Continuous-variable measurement-device-independent quantum key distribution

We propose a continuous-variable measurement-device-independent quantum key distribution (CV-MDI QKD) protocol, in which detection is conducted by an untrusted third party. Our protocol can defend all detector side channels, which seriously threaten the security of a practical CV QKD system. Its security analysis against arbitrary collective attacks is derived based on the fact that the entanglement-based scheme of CV-MDI QKD is equivalent to the conventional CV QKD with coherent states and heterodyne detection. We find that the maximal total transmission distance is achieved by setting the untrusted third party close to one of the legitimate users. Furthermore, an alternate detection scheme, a special application of CV-MDI QKD, is proposed to enhance the security of the standard CV QKD system.

Figure 1

(a) EB scheme of the CV-MDI QKD protocol. EPR: two-mode squeezed state. Het: heterodyne detection. ${\mathrm{Hom}}_{1\mathrm{x}}$: homodyne detection of measuring the $x$ quadrature. ${\mathrm{Hom}}_{2\mathrm{p}}$: homodyne detection of measuring the $p$ quadrature. $X_C,P_D$: measurement results of ${\mathrm{Hom}}_{1\mathrm{x}}$ and ${\mathrm{Hom}}_{2\mathrm{p}}$, respectively. BS: 50:50 beam splitter. (b) Equivalent one-way model of the EB scheme under the assumptions that Eve controls channels, Charlie and Bob's EPR state, and the displacement in (a).

Figure 2

PM scheme of CV-MDI QKD. ${\mathrm{Hom}}_{1\mathrm{x}}$: homodyne detection of measuring the $x$ quadrature. ${\mathrm{Hom}}_{2\mathrm{p}}$: homodyne detection of measuring the $p$ quadrature. BS: 50:50 beam splitter.

Figure 3

EB scheme of CV-MDI QKD with two independent entangled-cloner attacks. After two channels, mode $A_2$ becomes $A^{\prime }$, and mode $B_2$ becomes $B^{\prime }$. Charlie keeps the same structure as in Fig. 1.

Figure 4

Secret key rate in the symmetric case where $L_{AC}=L_{BC}$. The red dashed line is under the ideal condition that variance $V_A=V_B={10}^5$ and zero excess noise. The black solid line is under the practical condition that variance $V_A=V_B=40$ and excess noises ${\varepsilon }_A={\varepsilon }_B=0.002$ [14]. Both reconciliation efficiencies are ${\beta }_R=1.$

Figure 5

(a) Secret key rate vs transmission distance from Alice to Charlie $L_{AC}$ and from Bob to Charlie $L_{BC}$, under the practical conditions that $V_A=V_B=40$ and ${\varepsilon }_A={\varepsilon }_B=0.002$ [14]. (b) Secret key rate vs $L_{AC}$ given different $L_{BC}$. The dashed lines are under the ideal conditions that $V_A=V_B={10}^5$ and ${\varepsilon }_A={\varepsilon }_B=0$. The solid lines are under the same practical conditions as in (a). $L_{BC}$ is 0 km for the top black solid and dashed lines [45], 1 km for the middle blue solid and dashed lines, and 3 km for the bottom red solid and dashed lines. Reconciliation efficiency is set to ${\beta }_R=1$ for all simulations.

Figure 6

(a) PM model of our detection scheme for one-way CV QKD, which contains two steps; the first is the measurement step, and the second is the data-processing step. (b) The left panel is the secret key rate vs transmission distance $L_{AB}$ when using our detection scheme for a one-way protocol with coherent states. The reconciliation efficiency for the red dashed line is ${\beta }_R=1$, and for black solid line it is ${\beta }_R=0.95$. The right panel is $k_{\mathrm{opt}}$ vs $L_{AB}$. The simulation is under the conditions $V_A=V_B=40$ and ${\varepsilon }_A={\varepsilon }_B=0.002$ [45].