Self-coherent phase reference sharing for continuous-variable quantum key distribution

We develop a comprehensive framework to model and optimize the performance of continuous-variable quantum key distribution (CV-QKD) with a local local oscillator (LLO), when phase reference sharing and QKD are jointly implemented. We first analyze the limitations of the only existing approach, called LLO-sequential, and show that it requires high modulation dynamics and can only tolerate small phase noise. Our main contribution is to introduce two designs to perform LLO CV-QKD, respectively called LLO-delayline and LLO-displacement, and to study their performance. Both designs rely on a self-coherent approach, in which phase reference information and quantum information are coherently obtained from a single optical wavefront. We show that these designs can lift some limitations of the existing LLO-sequential approach. The LLO-delayline design can in particular tolerate much stronger phase noise and thus appears to be an appealing alternative to LLO-sequential in terms of network integrability. We also investigate, with the LLO-displacement design, how phase reference information and quantum information can be multiplexed within a single optical pulse. By studying the trade-off between phase reference recovery and phase noise induced by displacement, we, however, demonstrate that this design can only tolerate low phase noise. On the other hand, the LLO-displacement design has the advantage of minimal hardware requirements and provides a simple approach to multiplex classical and quantum communications, opening a practical path towards the development of ubiquitous coherent classical-quantum communications systems compatible with next-generation network requirements.

Figure 1

Transmitted local oscillator (TLO) design. In the TLO design, the phase reference (green pulse) and the quantum signal (red pulse) are derived from the same optical pulse and sent from Alice to Bob using multiplexing and demultiplexing (MD) techniques.

Figure 2

Local local oscillator (LLO) sequential design. In the LLO-sequential design, Alice sequentially sends weak quantum signal (red pulse) and bright phase reference (blue pulse) pulses. At reception, Bob performs consecutive coherent detections of each pulse received using is own LO pulses (green pulse).

Figure 3

Schematic representation of a general relative phase estimation process. The relative phase ${\theta }_{\mathrm{S}}$ at reception (red), which is defined with respect to the $LO$ phase [Eq. (1)], is estimated at reception with the estimator ${\widehat{\theta }}_{\mathrm{R}}$ inferred from specific reference phase information evaluation (blue).

Figure 4

Secret key rates of the LLO-sequential design for two different values of $V_{\mathrm{drift}}$ in the presence of AM finite dynamics $d_{\mathrm{dB}}$. Simulations are performed in the individual attacks and pessimistic (Eve can control Bob's detection) model [18]. The values of $V_A$ and $E_{\mathrm{R}}$ are chosen to optimize the secret key rate with $\beta =0.95,\eta =0.7,v_{\mathrm{elec}}=0.01$, and ${\xi }_{\mathrm{tech}}=0.01$.

Figure 5

Full experimental scheme of the LLO-delayline design. Alice sends consecutive phase-coherent signal/reference pulses pairs to Bob based on a balanced delay line interferometer. On his side, Bob uses his own laser as the LO for coherent detections using the same delay line technique to produce phase-coherent LO pulses. Phase estimation and phase correction are digitally performed after measurement acquisition.

Figure 6

Secret key rate comparison between the LLO-sequential and the LLO-delayline designs for different AM dynamics and relative phase drift $V_{\mathrm{drift}}$.

Figure 7

Secret key rate comparison between the LLO-sequential and the LLO-displacement designs for two relative phase drift $V_{\mathrm{drift}}$ and for different AM dynamics.

Figure 8

Scheme of a typical homodyne detector. Signal and local oscillator pulses interfere on a 50:50 beamsplitter (BS). Both resulting fields are detected on two photodiodes (PD1 and PD2), which convert photons into electrons. The electrical pulses (purple pulses) produced by the photodiodes are then substracted ($-$) and the resulting quadrature electrical pulse intensity is measured using a integrator circuit. The outcome of the integrator circuit is proportional to $N_{\mathrm{e}}=E_{\mathrm{S}}{E}_{\mathrm{LO}}$ up to an intensity threshold $N_{\mathrm{sat}}$.

Figure 9

Expected secret key rates for the LLO-sequential design for different value of linearity threshold $N_{\mathrm{sat}}$.