Towards a Finite Size Analysis of Decoy-State Quantum Key Distribution with Advantage Distillation

Kurzfassung

Quantum Key Distribution (QKD) allows two legitimate parties, Alice and Bob, to share a secret key with information-theoretic security, ensuring that an eavesdropper, Eve, cannot obtain any information about the key. A QKD protocol is provably secure only when the Quantum Bit Error Rate (QBER) is below a certain threshold and, therefore, the presence of noise inherently limits the maximum transmission distance. Advantage Distillation (AD) is a classical post-processing technique that enhances QKD protocols by increasing the maximum acceptable QBER and, thus, allows extending the communication range. AD operates by post-selecting blocks of bits and extracting fewer but highly correlated bits between Alice and Bob, which exhibit a reduced QBER, thus lowering the amount of information that has to be disclosed during the information reconciliation step. In this study, we present a new analytical expression for the secure key rate. This will enable a finite-size secure key length analysis of the decoy state version of the BB84 protocol including AD post-processing.