with no manual derivation of the difficult objects. The package builds the min-tradeoff function from the dual solution of an NPA-type or quadrature-based semidefinite relaxation, then evaluates the EAT bound $H^{\epsilon_s}_{\min}(A^nB^n|X^nY^nE) > nt - n(\epsilon_V+\epsilon_K) - \epsilon_\Omega$, where $t$ is the min-tradeoff function's value at the observed frequency and the three $\epsilon$ terms are finite-size penalties. In the modCHSH QRNG example, the asymptotic rate of about 1.4369 bits per event falls to roughly 947,240 secure bits per second at $10^6$ events per second after one hour of data, with smoothing $\epsilon_s=10^{-12}$ and completeness $p_\Omega=0.99$. In the CHSH QKD example, an asymptotic key rate near 0.96 bits per event yields about $8\times10^8$ key bits per second at roughly $10^9$ events per second on a ten-second data chunk. The authors also demonstrate the graphical workflow, from parsing data files to plotting how key rate depends on the protocol parameters.

Load-bearing premise

The security numbers stand or fall with the numerical semidefinite solver: if its dual solution is not a true feasible lower bound, or if the protocol's relaxation is mis-specified, the reported rate can overstate the certified randomness.

Editorial extensions

If this is right

  • An experimental group can turn a raw count table into a certified finite-size randomness rate without writing EAT code, either through the Python API or the graphical interface.
  • The automated parameter sweep lets users see how the secure rate depends on test-round probability, smoothing, and collection time, so they can choose an operating point to maximize output under their own noise and time budget.
  • Both min-entropy (for QRNG) and von Neumann entropy (for QKD) are supported, with the QKD error-correction leakage included in the rate calculation.
  • Because the certificate is built from a dual semidefinite solution, the same framework can accommodate arbitrary linear combinations of correlators and marginal probabilities, which can certify more randomness than a single Bell inequality.

Reading between the lines

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

  • Beyond the paper's own examples, exporting the raw primal and dual solver certificates alongside each rate would let anyone independently verify the security bound, since the entire argument rests on those dual solutions.
  • A natural test is to benchmark the automatically generated min-tradeoff function against known analytical constructions, such as tilted CHSH bounds; the gap would quantify how much rate the generic SDP route sacrifices for automation.
  • The same modular pipeline could extend to multi-party or multi-outcome Bell scenarios: the EAT machinery is not specific to two-party CHSH, but the semidefinite relaxations would need to be rebuilt.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. This manuscript introduces expdiqrng, a Python framework (with a GUI) for finite-size security analysis of device-independent QRNG and QKD protocols using the Entropy Accumulation Theorem (EAT). The framework is designed to construct min-tradeoff functions from semidefinite programming relaxations (NPA and BFF) and to feed them into an EAT-based rate calculation. Two case studies are presented: a modCHSH QRNG example using min-entropy through the API, and a CHSH QKD example using von Neumann entropy through the GUI. The authors state that the source code is publicly available and argue that the tool lowers the skill barrier for rigorous quantum cryptographic analysis.

Significance. If the numerical security certificates are sound, this is a useful and timely contribution: it packages the EAT pipeline with a GUI, public code, and step-by-step examples, which is valuable for experimentalists. The modular design and the reliance on established SDP hierarchies (NPA and BFF) are strengths, as is the explicit use of the Brown et al. EAT formulation. However, the central claim depends critically on unstated numerical certification of the SDP dual solutions, and the QKD example raises a serious question about which entropy quantity is actually bounded. With those issues resolved, the tool could have real impact; as written, the security guarantees are not sufficiently evidenced.

