B92 Protocol: Two-State Quantum Key Distribution

Quantum Channel

Transmission rate 6/s

Live Statistics

Photons sent

Sifted key bits

Conclusive rate

0.0%

QBER (errors)

0.0%

Sifted key: (none yet)

Eve is off — the channel is untouched, so the sifted key should stay error-free.

How it works

B92 (Bennett, 1992) needs only two non-orthogonal states instead of BB84's four. Alice encodes each bit as:

bit 0 → |0⟩
bit 1 → |+⟩ = (|0⟩ + |1⟩)/√2   (45° from |0⟩)
⟨0|+⟩ = 1/√2  → the states are NOT orthogonal

Bob randomly measures each photon in the Z basis {|0⟩,|1⟩} or the X basis {|+⟩,|−⟩} (50/50, his own choice, unknown to Alice). Because the states overlap, only two outcomes are ever conclusive:

Z-basis result |1⟩  →  bit must have been 1   (|0⟩ can never yield |1⟩)
X-basis result |−⟩  →  bit must have been 0   (|+⟩ can never yield |−⟩)
anything else        →  inconclusive, discarded

Each of those two discriminating outcomes needs the right basis (P=1/2) and the right random projection (P=1/2), so only P = 1/2 × 1/2 = 25% of photons survive sifting — half BB84's efficiency, the price of using one basis pair per bit value instead of two.

Non-orthogonal states can't be copied (no-cloning theorem), so an intercept-resend eavesdropper (toggle "Eve" on) is forced to measure and re-encode each photon herself. Whenever her own measurement is inconclusive she must guess a bit blind, and that guess disagrees with Alice's original bit half the time — surfacing as a non-zero QBER in Bob's sifted key, exactly the signal Alice and Bob use to detect an eavesdropper by comparing a public subset of the key.

bit 0 (|0⟩) bit 1 (|+⟩) sifted, correct sifted, error (Eve)

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