Photon-efficient quantum key distribution using time-energy entanglement with high-dimensional encoding

Conventional quantumkey distribution (QKD) typically uses binary encoding based on photon polarization or time-bin degrees of freedomand achieves a key capacity of atmost one bit per photon. Under photon-starved conditions the rate of detection events ismuch lower than the photon generation rate, because of losses in long distance propagation and the relatively long recovery times of available singlephoton detectors. Multi-bit encoding in the photon arrival times can be beneficial in such photonstarved situations. Recent security proofs indicate high-dimensional encoding in the photon arrival times is robust and can be implemented to yield high secure throughput. In this work we demonstrate entanglement-basedQKDwith high-dimensional encodingwhose security against collectiveGaussian attacks is provided by a high-visibility Franson interferometer. We achieve unprecedented key capacity and throughput for an entanglement-basedQKDsystembecause of four principal factors: Franson interferometry that does not degrade with loss; error correction coding that can tolerate high error rates; optimized time-energy entanglement generation; and highly efficientWSi superconducting nanowire single-photon detectors. The secure key capacity yields asmuch as 8.7 bits per coincidence. When optimized for throughput we observe a secure key rate of 2.7 Mbit s(-1) after 20 kmfiber transmissionwith a key capacity of 6.9 bits per photon coincidence. Our results demonstrate a viable approach to high-rate QKDusing practical photonic entanglement and single-photon detection technologies.