major comments (3)
  1. [Section III, Section IV C, Appendix A] The only description of the core certificate construction is that "min-tradeoff functions were calculated using the dual SDP solutions, as described in Section 3.4 of [25]". A floating-point dual solution returned by ncpol2sdpa is not automatically a feasible dual certificate for the NPA/BFF relaxation; if the dual is infeasible at the solver tolerance, the affine function f can overestimate the true conditional entropy for some distribution consistent with the observed data, which would invalidate the EAT bound (7) without changing any printed output. The manuscript must specify the exact SDP and dual variables used, the solver and tolerances, and any post-processing that certifies feasibility (e.g., residual checks, interval arithmetic, or exact rational reconstruction), and it should provide a way for the user to verify each certificate. No test suite, independent analytical comparison, or existing-software comparison is currently reported, so the central claim in the abstract is not yet supported.
  2. [Section V, Eq. (11), Definition 2, Appendix A] The Devetak-Winter rate in Eq. (11) is r = H(A|E) - H(A|B), but the min-tradeoff function in Definition 2 and the BFF relaxation in Appendix A are stated for the joint quantity H(A_iB_i|X_iY_iR') / H(Q_AQ_B|...E). The QKD example subtracts H(A|B)=0.01 from a min-tradeoff certificate value of 0.979964 and treats the result as the asymptotic key rate. This is only valid if the certificate already lower-bounds H(A_i|X_iY_iE). If the certificate bounds the joint entropy, the computed expression is H(A_i|E)+H(B_i|A_iE)-H(A_i|B_i), which does not generally lower-bound the true Devetak-Winter rate. Please clarify which entropy quantity the package computes for "Key Distribution", and either correct the example or re-derive the key-rate formula.
  3. [Section IV F, Listing 8] The headline output is called net_gain_per_second and is described as the "actual secure randomness generation rate", yet the printed parameters include subtract_consumption_for_test_rounds: False, and the text explicitly states that the 2.585 bits per round of input randomness are not subtracted. For a randomness expansion protocol, input randomness consumption is part of the net gain calculation; reporting 947,239 bits/s as a "net gain" while assuming free input randomness is misleading. Rename the quantity (e.g., gross generation rate) or change the example to subtract the consumption and report a true net expansion rate.
minor comments (5)
  1. [Section II E, Eq. (9)] The set Gamma appearing in Var[f|Gamma], Min[f|Gamma], and d_f is never defined. Define it (e.g., as the set of distributions compatible with the protocol constraints and the event Omega) so the formulas are self-contained.
  2. [Section II B, Listing 5] The variable confidence_interval_list takes the value 0.99 and is used as p_Omega; the name is nonstandard and could be confused with a statistical confidence interval. Rename it to pOmega or explain the correspondence with the completeness level.
  3. [Section V, Listing 10] The example data rows do not clearly match the described parsing schema: the text says the first column identifies settings by values 1, 2, 3, 4, while the listed file appears to contain rows with first-column values such as 2 and 73. Please supply a self-consistent sample file or explicitly state the column mapping for the printed rows.
  4. [Data availability] Provide a versioned release (or DOI) and list the exact versions of Python, ncpol2sdpa, and the SDP solver used to produce Listing 8 and the GUI results, so that the numerical outputs are reproducible.
  5. [References] Reference [12] is marked "to appear" although it is dated 2021; update the citation, and check [11] and [25] for final published versions.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found: the EAT theorem, min-tradeoff construction, and case-study rates are based on external prior work or on fixed example inputs, not on self-referential definitions.

full rationale

The paper's derivation chain is self-contained in the relevant sense: the EAT bound (Theorem 1, Eqs. (7)-(9)) is quoted from the external framework of Brown, Ragy, and Colbeck [11] and Dupuis-Fawzi [12], and the min-tradeoff function is defined in Definition 2 as a lower bound on per-round conditional entropy, with construction delegated to standard SDP relaxations ("In practice, one constructs f by solving suitable SDP, e.g. using Navascués-Pironio-Acín (NPA) or BFF relaxations... [23-25]"; "The min-tradeoff functions were calculated using the dual SDP solutions, as described in Section 3.4 of [25]"). This is an implementation of an external mathematical method, not a definition of the target result in terms of itself. The case-study outputs (e.g., about 947,240 bits/second in the modCHSH example) are computed from explicitly fixed inputs such as certificate value 3.8 and a stated parameter set; they are illustrative outputs of the software, not predictions of quantities that were fitted to those same outputs. Self-citations appear (the author's review [25], the modCHSH expression [31], and the optimization reference [22]), but none carries a load-bearing uniqueness claim or an ansatz smuggled in to force the conclusion; the central EAT formulas and the BFF/NPA relaxations are attributed to independent prior literature. The concern that floating-point dual SDP solutions may not be certified rigorous lower bounds is a correctness or robustness issue about numerical certification, not a circularity of the derivation. No step in the paper's claimed chain reduces, by construction or by self-citation, to its own input.

