Continuous-variable measurement-device-independent quantum key distribution using squeezed states

A continuous-variable measurement-device-independent quantum key distribution (CV-MDI QKD) protocol using squeezed states is proposed where the two legitimate partners send Gaussian-modulated squeezed states to an untrusted third party to realize the measurement. Security analysis shows that the protocol can not only defend all detector side channels, but also attain higher secret key rates than the coherent-state-based protocol. We also present a method to improve the squeezed-state CV-MDI QKD protocol by adding proper Gaussian noise to the reconciliation side. It is found that there is an optimal added noise to optimize the performance of the protocol in terms of both key rates and maximal transmission distances. The resulting protocol shows the potential of long-distance secure communication using the CV-MDI QKD protocol.

Figure 1

The prepare-and-measurement scheme of the CV-MDI QKD protocol using squeezed states where quantum channels and Charlie are fully controlled by Eve. Practical detectors on Charlie's side have the same quantum efficiency and electronic noise.

Figure 2

The entanglement-based scheme of the CV-MDI QKD protocol using squeezed states where all detectors represent homodyne detection and Einstein-Podolsky-Rosen (EPR) states are two-mode squeezed states. Two quantum channels and Charlie are fully controlled by Eve, but Eve has no access to the apparatuses in Alice's and Bob's stations. The imperfection of the detectors is characterized by quantum efficiency $\eta$ and electronic noise ${\upsilon }_1={\upsilon }_2={\upsilon }_{el}$.

Figure 3

The entanglement-based scheme of the modified squeezed-state CV-MDI QKD protocol with general Gaussian added noise on the reconciliation side. Two quantum channels and Charlie are fully controlled by Eve, but Eve has no access to the apparatuses in Alice's and Bob's stations. The imperfection of the detectors is characterized by quantum efficiency $\eta$ and electronic noise ${\upsilon }_1={\upsilon }_2={\upsilon }_{el}$.

Figure 4

Secret key rates of the coherent-state (black), squeezed-state (blue) CV-MDI QKD protocol, and the modified squeezed-state CV-MDI QKD protocol (red) in the symmetric case $\left(L_{AC}=L_{BC}\right)$ with perfect homodyne detectors $\left(\eta =1,{\upsilon }_{el}=0\right)$ and imperfect homodyne detectors ($\eta =0.9,{\upsilon }_{el}=0.015$). The dot-dashed line and solid line represent the situation for using perfect and imperfect detectors, respectively. Here we use the ideal reconciliation efficiency $\beta =1$, large variance $V_A=V_B={10}^5$, and $\varepsilon =0.002$.

Figure 5

Optimal added noise for the modified squeezed-state CV-MDI QKD protocol in a symmetric case $\left(L_{AC}=L_{BC}\right)$ using perfect homodyne detectors $\left(\eta =1,{\upsilon }_{el}=0\right)$ and imperfect homodyne detectors ($\eta =0.9,{\upsilon }_{el}=0.015$). Here we use the ideal reconciliation efficiency $\beta =1$, large variance $V_A=V_B={10}^5$, and $\varepsilon =0.002$.

Figure 6

A comparison among the maximal transmission distance for the coherent-state, squeezed-state CV-MDI QKD protocols, and the modified squeezed-state CV-MDI QKD protocol with perfect homodyne detectors $\left(\eta =1,{\upsilon }_{el}=0\right)$ and imperfect homodyne detectors $\left(\eta =0.9,{\upsilon }_{el}=0.015\right)$, within which the key rate $K$ is positive. Here we use the ideal reconciliation efficiency $\beta =1$, large variance $V_A=V_B={10}^5$, and $\varepsilon =0.002$.

Figure 7

A comparison among the maximal transmission distance for the coherent-state, squeezed-state CV-MDI QKD protocols, and the modified squeezed-state CV-MDI QKD protocol with perfect homodyne detectors $\left(\eta =1,{\upsilon }_{el}=0\right)$ and imperfect homodyne detectors $\left(\eta =0.9,{\upsilon }_{el}=0.015\right)$, within which the key rate $K$ is positive. Here we use the realistic variances $V_A=V_B=5.04$ and $\varepsilon =0.002$.

Figure 8

Secret key rates of the coherent-state (black), squeezed-state (blue) CV-MDI QKD protocols, and the modified squeezed-state CV-MDI QKD protocol (red) in the most asymmetric case $\left(L_{BC}=0\mathrm{km}\right)$ with perfect homodyne detectors $\left(\eta =1,{\upsilon }_{el}=0\right)$ and imperfect homodyne detectors ($\eta =0.9,{\upsilon }_{el}=0.015$). The dot-dashed line and solid line represent the situation for using perfect and imperfect detectors, respectively. Here we use the realistic parameters: $V_A=V_B=5.04$ and $\varepsilon =0.002$.

Figure 9

Optimal input noise for the modified squeezed-state CV-MDI QKD protocol in the most asymmetric case $\left(L_{BC}=0\mathrm{km}\right)$ using perfect homodyne detectors $\left(\eta =1,{\upsilon }_{el}=0\right)$ and imperfect homodyne detectors ($\eta =0.9,{\upsilon }_{el}=0.015$). Here we use the realistic parameters: $V_A=V_B=5.04$ and $\varepsilon =0.002$.