Fig. 1: The schematic diagram of the proposed free-running RFI QKD scheme.

The scheme mainly contains four phases: physical communication, data classification, secure key length estimation and post-processing. Alice (Bob) prepares (measures) the quantum state, and generates raw data. Then, n interval sifted data s₀, s₁, … , s_n−1 are generated in the basis/sifting and quantum bit error rate (QBER) calculation procedure. Afterwards, s₀, s₁, … , s_n−1 are classified into m datasets \(({{{{\mathscr{D}}}}}_{0},{{{{\mathscr{D}}}}}_{1},\ldots \,,{{{{\mathscr{D}}}}}_{m-1})\) according to the estimated classification parameter. The final secure key length is estimated based on the classified datasets \(({{{{\mathscr{D}}}}}_{0},{{{{\mathscr{D}}}}}_{1},\ldots \,,{{{{\mathscr{D}}}}}_{m-1})\). (ρ₀, ρ₁, … , ρ_n−1) represent the classification parameter of n interval sifted data. m and \({\rho }^{\prime}\) are used to split [0, 2π) as m slices: P₀, P₁, … , P_m−1.