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arxiv: 2605.06249 · v1 · submitted 2026-05-07 · 🪐 quant-ph

Recognition: unknown

Finite-size general security for differential phase shift keying via variable-length quantum key distribution

Carlos Pascual-Garc\'ia
Authors on Pith no claims yet

Pith reviewed 2026-05-08 11:22 UTC · model grok-4.3

classification 🪐 quant-ph
keywords differential phase shift keyingquantum key distributionfinite-size securitygeneral securityRényi entropyvariable-length protocolsconic optimizationsecret key rate
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The pith

Variable-length Rényi entropy accumulation and conic optimization remove repetition-rate limits from general security proofs for differential phase shift keying.

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

The paper establishes a finite-size security proof for DPSK that works against general adversaries without the strong repetition-rate constraints and expensive statistical estimators required in earlier analyses. It does so by adapting recent variable-length techniques that combine Rényi leftover hashing with conic optimization. The resulting rates remain positive with only 10^5 signals at losses beyond 12 dB, which the authors present as evidence that DPSK can be realized with commercial hardware under realistic conditions.

Core claim

Applying entropy accumulation based on Rényi leftover hashing together with conic optimization methods yields a general security analysis for DPSK that eliminates repetition-rate constraints and costly estimators while still delivering positive secret-key rates with 10^5 signals at channel losses beyond 12 dB.

What carries the argument

Variable-length general security via Rényi leftover hashing combined with conic optimization, which relaxes block-size and repetition-rate requirements for finite-size DPSK proofs.

If this is right

  • DPSK systems can operate at higher repetition rates without security penalties from finite-size analysis.
  • Positive secret keys become feasible with smaller data blocks than previously required for general security.
  • The same variable-length framework can be ported to other DPSK-like phase-encoded protocols.
  • Experimental demonstrations no longer need to satisfy the stricter repetition-rate conditions of earlier proofs.

Where Pith is reading between the lines

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

  • Commercial DPSK transmitters already used in classical communications could be repurposed for QKD with only software changes to the security layer.
  • The method may extend to other continuous-variable or phase-modulated QKD schemes that currently face similar finite-size bottlenecks.
  • Lowering the required block size could enable real-time key generation in low-loss metropolitan networks.

Load-bearing premise

The variable-length general security techniques based on Rényi leftover hashing together with conic optimization methods can be applied to DPSK to remove repetition rate constraints and costly estimators without introducing new unaccounted assumptions or limitations.

What would settle it

A calculation or experiment showing that the secret-key rate becomes zero or negative for 10^5 signals at 12 dB loss under general attacks, or that the Rényi entropy bounds used in the conic program are violated by the actual DPSK statistics.

Figures

Figures reproduced from arXiv: 2605.06249 by Carlos Pascual-Garc\'ia.

Figure 1
Figure 1. Figure 1: Secret key generation rates for DPSK model under different block sizes view at source ↗
Figure 2
Figure 2. Figure 2: Secret key generation rates for DPSK under different dark count rates view at source ↗
Figure 3
Figure 3. Figure 3: Secret key generation rates for DPSK under values for the R view at source ↗
Figure 4
Figure 4. Figure 4: Secret key generation rates for DPSK under different asymmetry factors view at source ↗
read the original abstract

Differential phase shift keying (DPSK) constitutes a pathway towards practical quantum key distribution by using affordable commercial technologies, and robust theoretical foundations. Recent advances in the security of DPSK have proven its security against general adversaries, albeit requiring limitations, including strong repetition rate constraints at the security proof and costly statistical estimators. In this work, we overcome said limitations by leveraging recent techniques in variable-length general security by using entropy accumulation techniques based on R\'enyi leftover hashing, together with conic optimization methods. Our approach achieves secret key rates with $10^5$ signals beyond 12 dB, constituting a robust proof of the experimental implementability of industrial-grade DPSK.

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

2 major / 2 minor

Summary. The manuscript develops a finite-size general security proof for differential phase shift keying (DPSK) quantum key distribution. It applies variable-length techniques based on Rényi entropy accumulation and conic optimization to remove prior repetition-rate constraints and costly estimators. The central claim is that positive secret key rates are achieved with only 10^5 signals at channel losses beyond 12 dB, providing evidence for the experimental viability of industrial-grade DPSK.

