Experimental demonstration of post-selection-based continuous-variable quantum key distribution in the presence of Gaussian noise

In realistic continuous-variable quantum key distribution protocols, an eavesdropper may exploit the additional Gaussian noise generated during transmission to mask her presence. We present a theoretical framework for a post-selection-based protocol which explicitly takes into account excess Gaussian noise. We derive a quantitative expression of the secret key rates based on the Levitin and Holevo bounds. We experimentally demonstrate that the post-selection-based scheme is still secure against both individual and collective Gaussian attacks in the presence of this excess noise.

Figure 1

(Color online) Schematic of setup. Quantum channel of transmission $\eta$ and excess noise $\xi$ is simulated experimentally (a) and analyzed theoretically for the entangling cloner attack (b). $\lambda ∕2$, half-wave-plate; PBS, polarizing beam-splitter; AM (PM), amplitude (phase) modulators; RNG, independent white noise generators; EPR, entanglement source; $Q$-mem, quantum memory.

Figure 2

(Color online) Post-selection regions at $\eta =0.5$ are shown in red. (a) and (b) show the information rates $\mathrm{\Delta }I=I_{AB}-I_E$ with no excess noise for individual and collective attacks. (c) and (d) is when $\xi =0.2$. On the dashed line $m_B^c$ in (c), Eve can obtain the same amount of information from Alice as she can from Bob. The post-selection region asymptotes to the lines $m_B^{l\pm }$.

Figure 3

(Color online) Experimental results superimposed on theoretical lower bounds of secure key rates at transmission $\eta =0.47\pm 0.002$ when Eve does a collective attack and an individual attack (inset). Unfilled data points with arrows have error bars going to negative $\mathrm{\Delta }I$. The shaded region indicates the noise threshold for secure keys. The experimental results were obtained using an encoding variance optimized for the individual attack bound.

Figure 4

(Color online) Experimental results superimposed on theoretical contour plots of information rate after post-selection $\left(\mathrm{\Delta }I\right)$ as a function of channel transmission $\eta$ and EGN $\xi$. (a),(b),(c),(d),(e) indicates $\mathrm{\Delta }I={10}^{-1},{10}^{-2},{10}^{-3},{10}^{-4},{10}^{-7}$ (bits/state). Filled (unfilled) data points indicate $\mathrm{\Delta }{I}_{\exp }>0$ $(\mathrm{\Delta }{I}_{\exp }\le 0)$. No secure keys can be generated in the shaded regions. Dark shade indicates separability between Alice’s and Bob’s states.