BB84 protocol: eavesdropping detection
In the BB84 protocol, after Bob measures the photons and communicates his chosen bases publicly (as described in my previous post here), a process called reconciliation takes place. Bob reveals his measurement bases, and Alice discloses which bases were the correct ones she used to send the photons. Alice and Bob then discard the data from mismatched bases and keep only the bits where bases aligned, establishing a shared key. This communication of bases happens over a public channel.
Now, let’s consider an eavesdropper, Eve, attempting to intercept the key. Eve’s strategy would be to intercept photons sent by Alice, measure their polarization, and then resend photons to Bob. However, Eve doesn’t know which basis Alice used for each photon and must guess.
Due to the no-cloning theorem, Eve cannot perfectly copy an unknown quantum state. She must perform a measurement to gain information. If Eve guesses the wrong basis (50\% probability), measuring polarization in a non-orthogonal basis will inevitably disturb the quantum state.
When Eve resends a photon based on a measurement in a wrong basis, the polarization of this photon becomes uncorrelated with Alice’s original polarization in those specific mismatched basis cases. Consequently, when Bob measures in the correct basis (matching Alice’s original basis for these bits after reconciliation), he will statistically obtain an incorrect result with a certain probability in these instances where Eve intercepted using a “wrong basis”.
To detect Eve’s presence, Alice and Bob sacrifice a random subset of their reconciled key. Bob publicly announces the values he measured for these sacrificed bits. Alice then reveals the original bits she sent for these positions, and they compare them.
In the absence of Eve, and ideally with perfect equipment and no noise, the error rate should be zero. In practice, a low error rate is expected due to channel noise and imperfections. However, if Eve is eavesdropping using a measure-and-resend attack, the errors introduced by her wrong-basis measurements will significantly increase the error rate. This increased error rate serves as an alarm, alerting Alice and Bob to a potential eavesdropper. If the error rate is too high, they discard the key, assuming it is compromised.
The security of BB84 hinges on several fundamental quantum principles:
- quantum measurement disturbance: Measuring a quantum state in a non-orthogonal basis inevitably alters the state,
- no-cloning theorem: Unknown quantum states cannot be perfectly duplicated, forcing any eavesdropper to measure and risk disturbing the signal,
- statistical detectability: Errors introduced by eavesdropping attempts are statistically detectable through error checking procedures.
For more insights into this topic, you can find the details here.