Significance. If the security reduction holds, the result is significant for practical QKD. DPSK leverages affordable commercial components, and a general finite-size proof at modest block sizes directly supports deployment feasibility. The explicit use of entropy-accumulation theorems together with conic optimization constitutes a methodological advance that reduces fitted parameters and could transfer to related protocols.

major comments (2)
  1. [§3, Eq. (12)] §3 (Security Analysis) and Eq. (12): the direct invocation of the variable-length Rényi leftover-hashing bound on the DPSK raw-key string does not insert an explicit smoothing or chain-rule term to account for the Markovian dependence induced by differential phase encoding between adjacent pulses. Because the protocol encodes information in relative phases, the i.i.d. or single-shot Rényi bounds cited from the external framework may under-estimate the finite-size penalty; the subsequent conic program therefore optimizes an incomplete dual.
  2. [Table 1, Fig. 3] Table 1 and Fig. 3 (numerical key rates): the reported positive rates at 10^5 signals and >12 dB loss rest on the assumption that no additional correlation penalty appears. Restoring even a modest Markov-chain correction (e.g., via the chain rule for Rényi entropy) would shift the optimized rates; the manuscript must either derive the missing term or prove it is absorbed by the existing accumulation theorem.
minor comments (2)
  1. [§2] The notation for the variable-length block size n and the number of signals N is used interchangeably in §2; a single consistent symbol would improve readability.
  2. [References] Reference list omits the most recent experimental DPSK demonstrations (post-2022); adding two or three citations would better contextualize the claimed industrial relevance.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for highlighting potential subtleties in the application of entropy accumulation to DPSK. The comments focus on the treatment of Markovian dependencies arising from differential phase encoding. We address each point below, explaining why the existing framework already incorporates the necessary accounting.

read point-by-point responses

  1. Referee: [§3, Eq. (12)] §3 (Security Analysis) and Eq. (12): the direct invocation of the variable-length Rényi leftover-hashing bound on the DPSK raw-key string does not insert an explicit smoothing or chain-rule term to account for the Markovian dependence induced by differential phase encoding between adjacent pulses. Because the protocol encodes information in relative phases, the i.i.d. or single-shot Rényi bounds cited from the external framework may under-estimate the finite-size penalty; the subsequent conic program therefore optimizes an incomplete dual.

    Authors: The variable-length Rényi entropy accumulation theorem applied in §3 and Eq. (12) is formulated precisely for sequential protocols exhibiting Markovian dependence, including the relative-phase encoding of DPSK. The accumulation procedure iterates over the pulse sequence and directly yields a bound that incorporates chain-rule effects and smoothing without requiring an additional explicit term. The cited external framework (entropy accumulation with Rényi leftover hashing) has been proven to hold for such dependent processes; therefore the conic optimization dual remains complete and no modification to Eq. (12) is needed. revision: no

  2. Referee: [Table 1, Fig. 3] Table 1 and Fig. 3 (numerical key rates): the reported positive rates at 10^5 signals and >12 dB loss rest on the assumption that no additional correlation penalty appears. Restoring even a modest Markov-chain correction (e.g., via the chain rule for Rényi entropy) would shift the optimized rates; the manuscript must either derive the missing term or prove it is absorbed by the existing accumulation theorem.

    Authors: The key rates in Table 1 and Fig. 3 are computed by substituting the output of the variable-length entropy accumulation theorem directly into the conic program. Because the accumulation theorem already absorbs the worst-case Markovian correlations induced by differential encoding, no separate correlation penalty term is required. The numerical results therefore remain valid as stated; the positive rates at 10^5 signals and losses beyond 12 dB follow from the complete bound. revision: no

Circularity Check

0 steps flagged

No significant circularity; central claim applies external entropy-accumulation and conic-optimization techniques to DPSK

full rationale

The derivation relies on citing and applying recent external variable-length general security methods (Rényi leftover hashing plus conic optimization) to the DPSK protocol. No self-definitional loops, fitted inputs renamed as predictions, or load-bearing self-citation chains are present in the provided abstract or described approach. The key-rate results at 10^5 signals are presented as numerical outcomes of that external framework rather than reductions to the paper's own inputs by construction. This is the expected non-circular outcome for an application paper.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim depends on the applicability of entropy accumulation and conic optimization techniques to the DPSK protocol in the variable-length setting; no free parameters or new entities are mentioned.

