B92 Quantum Key Distribution

Eavesdropper

Transmission

Rate 2.0 photons/s

Live Statistics

Photons sent

Sifted key bits

Sift rate

QBER

—

Send bits to build the sifted key…

Sifted Key (Bob's side)

—

How it works

B92 encodes one bit per photon using two non-orthogonal polarization states: bit 0 → |0⟩ (vertical, 0°), bit 1 → |+⟩ (diagonal, 45°). Because ⟨0|+⟩ ≠ 0, no measurement can identify the state with certainty — that non-orthogonality is exactly what makes eavesdropping detectable.

Bob picks a random basis, Z {0°,90°} or X {45°,135°}.
Born rule:  P(outcome) = cos²(θ_state − θ_basis)

Z-basis: |0⟩ → always 0°   |+⟩ → 0° or 90° (50/50)
X-basis: |+⟩ → always 45°  |0⟩ → 45° or 135° (50/50)

Outcome 90° (Z) ⇒ bit was 1, conclusively.
Outcome 135° (X) ⇒ bit was 0, conclusively.
All other outcomes are discarded (inconclusive).

Only ~25% of photons yield a conclusive result — those form the sifted key, which matches Alice's original bit exactly when the channel is clean.

Eve has no better strategy: she must also guess a random basis, measure, and re-prepare a state to forward. Whenever her guess is wrong, the resent state no longer matches what Alice sent, so a fraction of Bob's otherwise-conclusive results now disagree with Alice — this shows up as a nonzero quantum bit error rate (QBER). Alice and Bob sacrifice a public sample of the sifted key to estimate QBER; a spike above the noise floor (here, roughly 20–30% under full intercept-resend) proves the channel was tapped, and they abort instead of using the key.

Alice

Eve

Bob

Bit 0 · |0⟩ vertical Bit 1 · |+⟩ diagonal

⚠ Couldn't load the 3D engineThree.js failed to load from the CDN. Check your connection and reload.