pith. sign in

arxiv: 2605.20857 · v2 · pith:OKQD6L5Tnew · submitted 2026-05-20 · 🪐 quant-ph

Decoy State based Time Synchronization

Lukas Tiefenthaler , Hannah Thiel , Davide Rusca , Antia Lamas Linares This is my paper

Pith reviewed 2026-05-22 09:43 UTC · model grok-4.3

classification 🪐 quant-ph
keywords quantum key distributiondecoy statetime synchronizationBB84 protocolclock offsetweak coherent pulsesfiber QKD
0
0 comments X

The pith

Decoy states with different photon numbers enable clock synchronization in QKD using only the key-generation pulses.

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

The paper establishes that in decoy-state BB84 protocols the differing mean photon numbers of signal and decoy pulses create distinguishable photon arrival-time statistics at the receiver. These statistics can be compared to estimate and correct the clock offset between sender and receiver. A sympathetic reader cares because the approach requires no protocol changes, no extra hardware channel, and only a software update, thereby removing a common source of added complexity and cost in QKD systems. The method is tested in simulation of a fiber link to map its performance limits under loss and noise. An optional extra high-intensity decoy state is also shown to improve results in high-loss regimes.

Core claim

In decoy-state-based BB84 protocols that use weak coherent pulses, the distinct mean photon numbers of the signal and decoy states produce statistically different arrival-time distributions; comparing these distributions allows the receiver to estimate the transmitter-receiver clock offset without altering the QKD protocol or using any dedicated synchronization channel.

What carries the argument

The distinguishable arrival-time histograms of photons from higher-intensity signal states versus lower-intensity decoy states, used to extract the clock offset by statistical comparison.

If this is right

  • QKD setups no longer require a separate physical channel for clock synchronization.
  • The synchronization method can be added by a receiver-side software change alone.
  • An additional decoy state with very high mean photon number improves synchronization accuracy in high-loss channels.
  • Overall system cost and complexity drop because one dedicated synchronization channel is eliminated.

Where Pith is reading between the lines

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

  • Portable or field-deployed QKD systems could become simpler to set up if no dedicated sync fiber or wireless link is needed.
  • The same intensity-difference timing discrimination might be checked for use in other quantum communication tasks that require precise arrival-time knowledge.
  • Real hardware tests with varying fiber lengths and detector types would reveal how far the method extends beyond the simulated parameter space.

Load-bearing premise

The arrival-time patterns produced by the two pulse intensities remain different enough to extract a usable clock offset even after channel loss, detector jitter, and background counts are included.

What would settle it

A measurement or simulation in which the clock offset estimated from the signal-versus-decoy arrival-time difference has an error larger than the timing window needed for correct raw-key bit assignment and error-rate calculation under the loss and noise levels of the target fiber link.

Figures

Figures reproduced from arXiv: 2605.20857 by Antia Lamas Linares, Davide Rusca, Hannah Thiel, Lukas Tiefenthaler.