Assumptions & free parameters 7 free parameters · 3 assumptions · 0 invented entities

The software does not introduce new physical entities or mathematical axioms. Its correctness depends on the standard EAT theorem, the SDP hierarchy bounds, and the protocol assumptions. The user-supplied numerical parameters listed above are not fitted to data but are required to reproduce the specific example outputs.

free parameters (7)
  • NPA relaxation level = 2
    User-selected hierarchy level for the NPA SDP; tighter levels give more accurate but more expensive bounds.
  • BFF quadrature parameter m_radau = 0
    User-selected parameter for the BFF hierarchy; in the QRNG example it is set to 0.
  • Certificate value (modCHSH) = 3.8
    Illustrative observed Bell value in the QRNG case study; the resulting min-tradeoff function depends on this value.
  • Smoothing parameter epsS = 1e-12
    User-set smoothing parameter for the smooth min-entropy in the QRNG example.
  • Completeness level pOmega = 0.99
    User-set probability that the protocol does not abort; used in the EAT error term.
  • Test round probability gamma = 0.01
    User-set fraction of test rounds, balancing statistical estimation and randomness generation.
  • H(A|B) error-correction term for spot setting = 0.01
    User-provided conditional entropy used for QKD error correction in the CHSH example.
assumptions (3)
  • domain assumption Entropy Accumulation Theorem (Theorem 1) holds for the considered protocols and provides valid smooth min-entropy bounds.
    The entire software pipeline relies on the EAT statement as formulated by Brown et al. and Dupuis et al.; the security certificates inherit this theorem's assumptions, including the EAT channel definition and Markov condition.
  • domain assumption The NPA hierarchy and the BFF relaxation give rigorous lower bounds on the conditional von Neumann and min-entropy.
    Min-tradeoff functions are constructed from dual SDP solutions of these hierarchies; the validity of these bounds is established in the cited literature and is not re-derived in the paper.
  • domain assumption The devices and protocol satisfy the no-signaling conditions and the spot-checking structure assumed in the data model.
    The probability constraints and data parsing assume correlations are no-signaling, and the entropy bounds require the spot-checking protocol's input distribution and Markov structure. Experimental violations of these assumptions would invalidate the security claim.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Finite-size security analysis for quantum protocols: A Python framework using the Entropy Accumulation Theorem with graphical interface." pith.science (2026). https://pith.science/paper/JS6G34FL

@misc{pith2026250618888,
  author       = {Pith},
  title        = {Pith review of: Finite-size security analysis for quantum protocols: A Python framework using the Entropy Accumulation Theorem with graphical interface},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JS6G34FL}},
  note         = {Machine review of arXiv:2506.18888}
}
read the original abstract

We present a comprehensive software framework for the finite-size security analysis of quantum random number generation (QRNG) and quantum key distribution (QKD) protocols, based on the Entropy Accumulation Theorem (EAT). Our framework includes both a Python API and an intuitive graphical user interface (GUI), designed to support protocol designers and experimentalists in certifying randomness and key rates under realistic, finite-resource conditions. At its core, the framework automates the construction of min-tradeoff functions via semi-definite programming and integrates them into a full entropy analysis pipeline. Users can specify device configurations, Bell-type inequalities or probability constraints, and select entropy measures such as min-entropy or von Neumann entropy. The package further provides tools for setting test parameters, computing secure randomness rates, and exploring tradeoffs between statistical confidence, protocol duration, and randomness output. We demonstrate the framework showing how users can move from theoretical constraints to practical security bounds with minimal overhead. This work contributes a reproducible, modular, and extensible platform for certifying quantum protocols under finite-size effects, significantly lowering the skill barrier to rigorous quantum cryptographic analysis.

Figures

Figures reproduced from arXiv: 2506.18888 by the authors.