axioms (2)
  • domain assumption Entropy accumulation techniques based on Rényi leftover hashing apply to the DPSK protocol in the variable-length setting.
    Invoked to achieve general security without repetition rate constraints.
  • domain assumption Conic optimization methods can efficiently compute the finite-size security bounds for DPSK.
    Combined with entropy accumulation to derive the key rates.

pith-pipeline@v0.9.0 · 5405 in / 1432 out tokens · 33651 ms · 2026-05-08T11:22:28.615349+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

157 extracted references · 73 canonical work pages

  1. [1]

    TEFNET24: reference packet optical network topology for edge to core transport , volume =

    Jos\'. TEFNET24: reference packet optical network topology for edge to core transport , volume =. J. Opt. Commun. Netw. , keywords =. 2024 , url =

    2024

  2. [2]

    Optimal quantum key distribution networks: capacitance versus security , url =

    Cirigliano, Lorenzo and Brosco, Valentina and Castellano, Claudio and Conti, Claudio and Pilozzi, Laura , date =. Optimal quantum key distribution networks: capacitance versus security , url =. npj Quantum Information , doi =. 2024 , month =

    2024

  3. [3]

    Statistical properties of the quantum internet,

    Brito, Samuraí and Canabarro, Askery and Chaves, Rafael and Cavalcanti, Daniel , date =. Statistical. doi:10.1103/PhysRevLett.124.210501 , url =

    work page doi:10.1103/physrevlett.124.210501

  4. [4]

    Composable finite-size security of high-dimensional quantum-key-distribution protocols , volume=

    Kanitschar, Florian and Huber, Marcus , year=. Composable finite-size security of high-dimensional quantum-key-distribution protocols , volume=. Physical Review Applied , publisher=. doi:10.1103/v51y-vkfr , number=

    work page doi:10.1103/v51y-vkfr

  5. [5]

    and Wolf, Ramona , journal =

    Sandfuchs, Martin and Haberland, Marcus and Vilasini, V. and Wolf, Ramona , journal =. Security of differential phase shift. doi:10.22331/q-2025-01-27-1611 , url =

    work page doi:10.22331/q-2025-01-27-1611 2025

  6. [6]

    Trinh, Alberto Carrasco-Casado, Hideki Takenaka, Mikio Fujiwara, Mitsuo Kitamura, Masahide Sasaki, and Morio Toyoshima

    Statistical verifications and deep-learning predictions for satellite-to-ground quantum atmospheric channels , author =. Communications Physics , volume =. 2022 , publisher =. doi:10.1038/s42005-022-01002-1 , url =

    work page doi:10.1038/s42005-022-01002-1 2022

  7. [7]

    PRX Quantum , volume =

    Finite-Resource Performance of Small-Satellite-Based Quantum-Key-Distribution Missions , author =. PRX Quantum , volume =. 2024 , month =. doi:10.1103/PRXQuantum.5.030101 , url =

    work page doi:10.1103/prxquantum.5.030101 2024

  8. [8]

    2024 , month =

    Mizutani, Akihiro and Terashita, Masanori and Matsubayashi, Junya and Mori, Shogo and Matsukura, Ibuki and Tagawa, Suzuna and Tamaki, Kiyoshi , title =. 2024 , month =. doi:10.1088/2058-9565/ad71ec , url =

    work page doi:10.1088/2058-9565/ad71ec 2024

  9. [9]

    Finite-key security analysis of differential-phase-shift quantum key distribution , author =. Phys. Rev. Res. , volume =. 2023 , month =. doi:10.1103/PhysRevResearch.5.023132 , url =

    work page doi:10.1103/physrevresearch.5.023132 2023

  10. [10]

    Chung, Rebecca R. B. and Ng, Nelly H. Y. and Cai, Yu , journal =. Generalized numerical framework for improved finite-sized key rates with. 2025 , publisher =. doi:10.1103/tyts-8v8j , eprint=

    work page doi:10.1103/tyts-8v8j 2025

  11. [11]

