The Principle
You cannot precisely measure certain pairs of properties simultaneously. Measuring one disturbs the other.
This isn’t a technology limitation. It’s a fundamental law of quantum mechanics.
Applied to Polarization
The two filter types (standard and diagonal) are conjugate bases.
This means:
- If a photon is definitely vertical (↑), its diagonal polarization is completely uncertain
- If a photon is definitely diagonal (↗), its standard polarization is completely uncertain
- You cannot know both at once
Measuring in one basis destroys information about the other.
Why This Matters for BB84
This is the physics behind quantum key exchange security.
Eve faces an impossible choice:
| If she measures with… | And Alice used… | Result |
|---|---|---|
| Standard filter | Standard | Correct value, no disturbance |
| Standard filter | Diagonal | Random result, photon disturbed |
| Diagonal filter | Diagonal | Correct value, no disturbance |
| Diagonal filter | Standard | Random result, photon disturbed |
Eve cannot measure in both bases. She must guess. When she guesses wrong, she disturbs the photon.
Heisenberg’s uncertainty principle guarantees that eavesdropping is physically detectable.