Figure 1
Figure 1. FIG. 1. Menu with EAT analysis options in execution order, [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. The Data Config screen where column mappings for [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Screen for managing loaded experimental data [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Create certificate screen with options for entropy type [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Results screen to visualize key length vs. parameters. [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Generated key bits per second vs. test round proba [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

45 extracted references · 35 canonical work pages

  1. [25]

    Optimization of experimental quantum randomness expansion,

    A. Piveteau, A. Seguinard, P. Mironowicz, and M. Bourennane, “Optimization of experimental quantum randomness expansion,” arXiv preprint arXiv:2411.04934, 2024

    arXiv 2024

  2. [1]

    Ai,Bi,Xi,Yi,Ci are finite-dimensional classical registers, and Ci is the output of a deterministic function of the classical registers(Ai,Bi,Xi,Yi)

    work page

  3. [2]

    Ri is an arbitrary quantum register; 3

    work page

  4. [3]

    C( 0 , 0 ) + C( 0 , 1 ) + C( 1 , 0 ) − C( 1 , 1 ) + C( 2 , 1 )

    For any initial stateρR0E (with E the adversary register), the final global state ρAnBnX nY nCnE := TrRn h Nn◦···◦N 1⊗ idE (ρR0E) i (2) satisfies, for everyi∈ [n], the Markov chain condi- tion I Ai−1Bi−1 :XiYi|Xi−1Yi−1E = 0. (3) The Markov chain condition (3) implies that the choice of inputs (Xi,Yi) at roundi is (conditionally) indepen- dent of all previ...

    work page

  5. [4]

    Quan- tum cryptography,

    N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quan- tum cryptography,”Reviews of modern physics, vol. 74, no. 1, p. 145, 2002

    work page 2002

  6. [5]

    The security of practical quantum key distribution,

    V. Scaraniet al., “The security of practical quantum key distribution,” Reviews of Modern Physics, vol. 81, no. 3, pp. 1301–1350, 2009

    work page 2009

  7. [6]

    M. A. Nielsen and I. L. Chuang,Quantum Computation and Quantum Information. Cambridge University Press, 2010

    2010

  8. [7]

    Advances in quantum cryptography,

    S. Pirandola, U. L. Andersen, L. Banchi, M. Berta, D. Bunandar, R. Colbeck, D. Englund, T. Gehring, C. Lupo, C. Ottaviani, et al., “Advances in quantum cryptography,” Advances in optics and photonics, vol. 12, no. 4, pp. 1012–1236, 2020

    2020

Show all 45 references
  1. [8]

    Random numbers certified by Bell’s theorem,

    S. Pironio et al., “Random numbers certified by Bell’s theorem,” Nature, vol. 464, pp. 1021–1024, 2010

    2010

  2. [9]

    Certified randomness in quan- tum physics,

    A. Acín and L. Masanes, “Certified randomness in quan- tum physics,”Nature, vol. 540, pp. 213–219, 2016

    2016

  3. [10]

    Tomamichel,Quantum Information Processing with Finite Resources: Mathematical Foundations , vol

    M. Tomamichel,Quantum Information Processing with Finite Resources: Mathematical Foundations , vol. 5 of SpringerBriefs in Mathematical Physics. Springer, Cham, 1 ed., 2016. 4 illustrations in colour

    2016

  4. [11]

    Entropy accu- mulation,

    F. Dupuis, O. Fawzi, and R. Renner, “Entropy accu- mulation,” Communications in Mathematical Physics, vol. 379, pp. 867–913, 2020

    2020

  5. [12]

    Quantum probability estimation for randomness with quantum side informa- tion,

    E. Knill, Y. Zhang, and H. Fu, “Quantum probability estimation for randomness with quantum side informa- tion,” arXiv preprint arXiv:1806.04553, 2018

    2018 arXiv

  6. [13]

    Proposed experiment to test local hidden-variable the- ories,

    J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, “Proposed experiment to test local hidden-variable the- ories,” Physical Review Letters, vol. 23, no. 15, p. 880, 1969

    1969

  7. [14]

    A framework for quantum-secure device-independent randomness expan- sion,

    P. J. Brown, S. Ragy, and R. Colbeck, “A framework for quantum-secure device-independent randomness expan- sion,” IEEE Transactions on Information Theory, 2019

    2019

  8. [15]

    Entropy accumulation with improved second-order term,

    F. Dupuis and O. Fawzi, “Entropy accumulation with improved second-order term,”IEEE Transactions on In- formation Theory, 2021. to appear

    2021

  9. [16]

    Gener- alised entropy accumulation,

    T. Metger, O. Fawzi, D. Sutter, and R. Renner, “Gener- alised entropy accumulation,”Communications in Math- ematical Physics, vol. 405, no. 11, p. 261, 2024. 11

    2024

  10. [17]

    General- ized r\’enyi entropy accumulation theorem and gener- alized quantum probability estimation,

