Unconditionally Secure Key Distribution Based on Two Nonorthogonal States

We prove the unconditional security of the Bennett 1992 protocol, by using a reduction to an entanglement distillation protocol initiated by a local filtering process. The bit errors and the phase errors are correlated after the filtering, and we can bound the amount of phase errors from the observed bit errors by an estimation method involving nonorthogonal measurements. The angle between the two states shows a trade-off between accuracy of the estimation and robustness to noises.

Figure 1

(a) The optimum value of $|⟨{\phi }_0|{\phi }_1⟩{|}^2$ and the key generation rate $G$ in the depolarizing channel. (b) The error rates (normalized by $n_{\mathrm{f}\mathrm{i}\mathrm{l}}$) in the data qubits for the depolarizing channel with $p=0.03$. The estimated upper bound for phase errors (dot-dashed line), the actual phase errors (solid line), and the bit errors (dotted line).