Carrier-phase estimation for simultaneous quantum key distribution and classical communication using a real local oscillator

The simultaneous quantum and classical communication (SQCC) protocol is an appealing protocol since it allows continuous-variable quantum key distribution (CV-QKD) and classical communication to be implemented simultaneously by using the same communication infrastructure and on a single wavelength. However, the main challenge of the SQCC protocol is its low tolerance of phase noise, limiting the transmission distance under the real local oscillator (LO) design. To eliminate the phase drift without the aid of the reference signal, the classical carrier phase estimation (CPE) algorithm in the field of coherent optical communication is employed for phase recovery and data extraction. Besides, the power of the residual phase noise in classical communication and the power of the excess phase noise in CV-QKD are derived, including the effects of the employed laser linewidth, the transversal filter length, and the classical signal power. On this basis, the performances of the SQCC protocol under the trusted and the untrusted phase noise model are discussed, respectively. Our work confirms the feasibility of the CPE algorithm in the SQCC protocol and demonstrates the conditions required for this protocol to operate on a coherent optical communication system.

Figure 1

Phase-space representations of various modulation formats: (a) Classical QPSK format, (b) GMCS QKD format, (c) SQCC format.

Figure 2

Implementation of the SQCC protocol. The above illustration shows the overall optical path of the SQCC implementation, and the following illustrations show the distribution of the signal in the phase space from preparation to reception to phase recovery. IQ mod: in-phase and quadrature modulator; VOA: variable optical attenuator; SMF: single mode fiber; PC: polarization controller; BD: balanced detector; ADC: analog-to-digital converter; LO: local oscillator.

Figure 3

Schematic of carrier recovery and data extraction.

Figure 4

Phase noise as a function of the signal power ${\alpha }^2$. The solid lines represent the analytical approximation of the phase noise according to Eq. (10), and the dashed lines represent the estimation of the phase noise through the Monte Carlo simulation. From top to bottom, the solid and the dashed lines show the phase noise with the laser linewidth of 100, 10, and 1 kHz, respectively. Parameters are typically set as the modulation variance $V_A=5$, the quantum efficiency $\eta =0.6$, the channel distance $L=50$ km, the attenuation coefficient $\gamma =0.2$ dB/km, the electronic noise $v_{el}=0.01$, the block size $N_b=100$, and the symbol rate $B_r=10$ GS/s.

Figure 5

Optimal block length $N_b^{\mathrm{opt}}$ as a function of the signal power ${\alpha }^2$. These solid lines from top to bottom represent the optimal block length with the laser linewidths of 1, 5, 10, and 100 kHz. Parameters are set as the modulation variance $V_A=5$, the quantum efficiency $\eta =0.6$, the channel distance $L=50$ km, the electronic noise $v_{el}=0.01$, and the symbol rate $B_r=10$ GS/s.

Figure 6

Relationship between the excess phase noise and the classical signal power at different laser linewidths. The solid lines represent the analytical function of the excess phase noise, and the dashed lines represent that the phase noise is evaluated by the MC method first and then the excess noise is calculated. From top to bottom, the solid and the dashed lines show the excess noise with the linewidth of 100, 50, 10, and 1 kHz, respectively. Parameters are $V_A=5$, $\eta =0.6$, $L=50$ km, $v_{el}=0.01$, $N_b=100$, $B_r=10$ GS/s.

Figure 7

Excess noise as a function of the signal power ${\alpha }^2$ with various modulation variance. The solid lines represent the analytical expression of the excess noise, and the dashed lines represent that the phase noise is evaluated by the MC method first and then the excess noise is calculated. From top to bottom, the solid and the dashed lines show the excess noise when the modulation variance $V_A$ is 20, 15, 10, and 5, respectively. Parameters are $\mathrm{\Delta }v=1$ kHz, $\eta =0.6$, $L=50$ km, $v_{el}=0.01$, $N_b=500$, $B_r=10$ GS/s.

Figure 8

SQCC performance under untrusted phase noise model. The solid and the dashed lines represent the BER of classical communication. The dotted and dash-dotted lines represent the SKR of quantum communication. The laser linewidths are set to two typical values of 1 and 10 kHz, and the signal power is set to $1\times {10}^3$ and $2\times {10}^3$, respectively, for comparison. Other parameters are set as $V_A=5$, $\eta =0.6$, ${\varepsilon }_0=0.01$, $v_{el}=0.1$, $\beta =0.95$.

Figure 9

SQCC performance under trusted phase noise model. The solid and the dashed lines represent the BER of classical communication. The dotted and dash-dotted lines represent the SKR of quantum communication. The laser linewidths are set to two typical values of 1 and 10 MHz, and the signal power is set to $1\times {10}^3$ and $2\times {10}^3$ for comparison. Other parameters are set as $V_A=5$, $\eta =0.6$, ${\varepsilon }_0=0.01$, $v_{el}=0.1$, $\beta =0.95$.