Continuous Variable Quantum Key Distribution: Finite-Key Analysis of Composable Security against Coherent Attacks

We provide a security analysis for continuous variable quantum key distribution protocols based on the transmission of two-mode squeezed vacuum states measured via homodyne detection. We employ a version of the entropic uncertainty relation for smooth entropies to give a lower bound on the number of secret bits which can be extracted from a finite number of runs of the protocol. This bound is valid under general coherent attacks, and gives rise to keys which are composably secure. For comparison, we also give a lower bound valid under the assumption of collective attacks. For both scenarios, we find positive key rates using experimental parameters reachable today.

Figure 1

Key rate $\ell /N$ in bits per signal against coherent attacks for an input squeezing of $11\mathrm{dB}$, antisqueezing of $16\mathrm{dB}$ and additional symmetric losses of 0% (solid line), 4% (dashed line) and 6% (dash-dotted line). We assumed an error correction efficiency of 0.95 and set ${ϵ}_s={ϵ}_c={10}^{-6}$.

Figure 2

Key rate $\ell /N$ in bits per signal against collective Gaussian attacks for losses of 0% (solid line), 15% (dashed line), 25% (dash-dotted line). Squeezing strength, error correction efficiency, and security parameters are chosen as in the case of coherent attacks.

Figure 3

Key rate $\ell /N$ versus losses secure against coherent attacks at $N={10}^9$ (dash-dotted line), collective Gaussian attacks at $N={10}^9$ (dashed line), and the Devetak-Winter rate [7] for perfect information reconciliation (solid line). Squeezing strength, error correction efficiency, and security parameters are chosen as in the case of coherent attacks.