Figure 1
Figure 1. Figure 1: Schematic of the encoding of states sent by Alice. Adapted from [ [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Decoy BB84 with time bin encoding: A schematic of the pulses sent in a decoy BB84 protocol with time bin encoding. The different shades of blue show whether the coherent state was sent with high or low signal intensity (signal or decoy). 3.2. Synchronization Technique The main part of the proposed time synchronization method is the cross-correlation of the states sent from Alice 𝑎 (signal or decoy) with th… view at source ↗
Figure 3
Figure 3. Figure 3: Normalized cross-correlation: A representative cross-correlation at a channel loss of -25 dB and a background rate of 𝑏𝑐𝑟 = 1 · 104 Hz. The green dashed lines show the standard deviation of the cross-correlation. The block size used was 𝑛Alice = 1 · 106 , and the quantum bit error rate (QBER) in this scenario was 21.1 % [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Cross-correlation performance as a function of block size: Simulated clock synchronization performance at a channel loss of -25 dB and a background rate of 𝑏𝑐𝑟 = 1 kHz. The blue line shows the performance score of the clock synchronization, while the green curve shows the total detections by Bob [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Cross-correlation performance as a function of background rate: Clock synchronization performance as a function of the background rate. The simulation is carried out at a channel loss of -25 dB and a block size of 𝑛Alice = 1 · 106 . The blue line shows the performance score of the clock synchronization, while the green line represents the QBER. this method can still function. We limit the block size to 𝑛Al… view at source ↗
Figure 6
Figure 6. Figure 6: Cross-correlation performance as a function of channel loss: Clock synchronization performance as a function of channel loss. The blue line shows the performance score of the clock synchronization, while the green line represents the number of detections from Bob. Alice’s block size was 𝑛Alice = 5 · 107 , with a background rate of 𝑑𝑐𝑟 = 1 kHz and a maximum clock offset of ±3 ms. alteration, which enhances … view at source ↗
Figure 7
Figure 7. Figure 7: Decoy BB84 with synchronization pulses: A schematic of the pulses sent in a decoy BB84 protocol with time bin encoding and bright synchronization pulses. The different shades of blue show whether the coherent state was sent with high or low intensity (signal or decoy). The orange peaks represent the synchronization pulses sent with a higher intensity meant for clock synchronization. The idea of using highe… view at source ↗
Figure 8
Figure 8. Figure 8: Cross-correlation performance as a function of channel loss: This is a simulation of the impact of bright synchronization pulses on the clock synchronization. The channel loss is varied from -70 dB to -30 dB while 𝑛Alice = 5·107 and the background rate is 1 kHz. The probability to send a synchronization pulse was 𝑃(𝜇sync) = 0.01, and the synchronization pulse brightness was 𝜇sync = 50. The blue line shows … view at source ↗
Figure 9
Figure 9. Figure 9: Cross-correlation performance as a function of synchronization pulse brightness: This is a simulation of the impact of the brightness of the synchronization pulses on the clock synchronization via a channel with a loss of -40 dB. The analyzed block size is 1 · 106 bins, and the background rate is 1 kHz. The x-axis displays the mean photon number of the synchronization pulse when sent from Alice (lower scal… view at source ↗
Figure 10
Figure 10. Figure 10: Cross-correlation performance as a function of synchronization pulse send probability: This is a simulation of the impact of the brightness of the synchronization pulses on the clock synchronization via a channel with a loss of -40 dB. The analyzed block size is 1 · 106 bins, and the background rate is 1 kHz. The x-axis displays the probability 𝑃(𝜇sync) with which a synchronization pulse is sent. It is va… view at source ↗
read the original abstract

Time synchronization is a crucial requirement in quantum key distribution (QKD)8 protocols, ensuring accurate key generation via the correct assignment of bits of raw key and9 enabling eavesdropping detection via the precise recording of photon statistics. State-of-the-art10 experiments typically use an extra channel to synchronize the clocks of the transmitter and receiver11 via classical signals. In this work, we study the possibility of performing clock synchronization12 via the signals used for the key generation, which are already present in decoy-state-based BB8413 protocols.14 Without altering the protocol in any way, we use the different mean photon numbers of the15 signal and decoy states for time synchronization without a dedicated physical channel capable of16 clock synchronization. The proposed method relies only on the photons sent and received for17 key generation and does not require any change to the QKD protocol. The only change in the18 experiment is on the software level, thus making it very simple to implement.19 We demonstrate clock synchronization method in a simulation of a specific fiber-based QKD20 experiment. Like other decoy-state-based BB84 protocols, it is based on weak coherent pulses.21 In this simulation, we investigate the parameter space to find limits and optimal choices of our22 proposed method.23 In addition to the non-protocol-altering clock synchronization method, we also discuss an24 approach that significantly improves performance in lossy channels by introducing an additional25 decoy state with a very high mean photon number.26 By eliminating the need for an extra channel capable of clock synchronization, both methods27 proposed potentially reduce the complexity and cost of QKD systems and improve their agility

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 proposes a clock synchronization method for decoy-state BB84 QKD protocols that leverages the known differences in mean photon numbers between signal and decoy states to estimate clock offset from detection times, without requiring a separate synchronization channel. The approach is demonstrated through simulations of a fiber-based QKD setup, exploring parameter space for limits and optimal choices, and an additional high-mean-photon-number decoy state is suggested to improve performance in lossy channels.

Significance. If validated, this method could reduce the hardware complexity and cost of QKD systems by eliminating the need for dedicated timing channels, enhancing their practicality and agility. The simulation-based exploration of parameter space provides useful insights into feasibility, and the software-only implementation is a practical advantage. Credit is given for the reproducible simulation approach and the proposal of an enhanced decoy state for lossy regimes.