    Security proof for variable-length quantum key distribution , author =. Phys. Rev. Res. , volume =. 2024 , publisher =. doi:10.1103/PhysRevResearch.6.023002 , archivePrefix =. 2311.01600 , primaryClass =

    work page doi:10.1103/physrevresearch.6.023002 2024

  12. [12]

    2023 , eprint=

    Information reconciliation for discretely-modulated continuous-variable quantum key distribution , author=. 2023 , eprint=

    2023

  13. [13]

    Proceedings of the Royal Society A: Mathematical, Physical and engineering sciences , volume=

    Distillation of secret key and entanglement from quantum states , author=. Proceedings of the Royal Society A: Mathematical, Physical and engineering sciences , volume=. 2005 , publisher=

    2005

  14. [14]

    doi:10.22331/q-2021-09-13-540 , url =

    Explicit asymptotic secret key rate of continuous-variable quantum key distribution with an arbitrary modulation , author =. doi:10.22331/q-2021-09-13-540 , url =

    work page doi:10.22331/q-2021-09-13-540 2021

  15. [15]

    Continuous Variable Quantum Cryptography: Beating the 3 dB Loss Limit , author =. Phys. Rev. Lett. , volume =. 2002 , publisher =. doi:10.1103/PhysRevLett.89.167901 , url =

    work page doi:10.1103/physrevlett.89.167901 2002

  16. [16]

    2009 , school=

    Theoretical study of continuous-variable quantum key distribution , author=. 2009 , school=

    2009

  17. [17]

    Quantum Information Processing with Finite Resources

    Tomamichel, Marco , year=. Quantum Information Processing with Finite Resources , ISBN=. doi:10.1007/978-3-319-21891-5 , journal=

    work page doi:10.1007/978-3-319-21891-5

  18. [18]

    2006 , eprint=

    Security of Quantum Key Distribution , author=. 2006 , eprint=

    2006

  19. [19]

    de Finetti Representation Theorem for Infinite-Dimensional Quantum Systems and Applications to Quantum Cryptography , author =. Phys. Rev. Lett. , volume =. 2009 , publisher =. doi:10.1103/PhysRevLett.102.110504 , url =

    work page doi:10.1103/physrevlett.102.110504 2009

  20. [20]

    Asymptotic Security Analysis of Discrete-Modulated Continuous-Variable Quantum Key Distribution , author =. Phys. Rev. X , volume =. 2019 , publisher =. doi:10.1103/PhysRevX.9.041064 , url =

    work page doi:10.1103/physrevx.9.041064 2019

  21. [21]

    PRX Quantum , volume =

    Dimension Reduction in Quantum Key Distribution for Continuous- and Discrete-Variable Protocols , author =. PRX Quantum , volume =. 2021 , publisher =. doi:10.1103/PRXQuantum.2.020325 , url =

    work page doi:10.1103/prxquantum.2.020325 2021

  22. [22]

    Entropy , VOLUME =

    Diamanti, Eleni and Leverrier, Anthony , TITLE =. Entropy , VOLUME =. 2015 , NUMBER =

    2015

  23. [23]

    2009 , publisher =

    M Peev and others , title =. 2009 , publisher =. doi:10.1088/1367-2630/11/7/075001 , url =

    work page doi:10.1088/1367-2630/11/7/075001 2009

  24. [24]

    Zubkov, A. M. and Serov, A. A. , title =. Theory of Probability & Its Applications , volume =. 2013 , doi =

    2013

  25. [25]

    The European satellite-based QKD system EAGLE-1 , url=

    Hiemstra, Thomas and Hasler, David and Paone, Domenico and Reichert, Fabian and Heine, Frank and Struck, Julian , editor=. The European satellite-based QKD system EAGLE-1 , url=. 2025 , month=mar, pages=. doi:10.1117/12.3042856 , booktitle=

    work page doi:10.1117/12.3042856 2025

  26. [26]

    Sasaki and M

    M. Sasaki and M. Fujiwara and H. Ishizuka and W. Klaus and K. Wakui and M. Takeoka and S. Miki and T. Yamashita and Z. Wang and A. Tanaka and K. Yoshino and Y. Nambu and S. Takahashi and A. Tajima and A. Tomita and T. Domeki and T. Hasegawa and Y. Sakai and H. Kobayashi and T. Asai and K. Shimizu and T. Tokura and T. Tsurumaru and M. Matsui and T. Honjo a...

