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The security of quantum key distribution (QKD) has been proven for differentprotocols, in particular for the BB84 protocol. It has been shown that thisscheme is robust against eventual imperfections in the state preparation, andsending only three different states delivers the same secret key rateachievable with four states. In this work, we prove, in a finite-key scenario,that the security of this protocol can be maintained even with less measurementoperators on the receiver. This allows us to implement a time-bin encodingscheme with a minimum amount of resources.

Security proof for a simplified BB84-like QKD protocol