Workbench tool

Entanglement-based BBM92 and E91 estimator

Estimate source-in-the-middle coincidence rates, QBER, and Bell-correlation teaching outputs while keeping entanglement-based assumptions separate from prepare-and-measure BB84.

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.

PresetProtocolBoth modes use the same entangled-pair link model here, but E91 reserves more samples for Bell-correlation monitoring.Alice arm lengthkmBob arm lengthkmFiber attenuationdB/kmAlice insertion lossdBBob insertion lossdBPair generation rateHzPair emission probabilityProbability that the source emits a usable entangled pair in each attempt.Source visibilityBundles interferometric visibility, polarization alignment, and mode overlap into a single entanglement-quality proxy.Bell-state fidelityMaps source quality into the CHSH and QBER teaching proxies without claiming state tomography.Alice detector efficiencyBob detector efficiencyAlice dark count probabilityBob dark count probabilityAlice background probabilityBob background probabilityCoincidence windownsWider coincidence windows increase accidental-pair proxies and should be interpreted cautiously.Misalignment errorBasis sifting factorBell-test sample fractionFor E91 this reserves detected pairs for Bell-style monitoring; BBM92 uses it as a lighter parameter-estimation reserve.Reconciliation efficiencyBlock sizeattempts

Total span

40km

Coincidence probability

0.165%

QBER proxy

7.85%

Secret-key-rate proxy

11,490Hz

CHSH score proxy

2.0815

Classical threshold is 2 for E91-style monitoring.

Bell-violation margin

0.081548

Effective visibility

87.3%

Key-generation fraction

97.5%

After Bell-test or parameter-estimation reservations.

Entangled-pair link accounting

Alice arm loss

7dB

Bob arm loss

7dB

Pair collection probability

0.165%

Accidental coincidences

0.00000015%

Estimated coincidences

1651per block

Key-generation pairs

1609per block

Distance vs secret-key-rate proxy

totalDistanceKm spans 0.00 to 80.0 while secretKeyRateHz spans 1.82e+3 to 7.25e+4. Midpoint sample: totalDistanceKm 40.0, secretKeyRateHz 1.15e+4.

Distance vs CHSH-style Bell score

totalDistanceKm spans 0.00 to 80.0 while chshScore spans 2.08 to 2.08. Midpoint sample: totalDistanceKm 40.0, chshScore 2.08.

Warnings and cautions

info: The BBM92 result is entanglement-source-based and intentionally separated from prepare-and-measure BB84 assumptions.
info: Source visibility and Bell-state fidelity reduce entanglement correlations, increasing the coincidence-error proxy.

Formulas and assumptions

This estimator models entanglement-based BBM92 and E91 links as source-in-the-middle teaching proxies rather than prepare-and-measure BB84 variants.
Coincidences are estimated from pair-emission probability, two independent lossy arms, scalar detector efficiencies, and accidental-noise terms.
E91 Bell monitoring is represented by a CHSH-style visibility proxy and a configurable Bell-test sample fraction, not by a loophole-free or device-independent security proof.
Secret-key output is an asymptotic teaching proxy with explicit caution about source quality, timing, and detector assumptions. It is not a certified deployment-grade key-rate guarantee.
Each arm uses eta = eta_det 10^(-loss_dB / 10), so the emitted entangled pair must survive both lossy detection paths.
Accidental coincidences are scaled by a coincidence-window factor and arm noise probabilities, then contribute a random-bit 50% error term.
BBM92 and E91 share the same entanglement-source coincidence model here, while E91 additionally reserves Bell-test samples before key-generation accounting.

References

Ekert (1991) entanglement-based QKD and Bell-correlation motivation.
Bennett, Brassard, and Mermin (1992) BBM92 entanglement-based key distribution.
Entanglement-based QKD reviews covering source visibility, accidental coincidences, and detector assumptions.

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.

Workbench tool

Entanglement-based BBM92 and E91 estimator

Estimate source-in-the-middle coincidence rates, QBER, and Bell-correlation teaching outputs while keeping entanglement-based assumptions separate from prepare-and-measure BB84.

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.

Total span

40km

Coincidence probability

0.165%

QBER proxy

7.85%

Secret-key-rate proxy

11,490Hz

CHSH score proxy

2.0815

Classical threshold is 2 for E91-style monitoring.

Bell-violation margin

0.081548

Effective visibility

87.3%

Key-generation fraction

97.5%

After Bell-test or parameter-estimation reservations.

Entangled-pair link accounting

Alice arm loss

7dB

Bob arm loss

7dB

Pair collection probability

0.165%

Accidental coincidences

0.00000015%

Estimated coincidences

1651per block

Key-generation pairs

1609per block

Distance vs secret-key-rate proxy

totalDistanceKm spans 0.00 to 80.0 while secretKeyRateHz spans 1.82e+3 to 7.25e+4. Midpoint sample: totalDistanceKm 40.0, secretKeyRateHz 1.15e+4.

Distance vs CHSH-style Bell score

totalDistanceKm spans 0.00 to 80.0 while chshScore spans 2.08 to 2.08. Midpoint sample: totalDistanceKm 40.0, chshScore 2.08.

Warnings and cautions

info: The BBM92 result is entanglement-source-based and intentionally separated from prepare-and-measure BB84 assumptions.
info: Source visibility and Bell-state fidelity reduce entanglement correlations, increasing the coincidence-error proxy.

Formulas and assumptions

This estimator models entanglement-based BBM92 and E91 links as source-in-the-middle teaching proxies rather than prepare-and-measure BB84 variants.
Coincidences are estimated from pair-emission probability, two independent lossy arms, scalar detector efficiencies, and accidental-noise terms.
E91 Bell monitoring is represented by a CHSH-style visibility proxy and a configurable Bell-test sample fraction, not by a loophole-free or device-independent security proof.
Secret-key output is an asymptotic teaching proxy with explicit caution about source quality, timing, and detector assumptions. It is not a certified deployment-grade key-rate guarantee.
Each arm uses eta = eta_det 10^(-loss_dB / 10), so the emitted entangled pair must survive both lossy detection paths.
Accidental coincidences are scaled by a coincidence-window factor and arm noise probabilities, then contribute a random-bit 50% error term.
BBM92 and E91 share the same entanglement-source coincidence model here, while E91 additionally reserves Bell-test samples before key-generation accounting.

References

Ekert (1991) entanglement-based QKD and Bell-correlation motivation.
Bennett, Brassard, and Mermin (1992) BBM92 entanglement-based key distribution.
Entanglement-based QKD reviews covering source visibility, accidental coincidences, and detector assumptions.