Time-bin encoded quantum key distribution over 120 km with a telecom quantum dot source

Abstract

Quantum key distribution (QKD) with deterministic single photon sources has been demonstrated over intercity fiber and free-space channels. The previous implementations relied mainly on polarization encoding schemes, which are susceptible to birefringence, polarization-mode dispersion and polarization-dependent loss in practical fiber networks. In contrast, time-bin encoding offers inherent robustness and has been widely adopted in mature QKD systems using weak coherent laser pulses. However, its feasibility in conjunction with a deterministic single-photon source has not yet been experimentally demonstrated. In this work, we construct a time-bin encoded QKD system employing a high-brightness quantum dot (QD) single-photon source operating at telecom wavelength. Our proof-of-concept experiment successfully demonstrates the possibility of secure key distribution over fiber link of 120 km, while maintaining extraordinary long-term stability over 6 hours of continuous operation. This work provides the first experimental validation of integrating a quantum dot single-photon source with time-bin encoding in a telecom-band QKD system. In addition, it demonstrates the highest secure key rate among the time-bin QKDs based on single-photon sources. This development signifies a substantial advancement in the establishment of a robust and scalable QKD network based on solid-state single-photon technology

Figures (4)

• Figure 1: Encoding and decoding schemes of time-bin QKD. (a) Encoder for preparing three time-bin states. Single photons emitted by the QD pass through the port 1$\to$2 of the optical circulator (Cir) and then through the beam splitter 1 ($BS_1$). A phase of $\theta_1$ in the set $\left \{ 0, \pi/2, \pi \right \}$ is randomly encoded to the single photons via an electro-optic phase modulator (PM) within the SNI. Depending on the phase of single-photon interference, photons leave $BS_1$ via the short downward path or the long upward path (2$\to$3) to reach $BS_2$. Three single-photon path state $\ket{L}$ (green), $1/\sqrt{2}\left ( \ket{S}+\ket{L} \right )$ and $\ket{S}$ (red) that are generated from the single-photon interference due to the phase $\theta_1$, are translated into three time-bin states $\left ( \ket{Z_0}, \ket{Z_1}, \ket{X_0} \right )$ after $BS_2$. After the transmission of the single photons through the optical channel, a phase shifter (PS) involved $AMZI_2$ at the decoder interpret the time-bin states to be measurable using the single-photon detection. The solid lines of $BS_2$ and $BS_4$ outputs denote the active port being used in the scheme, while the inactive ports are specified as dashed arrow lines. Raw keys are sifted from the time windows $W_1$ (red), $W_2$ (blue) and $W_3$ (green) after base comparison between the encoder and decoder, respectively, corresponding to the encoded qubits $Z_1$, $Z_0$ and $X_0$. (b) Sketch of the active phase control of single photons (yellow) via the PM in SNI configuration. Each single-photon period is divided into two time slots, considering the different arrival time of single photons at PM along superposition of clockwise $\left ( \circlearrowright \right)$ and counter-clockwise $\left ( \circlearrowleft \right)$ paths with a time delay of $\Delta$. One constant voltage in the set $\left \{ 0,V_{\pi}, V_{\pi/2} \right \}$ (gray background) is applied to the PM to tune the phase of photons at the first time slot of each single-photon period, resulting in the generation of different path states from the SNI. (c) Sketch of single-photon correlation histograms with three time-bin states $\left ( \ket{Z_0}, \ket{Z_1}, \ket{X_0} \right )$ after the encoder. The time delay of $\Delta_1$ from $AMZI_1$ is revealed as the time delay between early $\ket{e}$ and late $\ket{l}$ photons . (d) Sketch of the time-bin states correlation histograms from output 1 of the $AMZI_2$ decoder. The histogram is normalised with the photon counts in (c).
• Figure 2: Experimental setups and source characteristics. (a) Fiber-coupled excitation pulse laser, triggered by the arbitrary wave-function generator (AWG), transmits through a BS (R:T=98.5:1.5) and is used to excite the telecom QD loaded in the cryostat. The emitted single photons collected by the objective are obtained by filtering out the laser using a notch filter. Then, single photons are coupled to the in-line fiber polarizer (ILFP), through a series of free-space half- and quarter- waveplates (HWP and QWP) for the polarization control. The PM inside the encoder is synchronized with the excitation laser via the AWG, and randomly generate three single-photon time-bin states. The time-bin qubits are decrypted at the receiver setup from Bob, which consists of a decoder, superconducting nanowire single-photon detector (SNSPD), and a time-to-digital converter (TDC). The excitation laser and PM at Alice are synchronized with the TDC at Bob via the AWG, which distributes electronic triggering signals through electrical cables. FPC, fiber polarization controller; PPS, programmable power source. (b) The photoluminescence spectrum and time-resolved lifetime histogram (logarithm scale) of the single-photon emissions from the QD. The inset shows the decay process of the p-shell excitation within the QD band structure. (c) Normalized second-order autocorrelation histogram for the single photons from the trion state emissions with the inset showing the zoomed-in view of the central peak.
• Figure 3: Time-dependent QKD performance at various transmission distances. (a) Schematic of QBER extraction with the bases comparison of statistical data. The time windows $\left \{ W1, W2, W3 \right \}$ are indicated by the red, blue, and green columns, respectively. The height of each columns denotes the probability of detecting photons within a given time window when specific states are encoded. (b) Time-dependent QBER for different fiber spool lengths of 0km, 40km, 80km, and 120km. Each data point represents 1min of measurement time. The dashed lines indicate the average QBERs on the bases over the 6 hours. (c) Secure key bits (SKBs) per pulse as a function of measurement time for the different fiber spool lengths ranging from 0km to 120km. For the spool lengths of 0km, 40km, and 80km, an acquisition time of 1min $\left ( N_{sum} = 4.56 \times 10^9 \right )$ is used in the finite key analysis. For the 120km transmission distance, an acquisition time of 20min $\left ( N_{sum} = 9.12 \times 10^{10} \right )$ is used.
• Figure 4: Time-bin QKD performance versus transmission distance and gain in secure key rate with improved source qualities. (a) QBERs at the $\ket{X} \text{and} \ket{Z}$ bases and SKB per pulse as a function of the secret key transmission distance. A received block size of $N_{sum}=10^{11}$ is employed for the finite key analysis. (b) Gain of simulated SKR as a function of the mean photon number per pulse $\left \langle n \right \rangle$ and second order autocorrelation $g^{(2)}(0)$, compared with this experiment. (c) Gain of simulated SKR as a function of the repetition rate of the excitation laser and the QD lifetime, compared with this experiment. The blue circles indicate the parameters in the current time-bin QKD system.