    2011

  27. [27]

    and Sekatski, Pavel and Bancal, Jean-Daniel and Schwonnek, Ren

    Tan, Ernest Y.-Z. and Sekatski, Pavel and Bancal, Jean-Daniel and Schwonnek, Ren. Improved. doi:10.22331/q-2022-12-22-880 , url =

    work page doi:10.22331/q-2022-12-22-880 2022

  28. [28]

    Applied Physics Reviews , volume =

    Zhang, Yichen and Bian, Yiming and Li, Zhengyu and Yu, Song and Guo, Hong , title = ". Applied Physics Reviews , volume =. 2024 , month =. doi:10.1063/5.0179566 , url =

    work page doi:10.1063/5.0179566 2024

  29. [29]

    doi:10.22331/q-2024-07-18-1418 , url =

    Security of discrete-modulated continuous-variable quantum key distribution , author =. doi:10.22331/q-2024-07-18-1418 , url =

    work page doi:10.22331/q-2024-07-18-1418 2024

  30. [30]

    2022 , MONTH = Dec, KEYWORDS =

    Neves, Simon , URL =. 2022 , MONTH = Dec, KEYWORDS =

    2022

  31. [31]

    Improved finite-size key rates for discrete-modulated continuous-variable quantum key distribution under coherent attacks , author =. Phys. Rev. A , volume =. 2025 , month =. doi:10.1103/PhysRevA.111.022610 , url =

    work page doi:10.1103/physreva.111.022610 2025

  32. [32]

    Information Reconciliation for High-Dimensional Quantum Key Distribution using Nonbinary LDPC codes , year=

    Müller, Ronny and Bacco, Davide and Oxenløwe, Leif Katsou and Forchhammer, Søren , booktitle=. Information Reconciliation for High-Dimensional Quantum Key Distribution using Nonbinary LDPC codes , year=

  33. [33]

    Quantum cryptography without Bell's theorem , author =. Phys. Rev. Lett. , volume =. 1992 , month =. doi:10.1103/PhysRevLett.68.557 , url =

    work page doi:10.1103/physrevlett.68.557 1992

  34. [34]

    Journal of Mathematical Physics , volume=

    The smooth entropy formalism for von Neumann algebras , author=. Journal of Mathematical Physics , volume=. 2016 , publisher=

    2016

  35. [35]

    , journal=

    Winter, A. , journal=. Coding theorem and strong converse for quantum channels , year=

  36. [36]

    2012 , publisher=

    Security of continuous-variable quantum key distribution and aspects of device-independent security , author=. 2012 , publisher=

    2012

  37. [37]

    Security Bounds for Continuous Variables Quantum Key Distribution , author =. Phys. Rev. Lett. , volume =. 2005 , publisher =. doi:10.1103/PhysRevLett.94.020505 , url =

    work page doi:10.1103/physrevlett.94.020505 2005

  38. [38]

    and Guosen Yue and Li Ping and Xiaodong Wang , journal=

    Leung, W.K.R. and Guosen Yue and Li Ping and Xiaodong Wang , journal=. Concatenated zigzag hadamard codes , year=

  39. [39]

    PRX Quantum , volume =

    Finite-Size Security for Discrete-Modulated Continuous-Variable Quantum Key Distribution Protocols , author =. PRX Quantum , volume =. 2023 , publisher =. doi:10.1103/PRXQuantum.4.040306 , url =

    work page doi:10.1103/prxquantum.4.040306 2023

  40. [40]

    and Gulak, P

    Milicevic, Mario and Feng, Chen and Zhang, Lei M. and Gulak, P. Glenn , title =. npj Quantum Information , volume =. 2018 , issue =. doi:10.1038/s41534-018-0070-6 , url =

    work page doi:10.1038/s41534-018-0070-6 2018

  41. [41]

    Quantum Info

    Martinez-Mateo, Jesus and Pacher, Christoph and Peev, Momtchil and Ciurana, Alex and Martin, Vicente , title =. Quantum Info. Comput. , pages =. 2015 , issue_date =

    2015

  42. [42]

