Figure 5

Secret key rate \(K\) as a function of the overall channel loss \(\Lambda \) measured in dB for generic photonic sources and assuming the ESR architecture. (a) considers a detection and coupling efficiency \({\eta }_{{\rm{c}},{\rm{d}}}=100{\rm{ \% }}\) and (b) considers \({\eta }_{{\rm{c}},{\rm{d}}}=98.7{\rm{ \% }}\). Each figure evaluates three different cases. The first (second) case, assumes that the entanglement source \({\rho }_{bc}\) (\({\rho }_{ab}\)) is an ideal entanglement source, while \({\rho }_{ab}\) (\({\rho }_{bc}\)) is characterised by the parameters \({p}_{0}\) and \(q={p}_{2}/{p}_{1}\). The third case considers that both \({\rho }_{bc}\) and \({\rho }_{ab}\) are characterised by the parameters \({p}_{0}\) and \(q={p}_{2}/{p}_{1}\). All figures consider two possible values for \({p}_{0}\), i.e., \({p}_{0}=0.5\) (solid lines) and \({p}_{0}=0.9\) (dotted lines), and four different values for the parameter \(q\in {\mathscr{Q}}=\{0,1{0}^{-2},1{0}^{-1.5},1{0}^{-1}\}\). Also, for concreteness, in all cases we set \({n}_{{\rm{S}}{\rm{H}}}=1{0}^{9}\) and choose the security settings \({S}_{1}\).