Workbench tool

Finite-key BB84 teaching estimator

Translate the simplified BB84 link budget into an explicit finite-key teaching bound with configurable epsilon parameters, sampling fraction, and non-certified caution labels.

Shareable URL state

Keep the current calculator inputs in the URL so this teaching setup can be reopened or shared without exporting files.

Only model inputs are stored in the link. No keys or telemetry are added.

PresetProtocol familyThis slice keeps the same pedagogical decoy proxy as the link-budget tool; it does not implement a rigorous decoy optimization.LengthkmFiber attenuationdB/kmConnector/component lossdBSource rateHzBlock sizesignalsTeaching proxy for the emitted pulse block used in one finite-key batch.Sample fractionFraction of sifted bits revealed for parameter estimation.Mean photon numbermuDetector efficiencyDark count probabilityBackground count probabilityMisalignment errorDetector dead timensNon-paralyzable click-availability proxy folded into the shared link-budget kernel.Afterpulse probabilityClick-correlated noise proxy that raises QBER and can suppress the finite-key block.Sender Z-biasBias toward the Z basis. 0.5 recovers unbiased BB84.Receiver Z-biasReceiver basis bias enters the effective sifted fraction through basis agreement.Reconciliation efficiencyCorrectness epsilonPenalty term ceil(log2(2 / epsilon_correct)).Secrecy epsilonPenalty term ceil(2 log2(1 / epsilon_sec)).Parameter-estimation epsilonHoeffding-style slack applied to the observed QBER sample.

Observed QBER

1.51%

Finite-key QBER upper bound

6.49%

Final key block

36,852bits

Secret fraction per pulse

0.369%

Secret key rate

3,685,200bits/s

Statistical penalty

4.98%

Combined PE and secrecy slack added to the observed QBER bound.

Finite-key accounting

Emitted signals

10,000,000

Raw detections

157,269

Sifted bits

78,634

PE sample bits

7,864

Dead-time availability

100%

Imported from the shared link-budget proxy.

Afterpulse noise

Noise contribution that feeds the observed QBER teaching bound.

Effective sifted fraction

50%

Configured sifting factor adjusted by the sender/receiver basis agreement proxy.

PE slack

3.69%

Hoeffding-style penalty from the revealed sample size and epsilon_PE.

Secrecy slack

1.29%

Additional QBER slack tied to the configured secrecy bookkeeping epsilon.

Leakage

9,270bits

Privacy amplification

24,540bits

Correctness penalty

41bits

Secrecy penalty

67bits

Sensitivity sweeps

Explore how the same teaching kernel reacts to distance, added loss, observed QBER, detector efficiency, and block size.

Displayed sweep

Distance sensitivity: secret-key-rate proxy (km)

value spans 0.00 to 65.0 while secretKeyRateHz spans 3.06e+5 to 1.35e+7. Midpoint sample: value 32.5, secretKeyRateHz 2.43e+6.

Sweep start

0km

Sweep end

65km

Worst-case final key

3,062bits

Minimum across the selected sweep.

Distance sweep with statistical uncertainty band

Optimistic uses observed QBER only.Baseline adds parameter-estimation slack.Conservative adds the full finite-key QBER slack.

distanceKm spans 0.00 to 65.0 while the band spans 3.06e+5 to 1.66e+7. Midpoint sample: distanceKm 32.5, optimistic 3.78e+6, baseline 2.73e+6, conservative 2.43e+6.

Warnings and cautions

warning: The parameter-estimation sample is small, so the finite-key teaching bound is dominated by statistical slack.
info: This output is a non-certified teaching lower bound and should not be treated as an operational security guarantee.

Formulas and assumptions

This teaching model reuses the simplified BB84 link-budget proxy, then adds finite-size penalties through Hoeffding-style concentration terms.
Block size is treated as the emitted pulse batch for one finite-key round, and the reported key-rate proxy normalizes the final key fraction back onto the configured source rate.
Security epsilons are explicit bookkeeping knobs, not a substitute for a composable proof tied to a calibrated implementation.
Detector dead time, afterpulsing, and basis bias now enter through the shared link-budget teaching kernel, but they remain coarse proxies rather than calibrated hardware submodels.
Decoy-state mode reuses the shared single-photon lower-bound teaching proxy, but rigorous decoy-state estimation, intensity optimization, and composable implementation proofs remain out of scope in this slice.
Sensitivity sweeps and uncertainty bands are teaching aids based on the same simplified kernel; they are not confidence intervals for deployed hardware.
Asymptotic prepare-and-measure approximation with independent dark/background counts.
Detector dead time uses a non-paralyzable availability proxy, afterpulsing is modeled as a click-correlated noise term, and basis bias rescales the effective sifted fraction relative to the unbiased BB84 baseline.
Finite-key proof terms, rigorous decoy optimization, timing jitter, and side channels are still outside this teaching slice.
Secret fraction uses max(0, 1 - f_ec h2(Q) - h2(Q)); decoy-state mode replaces that asymptotic fraction with a single-photon lower-bound teaching proxy.

References

Finite-key BB84 teaching literature
ETSI ISG QKD publications
Simplified model limitations page: /resources/model-limitations

Tools

Engineering and research workbench

Loading the selected calculator, defaults, and scientific caution notes.

Preparing tool

Loading workbench view

Preparing calibrated controls, default presets, and explanatory notes.