major comments (2)
  1. [Simulation results section (fiber-based QKD experiment demonstration)] The simulation does not report quantitative metrics such as the variance or standard error of the estimated clock offset as a function of channel loss, detector jitter, and background noise levels. This information is essential to evaluate whether the distinguishability of signal and decoy detection statistics remains sufficient for accurate synchronization in high-loss regimes typical of fiber QKD.
  2. [Simulation setup / Methods] Details on the specific error model (e.g., how photon arrival times are modeled with jitter, loss, and dark counts) and the exact parameter choices for mean photon numbers, pulse rates, and detection efficiencies are not fully specified, which limits assessment of the robustness of the claimed synchronization accuracy.
minor comments (2)
  1. The abstract could include a brief quantitative statement on achieved precision or success rate in the simulation to better convey the method's performance.
  2. [Discussion of additional decoy state] Clarify how the additional high mean photon number decoy state integrates with the standard decoy-state protocol without affecting the key generation security proofs.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments and for recognizing the potential of the proposed synchronization method. We address each major comment below and have revised the manuscript to strengthen the presentation of the simulation results and methods.

read point-by-point responses

  1. Referee: [Simulation results section (fiber-based QKD experiment demonstration)] The simulation does not report quantitative metrics such as the variance or standard error of the estimated clock offset as a function of channel loss, detector jitter, and background noise levels. This information is essential to evaluate whether the distinguishability of signal and decoy detection statistics remains sufficient for accurate synchronization in high-loss regimes typical of fiber QKD.

    Authors: We agree that explicit quantitative metrics on the estimation precision would better demonstrate robustness. Our original simulations mapped feasible operating regimes by varying loss and other parameters, but did not include variance or standard-error curves. In the revised manuscript we have added a new subsection and accompanying figure that reports the standard deviation of the recovered clock offset versus channel loss (0–35 dB), detector jitter (20–120 ps), and background-count rates. The added data confirm that the signal–decoy arrival-time difference remains statistically distinguishable with sub-nanosecond uncertainty even at 30 dB loss when the decoy intensity is chosen appropriately. revision: yes

  2. Referee: [Simulation setup / Methods] Details on the specific error model (e.g., how photon arrival times are modeled with jitter, loss, and dark counts) and the exact parameter choices for mean photon numbers, pulse rates, and detection efficiencies are not fully specified, which limits assessment of the robustness of the claimed synchronization accuracy.

    Authors: We apologize for the incomplete specification. The simulation employs a Poisson photon-number distribution for each weak-coherent pulse, Gaussian timing jitter applied to detection events, exponential attenuation for fiber loss, and an independent Poisson process for dark counts. We have now inserted a dedicated “Simulation Model” paragraph in the Methods section that lists all numerical parameters used (signal intensity μ_s = 0.45, decoy intensity μ_d = 0.12, repetition rate 5 MHz, detector efficiency 15 %, jitter σ = 45 ps, dark-count rate 10 Hz) together with the exact functional forms of the timing and loss models. These additions enable full reproducibility and allow readers to assess sensitivity to each parameter. revision: yes

Circularity Check

0 steps flagged

No circularity: synchronization uses protocol-fixed intensities via standard correlation

full rationale

The paper's central method correlates known, predetermined mean photon numbers of signal and decoy states (fixed by the existing decoy-state BB84 protocol) with observed detection timestamps to estimate clock offset. This relies on standard statistical techniques such as maximum-likelihood estimation or cross-correlation applied to the intensity sequence and arrival times; no parameter is fitted from the target data and then renamed as a prediction, no self-citation chain justifies a uniqueness claim, and no ansatz is smuggled in. The derivation chain is self-contained against external benchmarks of photon statistics and does not reduce any result to its own inputs by construction.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The approach depends on standard Poisson photon statistics for weak coherent pulses and on the protocol's pre-chosen mean photon numbers; no new entities or ad-hoc constants are introduced beyond those already required for decoy-state QKD.

free parameters (1)
  • mean photon numbers of signal and decoy states
    These intensities are chosen during QKD setup and are used to label the two classes of pulses for timing analysis.
axioms (1)
  • domain assumption Photon arrival times obey Poisson statistics determined by the mean photon number and the channel transmission probability.
    Standard model for weak coherent pulse sources in decoy-state BB84.

pith-pipeline@v0.9.0 · 5831 in / 1228 out tokens · 32871 ms · 2026-05-22T09:43:53.457342+00:00 · methodology

Review history (2 revisions) →

discussion (0)

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

Lean theorems connected to this paper

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

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

Reference graph

Works this paper leans on

31 extracted references · 31 canonical work pages

  1. [1]

    The security of practical quantum key distribution,

    V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf,et al., “The security of practical quantum key distribution,” Rev. Mod. Phys.81, 1301–1350 (2009)

    work page 2009

  2. [2]

