Fig. 10: SKL vs \({d}_{\min }\) for fixed \({{{{{{{\boldsymbol{{{{{{{{\mathcal{F}}}}}}}}}}}}}}}}\).
From: Finite key performance of satellite quantum key distribution under practical constraints
a The fully optimised SKL is illustrated in black, with each fixed point j along the optimal curve generating the set \({{{{{{{{\mathcal{F}}}}}}}}}_{{d}_{\min }(j)}^{{{{{{{{\rm{opt}}}}}}}}}\), corresponding to the optimal fixed parameter values at ground track distance \({d}_{\min }(j)\) (in units of 106 m). The SKL for three illustrative fixed sets, \({{{{{{{{\mathcal{F}}}}}}}}}_{0}^{{{{{{{{\rm{opt}}}}}}}}}\), \({{{{{{{{\mathcal{F}}}}}}}}}_{0.60}^{{{{{{{{\rm{opt}}}}}}}}}\), and \({{{{{{{{\mathcal{F}}}}}}}}}_{1.27}^{{{{{{{{\rm{opt}}}}}}}}}\), are optimised over the remaining parameter space with their corresponding areas shaded to determine the expected annual SKL. The ideal fixed data set is highlighted with an orange star at \({d}_{\min }=0.43\times 1{0}^{6}\) m. b Variation in the expected annual SKL for each fixed set \({{{{{{{{\mathcal{F}}}}}}}}}_{{d}_{\min }(j)}^{{{{{{{{\rm{opt}}}}}}}}}\). The vertical solid line corresponds to the parameter set that maximises the estimated annual SKL and the horizontal dashed line to the annual SKL with no constraints.
