Improved composable key rates for CV-QKD

TL;DR

This paper refined and advanced the previous theory in this area providing a more rigorous formulation for the composable key rate of a generic CV-QKD protocol, allowing for more optimistic key rates with respect to previous literature.

Abstract

Modern security proofs of quantum key distribution (QKD) must take finite-size effects and composable aspects into consideration. This is also the case for continuous-variable (CV) protocols which are based on the transmission and detection of bosonic coherent states. In this paper, we refine and advance the previous theory in this area providing a more rigorous formulation for the composable key rate of a generic CV-QKD protocol. Thanks to these theoretical refinements, our general formulas allow us to prove more optimistic key rates with respect to previous literature.

Figures (3)

• Figure 1: Improved composable secret key rate [upper bound of Eq. \ref{['key_rate_final2_sub']}] for the Gaussian modulated coherent-state protocol with homodyne detection (blue solid line) and heterodyne detection (black solid line) with respect to channel loss in dB. These lines overlap with those associated with the lower bound of Eq. \ref{['LB']}. The corresponding dashed lines are computed using Eq. \ref{['LB_OLD']}, based on previous literature. We have set $\beta = 0.98$ and $p_\text{ec} = 0.95$. Excess noise is $\xi = 0.01$, detection efficiency is $\eta = 0.6$, and electronic noise is $u_\text{el} = 0.1$. Security epsilons have all been set to $2^{-32}$. The cardinality of the alphabet is $|\mathcal{L}| = 2^7$ for homodyne and $|\mathcal{L}|= 2^{14}$ for heterodyne. Block size is $N = 10^7$ and PE is based on $m = N/10$ sacrificed signals. We have optimized the results over the variance $V$ of Alice's Gaussian modulation.
• Figure 2: Improved composable secret key rate [upper bound of Eq. \ref{['key_rate_final2_sub']}] for the Gaussian modulated coherent-state protocol with homodyne detection (blue solid line) and heterodyne detection (red solid line) with respect to the block size $N$. These lines coincide with those computed from the lower bound of Eq. \ref{['LB']}. The corresponding dashed lines are computed using Eq. \ref{['LB_OLD']}, based on previous literature. Loss is set to $7$ dB, while all the other parameters are chosen as in Fig. \ref{['fig:fig_improved']}.
• Figure 3: Rate and epsilon security, from block to session.