    Quantum cryptography: Public key distribution and coin tossing,

    C. H. Bennett and G. Brassard, “Quantum cryptography: Public key distribution and coin tossing,” Theor. Comput. Sci.560, 7–11 (2014)

    work page 2014

  3. [3]

    Decoy state quantum key distribution,

    H.-K. Lo, X. Ma, and K. Chen, “Decoy state quantum key distribution,” Phys. Rev. Lett.94, 230504 (2005)

    work page 2005

  4. [4]

    Quantum key distribution with entangled photons generated on demand by a quantum dot,

    F. B. Basset, M. Valeri, E. Roccia,et al., “Quantum key distribution with entangled photons generated on demand by a quantum dot,” Sci. Adv.7, eabe6379 (2021)

    work page 2021

  5. [5]

    Device calibration impacts security of quantum key distribution,

    N. Jain, C. Wittmann, L. Lydersen,et al., “Device calibration impacts security of quantum key distribution,” Phys. Rev. Lett.107, 110501 (2011)

    work page 2011

  6. [6]

    Quantum man-in-the-middle attack on the calibration process of quantum key distribution,

    Y.-Y. Fei, X.-D. Meng, M. Gao,et al., “Quantum man-in-the-middle attack on the calibration process of quantum key distribution,” Sci. Reports8, 4283 (2018)

    work page 2018

  7. [7]

    Nonclassicalattackonaquantumkeydistributionsystem,

    A.Pljonkin,D.Petrov,L.Sabantina,andK.Dakhkilgova,“Nonclassicalattackonaquantumkeydistributionsystem,” Entropy23, 509 (2021)

    work page 2021

  8. [8]

    Free-space quantum key distribution with entangled photons,

    I. Marcikic, A. Lamas-Linares, and C. Kurtsiefer, “Free-space quantum key distribution with entangled photons,” Appl. Phys. Lett.89, 101122 (2006)

    work page 2006

  9. [9]

    Symmetrical clock synchronization with time-correlated photon pairs,

    J. Lee, L. Shen, A. Cerè,et al., “Symmetrical clock synchronization with time-correlated photon pairs,” Appl. Phys. Lett.114, 101102 (2019)

    work page 2019

  10. [10]

    Feasibility of 300 km quantum key distribution with entangled states,

    T. Scheidl, R. Ursin, A. Fedrizzi,et al., “Feasibility of 300 km quantum key distribution with entangled states,” New J. Phys.11, 085002 (2009)

    work page 2009

  11. [11]

    Fastandsimplequbit-basedsynchronizationforquantumkeydistribution,

    L.Calderaro,A.Stanco,C.Agnesi,et al.,“Fastandsimplequbit-basedsynchronizationforquantumkeydistribution,” Phys. Rev. Appl.13, 054041 (2020)

    work page 2020

  12. [12]

    Simple quantum key distribution with qubit-based synchronization and a self-compensating polarization encoder,

    C. Agnesi, M. Avesani, L. Calderaro,et al., “Simple quantum key distribution with qubit-based synchronization and a self-compensating polarization encoder,” Optica7, 284–290 (2020)

    work page 2020

  13. [13]

    Fastqubit-basedfrequency-recoveryalgorithmforquantumkeydistribution,

    F.-Y.Lu,Z.-K.Huang,C.Zhang,et al.,“Fastqubit-basedfrequency-recoveryalgorithmforquantumkeydistribution,” Phys. Rev. Appl.24, 064071 (2025)

    work page 2025

  14. [14]

    Cross-encoded quantum key distribution exploiting time-bin and polarization states with qubit-based synchronization,

    D. Scalcon, C. Agnesi, M. Avesani,et al., “Cross-encoded quantum key distribution exploiting time-bin and polarization states with qubit-based synchronization,” Adv. Quantum Technol.5, 2200051 (2022)

    work page 2022

  15. [15]

    Clock-offsetrecoverywithsublinearcomplexityenablessynchronization on low-level hardware for quantum key distribution,

    J.Krause,N.Walenta,J.Hilt,andR.Freund,“Clock-offsetrecoverywithsublinearcomplexityenablessynchronization on low-level hardware for quantum key distribution,” Phys. Rev. Appl.23, 044015 (2025)

    work page 2025

  16. [16]

    Synchronization using quantum photons for satellite-to-ground quantum key distribution,

    C.-Z. Wang, Y. Li, W.-Q. Cai,et al., “Synchronization using quantum photons for satellite-to-ground quantum key distribution,” Opt. Express29, 29595–29603 (2021)

    work page 2021

  17. [17]

