Secure coherent-state quantum key distribution protocols with efficient reconciliation

We study the equivalence of a realistic quantum key distribution protocol using coherent states and homodyne detection with a formal entanglement purification protocol. Maximally entangled qubit pairs that one can extract in the formal protocol correspond to secret key bits in the realistic protocol. More specifically, we define a qubit encoding scheme that allows the formal protocol to produce more than one entangled qubit pair per entangled oscillator pair or, equivalently for the realistic protocol, more than one secret key bit per coherent state. The entanglement parameters are estimated using quantum tomography. We analyze the properties of the encoding scheme and investigate the resulting secret key rate in the important case of the attenuation channel.

Figure 1

Schematic description of $\mathcal{Q}\mathcal{S}$.

Figure 2

Schematic description of $\mathcal{Q}\mathcal{E}$ and the use of the systems ${\mathsf{s}}_{1,\dots ,m}^{\prime }$.