Generating the Local Oscillator “Locally” in Continuous-Variable Quantum Key Distribution Based on Coherent Detection

Continuous-variable quantum key distribution (CV-QKD) protocols based on coherent detection have been studied extensively in both theory and experiment. In all the existing implementations of CV-QKD, both the quantum signal and the local oscillator (LO) are generated from the same laser and propagate through the insecure quantum channel. This arrangement may open security loopholes and limit the potential applications of CV-QKD. In this paper, we propose and demonstrate a pilot-aided feedforward data recovery scheme that enables reliable coherent detection using a “locally” generated LO. Using two independent commercial laser sources and a spool of 25-km optical fiber, we construct a coherent communication system. The variance of the phase noise introduced by the proposed scheme is measured to be 0.04 (${\text{rad}}^2$), which is small enough to enable secure key distribution. This technology also opens the door for other quantum communication protocols, such as the recently proposed measurement-device-independent CV-QKD, where independent light sources are employed by different users.

Popular Summary

Quantum mechanics can be used to create secret key distribution techniques that enable uncrackable cryptographic protocols. The majority of previous quantum key distribution (QKD) implementations have been costly because they typically required dedicated optical fibers for the key generation. Continuous-variable QKD protocols are less expensive because they use coherent communication techniques in which the quantum signal can easily coexist with classical signal channels thanks to the selectivity of the local oscillator employed in coherent detection. However, this approach also introduces a new barrier to QKD implementation: The need to transmit a phase reference for coherent detection. Here, we propose an intradyne continuous-variable QKD scheme and demonstrate that it is possible to perform low-noise coherent detection using a local oscillator generated from an independent laser source located at the receiver’s side.

In most setups, the local oscillator propagates insecurely; it is preferable to generate the local oscillator locally (i.e., at the receiver’s end). We experimentally demonstrate this procedure using commercially available lasers and a 25-km optical fiber as a quantum channel. We test sending a pattern of 1s and 0s, and we generate 25,000 signal pulses and 25,000 reference pulses. We introduce a postprocessing step in continuous-variable QKD. Although the quantum signal is measured in an arbitrarily rotated basis because of the phase drift between the signal laser and the local oscillator, the receiver can determine the phase drift by measuring a weak reference pulse from the signal laser. Using this phase drift, information carried by the quantum signal can be reliably recovered with noise well below the threshold for secure key distribution. Our solution not only simplifies the implementation of continuous-variable QKD but also greatly enhances its security by closing potential security loopholes associated with an untrusted local oscillator.

We expect that our scheme will be widely adopted in continuous-variable QKD. Our results may open the door to widespread adoption of quantum encryption.

Figure 1

Distribution of quantum signals ($S$) and reference pulses ($R$).

Figure 2

Security models. HD–heterodyne detection. (a) CV-QKD protocol using quadrature remapping scheme. (b) A virtual QKD scheme equivalent to (a). (c) Conventional QKD scheme.

Figure 3

Experimental setup. S is the signal laser, L is the LO laser, IM is the optical intensity modulator, PM is the optical phase modulator, AWG is the arbitrary waveform generator, SMF is the 25-km single -mode fiber spool, PC is the polarization controller, BD is the balanced photodetector, and OSC is the oscilloscope.

Figure 4

Histograms of the phase measurement results. (a) The measurement results corresponding to bit 0 (before phase correction). (b) The measurement results corresponding to bit 1 (before phase correction). (c) The measurement results corresponding to bit 0 (after phase correction). (d) The measurement results corresponding to bit 1 (after phase correction).

Figure 5

The measured quadrature values in phase space. Left panel: before quadrature remapping; right panel: after quadrature remapping (no phase information is encoded in this experiment).

Figure 6

Phase noise analysis.

Figure 7

Experimental setup for determining laser phase noise. L stands for laser, BS is for fiber beam splitter, PC is for polarization controller, BD is for balanced photodetector, and OSC is for oscilloscope.

Figure 8

Measured laser phase noise at different time delay $T_d$. The “open circle” shows the LO laser, and the “plus” is the signal laser.

Figure 9

Dependence of the phase noise variance on the average photon number of the reference pulse. The solid line shows simulation results using Eq. (a7). The square dots are experimental results.

Figure 10

Simulation results based on the security analysis given in Ref. [43]. Simulation parameters are as follows: $\alpha =0.2\mathrm{dB}/\mathrm{km}$, ${\nu }_{el}=0.1$, ${\sigma }_{\varphi }=0.04$, $\eta =0.5$, $f=0.95$, and $V_A=1$. We consider the asymptotic case where the finite data size effect is ignored.

Figure 11

Secure key rate simulation results for a finite number of pulses.