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In a quantum key distribution protocol such as BB84 how do Alice and Bob deal with lost or undetected photons in practice?

Imagine Alice sends 1001 using X Z X Z bases. Bob then receives 101 (second bit is lost) which he measures in X Z Z. He then announces these bases. How can they tell that the second bit was lost? How can Alice tell which bits Bob measured with his 3 bases choices to then be able to announce which are correct? Doesn't the loss of photons in practice render this protocol useless?

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2 Answers 2

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If the photons are sent sequentially, they can implement some synchronous control and detect the missed bits by timing. Also, they could implement additional control using public non-encrypted channels.

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To address this, the BB84 protocol involves several steps to maintain security and establish a shared key even when some photons are lost:

  1. Shared Basis Announcement: After sending the qubits, Bob announces the bases he used to measure each received qubit (without disclosing the measurement outcomes). Alice then compares these bases with the ones she used to prepare the qubits, indicating which bits they should keep for the key.

  2. Discarding Mismatched Bases: Alice and Bob discard the bits where their basis choices do not match. This step is where the effects of photon loss are typically detected. If Alice sent a photon that was lost, Bob might not have received or measured it, resulting in a missing basis announcement for that position.

  3. Handling Missing Bits: If Bob receives fewer bits due to lost photons, the BB84 protocol accommodates this by:

    • Alice and Bob disregarding the missing positions from the final key generation.
    • Maintaining a shared list of which bits are valid and should be retained for the key.

In your example, where Alice sends 1001 using bases X Z X Z, and Bob receives 101 (with the second bit lost), measured in X Z Z:

  • Bob announces the bases he used for each measured bit: X Z Z.
  • Alice then compares these with the bases she used: X Z X Z.
  • In this case, Alice and Bob will realize that the second bit is lost, since Bob does not announce a corresponding measurement basis for it.
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  • $\begingroup$ I'm not sure how they can realize that it was the second bit that was lost. How do they know it wasn't one of the other three? $\endgroup$
    – Omeglac
    Commented May 1 at 21:01

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