    Physical Review A , volume=

    Unification of different views of decoherence and discord , author=. Physical Review A , volume=. 2012 , publisher=

    2012

  43. [43]

    Quantum , volume=

    Reliable numerical key rates for quantum key distribution , author=. Quantum , volume=. 2018 , publisher=

    2018

  44. [44]

    Naval research logistics quarterly , volume=

    An algorithm for quadratic programming , author=. Naval research logistics quarterly , volume=. 1956 , publisher=

    1956

  45. [45]

    Solving natural conic formulations with

    Chris Coey and Lea Kapelevich and Juan Pablo Vielma , year=. Solving natural conic formulations with. INFORMS Journal on Computing , publisher=

  46. [46]

    2023 , journal=

    Performance enhancements for a generic conic interior point algorithm , author=. 2023 , journal=

    2023

  47. [47]

    JuMP 1.0: recent improvements to a modeling language for mathematical optimization

    Miles Lubin and Oscar Dowson and Joaquim. Mathematical Programming Computation , year =. doi:10.1007/s12532-023-00239-3 , archivePrefix =. 2206.03866 , primaryClass =

    work page doi:10.1007/s12532-023-00239-3

  48. [48]

    Julia: AFreshApproach to Numerical Computing.arXiv:1411.1607 [cs], July 2015

    Bezanson, Jeff and Edelman, Alan and Karpinski, Stefan and Shah, Viral B. , title =. SIAM Review , volume =. 2017 , doi =. 1411.1607 , archivePrefix=

    work page arXiv 2017

  49. [49]

    and Wolf, J

    Slepian, D. and Wolf, J. , journal=. Noiseless coding of correlated information sources , year=

  50. [50]

    2004 , publisher=

    Convex optimization , author=. 2004 , publisher=

    2004

  51. [51]

    MOSEK optimization suite , author=

  52. [52]

    K. C. Toh and M. J. Todd and R. H. Tütüncü , title =. Optimization Methods and Software , volume =. 1999 , publisher =

    1999

  53. [53]

    Tütüncü, R. H. and Toh, K. C. and Toh, K. C. , title =. Mathematical programming Ser.B , volume =

  54. [54]

    Computational Complexity of Continuous Variable Quantum Key Distribution , year=

    Zhao, Yi-Bo and Gui, You-Zhen and Chen, Jin-Jian and Han, Zheng-Fu and Guo, Guang-Can , journal=. Computational Complexity of Continuous Variable Quantum Key Distribution , year=

  55. [55]

    Unconditional Security Proof of Long-Distance Continuous-Variable Quantum Key Distribution with Discrete Modulation , author =. Phys. Rev. Lett. , volume =. 2009 , publisher =. doi:10.1103/PhysRevLett.102.180504 , url =

    work page doi:10.1103/physrevlett.102.180504 2009

  56. [56]

    Journal of the American Statistical Association , volume =

    Wassily Hoeffding , title =. Journal of the American Statistical Association , volume =. 1963 , publisher =. doi:10.1080/01621459.1963.10500830 , URL =

    work page doi:10.1080/01621459.1963.10500830 1963

  57. [57]

    Trusted Detector Noise Analysis for Discrete Modulation Schemes of Continuous-Variable Quantum Key Distribution , author =. Phys. Rev. Appl. , volume =. 2020 , publisher =. doi:10.1103/PhysRevApplied.14.064030 , url =

    work page doi:10.1103/physrevapplied.14.064030 2020

  58. [58]

    Composable Security Proof for Continuous-Variable Quantum Key Distribution with Coherent States , author =. Phys. Rev. Lett. , volume =. 2015 , publisher =. doi:10.1103/PhysRevLett.114.070501 , url =

    work page doi:10.1103/physrevlett.114.070501 2015

  59. [59]

    and Cardinal, J

    Van Assche, G. and Cardinal, J. and Cerf, N.J. , journal=. Reconciliation of a quantum-distributed Gaussian key , year=

  60. [60]

    Proceedings of the CACSD Conference , title =

    L. Proceedings of the CACSD Conference , title =

  61. [61]