    A. Arqand, T. A. Hahn, and E. Y.-Z. Tan, “General- ized r\’enyi entropy accumulation theorem and gener- alized quantum probability estimation,” arXiv preprint arXiv:2405.05912, 2024

    2024 arXiv

  11. [18]

    Practical device-independent quantum cryp- tography via entropy accumulation,

    R.Arnon-Friedman, F.Dupuis, O.Fawzi, R.Renner, and T. Vidick, “Practical device-independent quantum cryp- tography via entropy accumulation,”Nature communica- tions, vol. 9, no. 1, p. 459, 2018

    2018

  12. [19]

    Security of quantum key dis- tributionfromgeneralisedentropyaccumulation,

    T. Metger and R. Renner, “Security of quantum key dis- tributionfromgeneralisedentropyaccumulation,” Nature Communications, vol. 14, no. 1, p. 5272, 2023

    2023

  13. [20]

    Sim- ple and tight device-independent security proofs,

    R. Arnon-Friedman, R. Renner, and T. Vidick, “Sim- ple and tight device-independent security proofs,”SIAM Journal on Computing, vol. 48, no. 1, pp. 181–225, 2019

    2019

  14. [21]

    Device- independentrandomnessexpansionagainstquantumside information,

    W.-Z. Liu, M.-H. Li, S. Ragy, S.-R. Zhao, B. Bai, Y. Liu, P. J. Brown, J. Zhang, R. Colbeck, J. Fan,et al., “Device- independentrandomnessexpansionagainstquantumside information,” Nature Physics, vol. 17, no. 4, pp. 448–451, 2021

    2021

  15. [22]

    Experimental quantum key distribution certified by Bell’s theorem,

    D. P. Nadlinger, P. Drmota, B. C. Nichol, G. Araneda, D. Main, R. Srinivas, D. M. Lucas, C. J. Ballance, K. Ivanov, E.-Z. Tan,et al., “Experimental quantum key distribution certified by Bell’s theorem,”Nature, vol. 607, no. 7920, pp. 682–686, 2022

    2022

  16. [23]

    Bell nonlocality,

    N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, and S. Wehner, “Bell nonlocality,”Reviews of modern physics, vol. 86, no. 2, pp. 419–478, 2014

    2014

  17. [24]

    Universal security for random- ness expansion from the spot-checking protocol,

    C. A. Miller and Y. Shi, “Universal security for random- ness expansion from the spot-checking protocol,”SIAM Journal on Computing, vol. 46, no. 4, pp. 1304–1335, 2017

    2017

  18. [26]

    Bounding the set of quantum correlations,

    M. Navascués, S. Pironio, and A. Acín, “Bounding the set of quantum correlations,” Physical Review Letters, vol. 98, no. 1, p. 010401, 2007

    2007

  19. [27]

    A convergent hi- erarchy of semidefinite programs characterizing the set of quantum correlations,

    M. Navascués, S. Pironio, and A. Acín, “A convergent hi- erarchy of semidefinite programs characterizing the set of quantum correlations,” New Journal of Physics, vol. 10, no. 7, p. 073013, 2008

    2008

  20. [28]

    Semi-definite programming and quan- tum information,

    P. Mironowicz, “Semi-definite programming and quan- tum information,” Journal of Physics A: Mathematical and Theoretical, vol. 57, no. 16, p. 163002, 2024

    2024

  21. [29]

    Device-independent lower bounds on the conditional von neumann entropy,

    P. Brown, H. Fawzi, and O. Fawzi, “Device-independent lower bounds on the conditional von neumann entropy,” Quantum, vol. 8, p. 1445, 2024

    2024

  22. [30]

    Using complete measurement statistics for optimal device- independent randomness evaluation,

    O. Nieto-Silleras, S. Pironio, and J. Silman, “Using complete measurement statistics for optimal device- independent randomness evaluation,” New Journal of Physics, vol. 16, no. 1, p. 013035, 2014

    2014

  23. [31]

    More ran- domness from the same data,

    J.-D. Bancal, L. Sheridan, and V. Scarani, “More ran- domness from the same data,”New Journal of Physics, vol. 16, no. 3, p. 033011, 2014

    2014

  24. [32]

    Algorithm 950: Ncpol2sdpa—sparse semidef- inite programming relaxations for polynomial optimiza- tion problems of noncommuting variables,

