Enhancing the secure key rate in a quantum-key-distribution system using discrete-variable, high-dimensional, time-frequency states

High-dimensional (dimension d > 2) quantum key distribution (QKD) protocols that encode information in the temporal degree of freedom promise to overcome some of the challenges of qubit-based (d = 2) QKD systems. In particular, the long recovery time of single-photon detectors and large channel noise at long distance both limit the rate at which a final secure key can be generated in a low-dimension QKD system. We propose and demonstrate a practical discrete-variable time-frequency protocol with d = 4 at a wavelength of 1550 nm, where the temporal states are secured by transmitting and detecting their dual states under Fourier transformation, known as the frequency-basis states, augmented by a decoy-state protocol. We show that the discrete temporal and frequency states can be generated and detected using commercially-available equipment with high timing and spectral efficiency. In our initial experiments, we only have access to detectors that have low efficiency (1%) at 1550 nm. Together with other component losses, our system is equivalent to a QKD system with ideal components and a 50-km-long optical-fiber quantum channel. We find that our system maintains a spectral visibility of over 99.0% with a quantum bit error rate of 2.3%, which is largely due to the finite extinction ratio of the intensity modulators used in the transmitter. The estimated secure key rate of this system is 7.7×104 KHz, which should improve drastically when we use detectors optimized for 1550 nm.