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Protocol Simulation

E91

An entangled photon source distributes one photon to Alice and one to Bob. Security is not just inferred from basis mismatch - it is proven through Bell inequality violations. Any eavesdropper collapses the entanglement, and the violation disappears.

40
Alice's angles: 0°, 45°, 90°
Bob's angles: 45°, 90°, 135°
Bright = matched angles (key bits)  ·  Faded = mismatched (used for Bell test)

● Bit 0   ● Bit 1    Faded = different angles, used for CHSH Bell test


CHSH Bell Parameter |S| - max quantum: 2√2 ≈ 2.828
0 2 (classical limit) 2√2 (quantum max)
Run the simulation to see the Bell test result.
Sifted Key (matched angles)
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Est. Error Rate
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How E91 differs from BB84

BB84 uses prepare-and-measure: Alice prepares photons and sends them. E91 uses entanglement: a source creates pairs and sends one to each party simultaneously. Neither Alice nor Bob controls the initial state.

Security in BB84 comes from the disturbance caused by measurement. Security in E91 comes from Bell inequality violations - a mathematical test that only quantum-entangled particles can pass. Classical correlations (including those an eavesdropper might fake) cannot exceed |S| = 2.

Alice uses angles 0°, 45°, 90°. Bob uses 45°, 90°, 135°. Pairs where they chose the same angle form the key. Pairs with different angles are used to compute S.


Notes

At small pair counts the CHSH value has high variance - use 100+ pairs for stable results.

When Eve is present, her interception breaks the entanglement. The measured S value drops toward or below 2, flagging her presence.