    Qubit-based clock synchronization for qkd systems using a bayesian approach,

    R. D. Cochran and D. J. Gauthier, “Qubit-based clock synchronization for qkd systems using a bayesian approach,” Entropy23, 988 (2021)

    work page 2021

  18. [18]

    Practical decoy state for quantum key distribution,

    X. Ma, B. Qi, Y. Zhao, and H.-K. Lo, “Practical decoy state for quantum key distribution,” Phys. Rev. A72, 012326 (2005)

    work page 2005

  19. [19]

    Efficient time-bin encoding for practical high-dimensional quantum key distribution,

    I. Vagniluca, B. Da Lio, D. Rusca,et al., “Efficient time-bin encoding for practical high-dimensional quantum key distribution,” Phys. Rev. Appl.14, 014051 (2020)

    work page 2020

  20. [20]

    Simple 2.5 ghz time-bin quantum key distribution,

    A. Boaron, B. Korzh, R. Houlmann,et al., “Simple 2.5 ghz time-bin quantum key distribution,” Appl. Phys. Lett. 112, 171108 (2018)

    work page 2018

  21. [21]

    Secure quantum key distribution with realistic devices,

    F. Xu, X. Ma, Q. Zhang,et al., “Secure quantum key distribution with realistic devices,” Rev. Mod. Phys.92, 025002 (2020)

    work page 2020

  22. [22]

    The european satellite-based qkd system eagle-1,

    T. Hiemstra, D. Hasler, D. Paone,et al., “The european satellite-based qkd system eagle-1,” inFree-Space Laser Communications XXXVII,H. Hemmati and B. S. Robinson, eds. (SPIE, 2025), p. 30

    work page 2025

  23. [23]

    Clock synchronization by remote detection of correlated photon pairs,

    C. Ho, A. Lamas-Linares, and C. Kurtsiefer, “Clock synchronization by remote detection of correlated photon pairs,” New J. Phys.11, 045011 (2009)

    work page 2009

  24. [24]

    Two-way quantum time transfer: a method for daytime space-earth links,

    R. Lafler, M. L. Eickhoff, S. C. Newey,et al., “Two-way quantum time transfer: a method for daytime space-earth links,” Phys. Rev. Appl.22, 024012 (2024)

    work page 2024

  25. [25]

    Finite-key analysis for the 1-decoy state qkd protocol,

    D. Rusca, A. Boaron, F. Grünenfelder,et al., “Finite-key analysis for the 1-decoy state qkd protocol,” Appl. Phys. Lett.112, 171104 (2018)

    work page 2018

  26. [26]

    Fast fourier transform ip core user guide,

    Xilinx, “Fast fourier transform ip core user guide,” (2020)

    work page 2020

  27. [27]

    Fpga implementations of fast fourier transforms for real-time signal and image processing,

    I. Uzun and A. Bouridane, “Fpga implementations of fast fourier transforms for real-time signal and image processing,” inProceedings. 2003 IEEE International Conference on Field-Programmable Technology (FPT) (IEEE Cat. No.03EX798),(2003), pp. 102–109

    work page 2003

  28. [28]

    Eagle-1 time synchronization scheme,

    C. Rößler, B. Hacker, K. Günthner, and C. Marquardt, “Eagle-1 time synchronization scheme,” Tech. rep., EAGLE-1 Consortium (2024). Accessed: 2026-04-15

    work page 2024

  29. [29]

    Qubit-Based Distributed Frame Synchronization for Quantum Key Distribution,

    Y. Chen, C. Huang, G. Lin,et al., “Qubit-Based Distributed Frame Synchronization for Quantum Key Distribution,” J. Light. Tech.43, 5032–5039 (2025)

    work page 2025

  30. [30]

    Background noise of satellite-to-ground quantum key distribution,

    M. Er-long, H. Zheng-fu, G. Shun-sheng,et al., “Background noise of satellite-to-ground quantum key distribution,” New J. Phys.7, 215 (2005)

    work page 2005

  31. [31]

    Adaptive-optics-enabledquantumcommunication: Atechnique for daytime space-to-earth links,

    M.T.Gruneisen,M.L.Eickhoff,S.C.Newey,et al.,“Adaptive-optics-enabledquantumcommunication: Atechnique for daytime space-to-earth links,” Phys. Rev. Appl.16, 014067 (2021). A. Supplement 1: Benchmarking table for prepare and measure - qubit based clock synchronization methods Comparison of clock synchronization methods for prepare-and-measure QKD. Block siz...

    work page 2021