    P. Wittek, “Algorithm 950: Ncpol2sdpa—sparse semidef- inite programming relaxations for polynomial optimiza- tion problems of noncommuting variables,”ACM Trans- actions on Mathematical Software (TOMS) , vol. 41, no. 3, pp. 1–12, 2015

    2015

  25. [33]

    Updating ncpol2sdpa after Peter Wittek

    P. Wittek and P. J. Brown, “Updating ncpol2sdpa after Peter Wittek.” https://github.com/peterjbrown519/ ncpol2sdpa

  26. [34]

    Robustness of quantum-randomness expansion protocols in the pres- ence of noise,

    P. Mironowicz and M. Pawłowski, “Robustness of quantum-randomness expansion protocols in the pres- ence of noise,” Physical Review A—Atomic, Molecular, and Optical Physics, vol. 88, no. 3, p. 032319, 2013

    2013

  27. [35]

    Efficient quantum key distribution secure against no-signalling eavesdrop- pers,

    A. Acin, S. Massar, and S. Pironio, “Efficient quantum key distribution secure against no-signalling eavesdrop- pers,” New Journal of Physics, vol. 8, no. 8, p. 126, 2006

    2006

  28. [36]

    Distillation of secret key and entanglement from quantum states,

    I. Devetak and A. Winter, “Distillation of secret key and entanglement from quantum states,”Proceedings of the Royal Society A: Mathematical, Physical and engineering sciences, vol. 461, no. 2053, pp. 207–235, 2005

    2005

  29. [37]

    Proper- ties of dimension witnesses and their semidefinite pro- gramming relaxations,

    P. Mironowicz, H.-W. Li, and M. Pawłowski, “Proper- ties of dimension witnesses and their semidefinite pro- gramming relaxations,”Physical Review A, vol. 90, no. 2, p. 022322, 2014

    2014

  30. [38]

    Bounding the set of fi- nite dimensional quantum correlations,

    M. Navascués and T. Vértesi, “Bounding the set of fi- nite dimensional quantum correlations,”Physical Review Letters, vol. 115, no. 2, p. 020501, 2015

    2015

  31. [39]

    Exponentially de- creasing critical detection efficiency for any Bell inequality,

    N. Miklin, A. Chaturvedi, M. Bourennane, M. Pawłowski, and A. Cabello, “Exponentially de- creasing critical detection efficiency for any Bell inequality,” Physical Review Letters, vol. 129, no. 23, p. 230403, 2022

    2022

  32. [40]

    Distilling nonlocal- ity,

    M. Forster, S. Winkler, and S. Wolf, “Distilling nonlocal- ity,” Physical Review Letters, vol. 102, no. 12, p. 120401, 2009

    2009

  33. [41]

    Device independent quantum key activation,

    B. Ulu, N. Brunner, and M. Weilenmann, “Device independent quantum key activation,” arXiv preprint arXiv:2506.09772, 2025

    2025

  34. [42]

    Applications of semi-definite optimiza- tion in quantum information protocols,

    P. Mironowicz, “Applications of semi-definite optimiza- tion in quantum information protocols,”arXiv preprint arXiv:1810.05145, 2018

    2018 arXiv

  35. [43]

    Tre- visan’s extractor in the presence of quantum side infor- mation,

    A. De, C. Portmann, T. Vidick, and R. Renner, “Tre- visan’s extractor in the presence of quantum side infor- mation,” SIAM Journal on Computing, vol. 41, no. 4, pp. 915–940, 2012

    2012

  36. [44]

    A modular framework for randomness extraction based on trevisan’s construction,

    W. Mauerer, C. Portmann, and V. B. Scholz, “A modular framework for randomness extraction based on trevisan’s construction,” arXiv preprint arXiv:1212.0520, 2012

    2012 arXiv

  37. [45]

    Postprocessing for quantum random-number generators: Entropy evaluation and randomness extraction,

    X. Ma, F. Xu, H. Xu, X. Tan, B. Qi, and H.-K. Lo, “Postprocessing for quantum random-number generators: Entropy evaluation and randomness extraction,”Physi- cal Review A—Atomic, Molecular, and Optical Physics, vol. 87, no. 6, p. 062327, 2013. Appendix A: Semi-definite programm...

    2013

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.