Adaptive Frequency-Bin Encoding for Scalable Entanglement-Based Quantum Key Distribution

We demonstrate the first-time frequency-bin-encoded entanglement-based quantum key distribution (EBQKD) between two users, and a flexible entanglement distribution over long optical fiber links. Dynamic and resource-efficient solutions are crucial to realizing large-scale photonic quantum networks capable of accommodating a growing number of users over large distances and at the same time facilitating a reliable performance at a maintained security level. Here, we adopt the frequency-bin encoding approach for defining three frequency channels, namely, CH1, CH2, and CH3, from highly correlated signal and idler photon pairs from pulsed-excited spontaneous parametric down-conversion (SPDC) process. The adaptive frequency de/multiplexing capability of our approach facilitates dynamic allocation of multiple frequency channels to additional users without increasing the hardware overhead. We developed a frequency-bin-basis analyzer module (see Figure. 1 a & b) composed of a programmable filter (PF), a frequency mixer (FM) based on electro-optic phase modulation (EOPM), a fiber Bragg grating (FBG) for the frequency-to-time mapping (FTM), and a superconducting nanowire single photon detector (SNSPD) of high timing resolution. Through a fine-tuned frequency mixing, passive random projection measurements are realized in two mutually unbiased basis (MUB; here <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathrm{Z}=\{\vert 0\rangle, \vert 1\rangle\}$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathrm{X}=\{\vert +\rangle, \vert -\rangle\})$</tex>. The FTM technique applied on the frequency-mixed spectrum of each frequency channel allows for a time-resolved access to the projection measurement results in four basis states using only a single SNSPD. Remarkably, we showcase the capability of our approach for time-resolved detection of the four projection states corresponding to CH1, CH2, and CH3 using a single SNSPD per user. The performance metrics of the BBM92 protocol are shown in Figure. 1 c-e under different optical attenuations, at maximum 15.6 dB (equivalent to a 73 km fiber link). The qubit error ratio (QBER) was obtained for all channels well below the 11% upper threshold [1]. The maximum asymptotic secret key length <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$l^{A}$</tex> of 310-bits, 283-bits, and 149-bits were obtained for channels CH1, CH2, and CH3, respectively. From the finite key analysis, a positive non-zero secret key rate was obtained for less than 15.6 dB attenuation. The capability of the system was also assessed in preserving high quality frequency-insenstive entanglement for distribution across remote fiber links (see Figure.1 f-h). Overall, the presented approach enables passive random projection measurements in two MUB by each user and benefits from frequency-multiplexing capability for adaptive multi-user operations. A single SNSPD per user renders this approach resource-efficient compared to conventional implementation schemes requiring 4×N detectors corresponding to N channels [2]. A single SNSPD means a reduced vulnerability to detector side channel attacks, a minimized dark count contribution, and a diminished imbalance arising from detection probability mismatch. Our approach thus enables a resource-efficient and a scalable implementation of EBQKD required for the future large-scale quantum networks.