A Directly Modulated Laser Platform for High-Dimensional Quantum Key Distribution

Abstract

High-dimensional quantum key distribution (HD-QKD) offers a promising approach to enhance secret key rates beyond conventional binary-encoded QKD, addressing the growing demand for secure data transmission. However, the practical application of most HD-QKD systems has been hindered by their complexity, as they require the preparation and detection of quantum states in large Hilbert spaces. Here, we design and experimentally realize a directly modulated laser platform for HD-QKD. It operates at a repetition rate of 312.5 MHz, yielding a remarkably simple and scalable architecture. Through which, we achieve a record transmission distance of 250 km for HD-QKD, demonstrating its feasibility for long-distance quantum communication. Furthermore, we witness that the four-dimensional states outperform their two-dimensional counterpart in secret key rate, highlighting the practical advantage of high-dimensional encoding. This simple and scalable approach shows strong potential for chip-scale integration.

Figures (5)

• Figure 1: Quantum states involved in the four-dimensional QKD protocol. In the $Z$ basis, quantum states are generated by two pulses in adjacent time slots, whereas in the $X$ basis, quantum states are formed by two pulses separated by one time slot. Within each quantum state, two pulses of the same color indicate a phase difference of 0, while pulses of different colors correspond to a phase difference of $\pi$.
• Figure 2: Schematic of our experimental setup. Alice employs a directly phase-modulated light source composed of a pair of distributed-feedback (DFB) lasers in a master–slave configuration. Both lasers are driven by the arbitrary waveform generator (AWG), which provides the RF signals required for direct phase modulation. At Bob’s measurement station, two unbalanced Faraday–Michelson interferometers (FMIs) with path-length differences of 800 ps and 1.6 ns, respectively, are used to demodulate the $Z$ basis and $X$ basis pulses. Superconducting nanowire single-photon detectors (SNSPDs) record the interference outcomes. Circulator (CIR); Intensity modulator (IM); Attenuator (ATT); Beam splitter (BS); Fiber stretcher (FS); Faraday mirror (FM).
• Figure 3: Generation of four-dimensional BB84 states. The top trace shows the optical pulse train with an 800 ps spacing. The middle traces depict the electrical drive signals for the slave and master DFB lasers, respectively. The slave laser defines the occupied time bins, while the master laser provides phase modulation through 200 ps amplitude perturbations on its RF drive. States of the $Z$ basis are formed by selecting the first–second or third–fourth time bins and applying the appropriate phase shift. States of the $X$ basis are similarly produced using the first–third or second–fourth time bins. In every state period the global phase is randomized by a freshly seeded master pulse. Examples of the generated optical pulses and their corresponding quantum states are shown in the lower panel of the figure.
• Figure 4: Interference of the four-dimensional quantum states in our scheme. The figure presents representative interference results for four example states, corresponding to the matched-basis measurements, illustrating the interference behavior observed in the relevant time bins. Here, $D_0$ and $D_1$ denote the SNSPDs connected to the 800 ps FMI, and $D_2$ and $D_3$ denote the SNSPDs connected to the 1.6 ns FMI.
• Figure 5: The secret key generation rate is shown as a function of transmission distance, calculated using the parameters of the laboratory experiment, where the repetition rates for the 2D and 4D systems are 625 MHz and 312.5 MHz, respectively. The stars mark the experimentally obtained key rates at distances of 200 km and 250 km, while the other symbols represent the results reported in previous typical high-dimensional experiments. Entries marked with * correspond to asymptotic secret key rates, whereas the other data correspond to finite-key results.