    Multiedge-type low-density parity-check codes for continuous-variable quantum key distribution , author =. Phys. Rev. A , volume =. 2021 , publisher =. doi:10.1103/PhysRevA.103.062419 , url =

    work page doi:10.1103/physreva.103.062419 2021

  62. [62]

    and Wu, K.Y

    Li Ping and Leung, W.K. and Wu, K.Y. , journal=. Low-rate turbo-Hadamard codes , year=

  63. [63]

    SIAM Journal on Computing , volume =

    Arnon-Friedman, Rotem and Renner, Renato and Vidick, Thomas , title =. SIAM Journal on Computing , volume =. 2019 , doi =

    2019

  64. [64]

    Quantum , volume=

    Robust interior point method for quantum key distribution rate computation , author=. Quantum , volume=. 2022 , publisher=

    2022

  65. [65]

    Communications in Mathematical Physics , volume=

    Entropy Accumulation , author=. Communications in Mathematical Physics , volume=. 2020 , publisher=

    2020

  66. [66]

    IEEE Transactions on information theory , volume=

    Entropy accumulation with improved second-order term , author=. IEEE Transactions on information theory , volume=. 2019 , publisher=

    2019

  67. [67]

    arXiv preprint arXiv:2203.06554 , year=

    Finite-Key Analysis of Quantum Key Distribution with Characterized Devices Using Entropy Accumulation , author=. arXiv preprint arXiv:2203.06554 , year=

    work page arXiv

  68. [68]

    2024 , eprint=

    Discrete-modulated continuous-variable quantum key distribution secure against general attacks , author=. 2024 , eprint=

    2024

  69. [69]

    2024 , eprint=

    Quantum key distribution rates from non-symmetric conic optimization , author=. 2024 , eprint=

    2024

  70. [70]

    Security of quantum key distribution from gen- eralised entropy accumulation.Nature Communications, 14(1):5272, August 2023

    Security of quantum key distribution from generalised entropy accumulation , volume =. Nature Communications , author =. 2023 , pages =. doi:10.1038/s41467-023-40920-8 , number =

    work page doi:10.1038/s41467-023-40920-8 2023

  71. [71]

    2015 , journal=

    A homogeneous interior-point algorithm for nonsymmetric convex conic optimization , author=. 2015 , journal=

    2015

  72. [72]

    SIAM Review , volume =

    Iain Dunning and Joey Huchette and Miles Lubin , title =. SIAM Review , volume =. 2017 , doi =

    2017

  73. [73]

    Imperfect detectors for adversarial tasks with applications to quantum key distribution.Quantum, 10:2044, March 2026

    Nahar, Shlok and Tupkary, Devashish and Lütkenhaus, Norbert , year=. Imperfect detectors for adversarial tasks with applications to quantum key distribution , volume=. doi:10.22331/q-2026-03-24-2044 , journal=

    work page doi:10.22331/q-2026-03-24-2044 2026

  74. [74]

    Weedbrooket al., Gaussian quantum in- formation, Rev

    Gaussian. Reviews of Modern Physics , author =. 2012 , note =. doi:10.1103/RevModPhys.84.621 , number =

    work page doi:10.1103/revmodphys.84.621 2012

  75. [75]

    Bennett and Gilles Brassard

    Charles H. Bennett and Gilles Brassard. Quantum. Proceedings of the IEEE International Conference on Computers, Systems and Signal Processing

  76. [76]

    Ekert, A. K. , journal =. 1991 , publisher=

    1991

  77. [77]

    Physical Review Letters , volume=

    Continuous variable quantum cryptography using coherent states , author=. Physical Review Letters , volume=. 2002 , publisher=

    2002

  78. [78]

    Unconditional optimality of

    Garc. Unconditional optimality of. Physical Review Letters , volume=. 2006 , publisher=

    2006

  79. [79]

    Asymptotic security of binary modulated continuous-variable quantum key distribution under collective attacks , author =. Phys. Rev. A , volume =. 2009 , publisher =. doi:10.1103/PhysRevA.79.012307 , url =

    work page doi:10.1103/physreva.79.012307 2009

  80. [80]

    Nature , author =

    Quantum key distribution using gaussian-modulated coherent states , volume =. Nature , author =. 2003 , pages =. doi:10.1038/nature01289 , number =

    work page doi:10.1038/nature01289 2003

Showing first 80 references.