Quantum-key-distribution protocol with pseudorandom bases

Quantum key distribution (QKD) offers a way for establishing information-theoretical secure communications. An important part of QKD technology is a high-quality random number generator for the quantum-state preparation and for post-processing procedures. In this work, we consider a class of prepare-and-measure QKD protocols, utilizing additional pseudorandomness in the preparation of quantum states. We study one of such protocols and analyze its security against the intercept-resend attack. We demonstrate that, for single-photon sources, the considered protocol gives better secret key rates than the BB84 and the asymmetric BB84 protocols. However, the protocol strongly requires single-photon sources.

Figure 1

Base patterns on the Poincaré sphere. The BB84 protocol (left) uses two maximally conjugated bases with the angle $\pi /4$ between each other. For each pulse, the bases are chosen by Alice and Bob randomly and independently, so, the sifting procedure (discarding of positions where Alice's and Bob's bases are different) is required. In the suggested protocol (right), the standard basis $\left\{\right|0\rangle ,|1\rangle \}$ is rotated by an arbitrary angle (from a finite set) in not a random pseudorandom manner. Thus, the bases of Alice and Bob always coincide and there is no sifting.

Figure 2

Function $\zeta \left(M\right)$.

Figure 3

Secret key rates (per bit of the raw key, before sifting) of the presented pseudorandom bases (PRB) protocol, the BB84 protocol, and the asymmetric BB84 (aBB84) protocol with and without losses in the quantum channel, when the efficiency of error correction achieves the theoretical limit $f=1$ (a) and for practically achievable efficiency $f=1.22$ (b). It can be seen that the considered protocol gives better secret key rates than the BB84 protocol and approximately the same rates as the asymmetric BB84 protocol.

Figure 4

Results of analysis of the Legendre sequences in terms of $\delta \left(\gamma \right)={\nu }_{\mathrm{correct}}\left(\gamma \right)-1/2$ by formulas (C15) (top curve) and (C18) (bottom curve) for $L={10}^{10}-33$, ${log}_{2}L\approx 16$, $s=12$, and $S=1000$.