Modelling efficient BB84 with applications for medium-range, terrestrial free-space QKD

Abstract

Terrestrial free-space quantum key distribution is ideally suited for deployment in dense urban environments. The transition from laboratory to commercial deployment, however, raises a number of important engineering and deployment issues. Here, we investigate these issues for efficient BB84 using a weak coherent pulse-decoy state protocol. We calculate expected key lengths for different environmental conditions and when the scope for optimisation of protocol parameters is restricted due to practical considerations. In particular, we find that for a fixed receiver basis choice probability, it can be advantageous to allow the transmitter to have a different basis choice probability depending on varying channel loss and background light levels. Finally, we examine the effects of pulse intensity uncertainty finding that they can dramatically reduce the key length. These results can be used to determine the loss budget for the free-space optics of a QKD systems and assist in their design.

Finite key performance of satellite quantum key distribution under practical constraints

“…The value of 𝑃 𝐴 X can vary to compensate for the fixed value of 𝑃 𝐵 X . One can show that if both 𝑃 𝐵 X and 𝑃 𝐴 X can vary freely, then the optimal raw key length is found for 𝑃 𝐵 X = 𝑃 𝐴 X [29]. From Fig.…”

“…Alice prepares bits in the X-basis with probability 𝑃 𝐴 X , while Bob measures within the X-basis with probability 𝑃 𝐵 X . It is standard to take 𝑃 𝐴 X = 𝑃 𝐵 X = 𝑃 X , however, in general it is possible that 𝑃 𝐴 X ≠ 𝑃 𝐵 X , particularly if one probability is fixed due to practical considerations [29]. We consider phase-randomised coherent pulses where the intensity (mean photon number) 𝜇 𝑘 ∈ {𝜇 1 , 𝜇 2 , 𝜇 3 } is randomly chosen with probability 𝑝 𝜇 𝑘 .…”

“…This clearly demonstrates that when we fix 𝑃 𝐵 X , then choosing an equal basis bias is not optimal. However, when we are free to optimise both 𝑃 𝐵 X and 𝑃 𝐴 X , then choosing 𝑃 𝐴 X = 𝑃 𝐵 X is optimal [29]. Despite the impracticality of implementing a fully optimised parameter space, we find a number of ways SatQKD missions can enhance finite key generation.…”

“…( 2) and could also change the secret key formula itself. A different scenario has also been considered [29] where the existing formalism described in Refs. [27,39] is used, but simply assume that the true intensities are uncertain, though not necessarily fluctuating during a transmission block.…”

“…It is more realistic to consider a number of parameters as fixed, that include the operating basis bias at the OGS and the transmitted intensities. Parameter fixing has been explored in the context of terrestrial free-space QKD [29]. In SatQKD the highly variable channel losses in SatQKD with fixed parameters require more sophisticated modeling and analysis.…”