Photon-efficient quantum key distribution using time–energy entanglement with high-dimensional encoding
Tian Zhong, Hongchao Zhou, Robert D. Horansky, Catherine Lee, Varun Boehm Verma, Adriana E. Lita, Alessandro Restelli, Joshua C. Bienfang, Richard P. Mirin, Thomas Gerrits, Sae Woo Nam, Francesco Marsili, Matthew D. Shaw, Zheshen Zhang, Ligong Wang, Dirk Englund, Gregory W. Wornell, Jeffrey H. Shapiro, Franco N. C. Wong
Conventional quantum key distribution (QKD) typically uses binary encoding based on photon polarization or time-bin degrees of freedom and achieves a key capacity of at most one bit per photon. Under photon-starved conditions the rate of detection events is much lower than the photon generation rate, because of losses in long distance propagation and the relatively long recovery times of available single-photon detectors. Multi-bit encoding in the photon arrival times can be beneficial in such photon-starved 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-based QKD with high-dimensional encoding whose security against collective Gaussian attacks is provided by a high-visibility Franson interferometer. We achieve unprecedented key capacity and throughput for an entanglement-based QKD system because 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 efficient WSi superconducting nanowire single-photon detectors. The secure key capacity yields as much as 8.7 bits per coincidence. When optimized for throughput we observe a secure key rate of 2.7 Mbit s −1 after 20 km fiber transmission with a key capacity of 6.9 bits per photon coincidence. Our results demonstrate a viable approach to high-rate QKD using practical photonic entanglement and single-photon detection technologies.
Conventional quantum key distribution (QKD) typically uses binary encoding based on photon polarization or time-bin degrees of freedom and achieves a key capacity of at most one bit per photon. Under photon-starved conditions the rate of detection events is much lower than the photon generation rate, because of losses in long distance propagation and the relatively long recovery times of available single-photon detectors. Multi-bit encoding in the photon arrival times can be beneficial in such photon-starved 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-based QKD with high-dimensional encoding whose security against collective Gaussian attacks is provided by a high-visibility Franson interferometer. We achieve unprecedented key capacity and throughput for an entanglement-based QKD system because 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 efficient WSi superconducting nanowire single-photon detectors. The secure key capacity yields as much as 8.7 bits per coincidence. When optimized for throughput we observe a secure key rate of 2.7 Mbit s −1 after 20 km fiber transmission with a key capacity of 6.9 bits per photon coincidence. Our results demonstrate a viable approach to high-rate QKD using practical photonic entanglement and single-photon detection technologies.
Conventional quantum key distribution (QKD) typically uses binary encoding based on photon polarization or time-bin degrees of freedom and achieves a key capacity of at most one bit per photon. Under photon-starved conditions the rate of detection events is much lower than the photon generation rate, because of losses in long distance propagation and the relatively long recovery times of available single-photon detectors. Multi-bit encoding in the photon arrival times can be beneficial in such photon-starved 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-based QKD with high-dimensional encoding whose security against collective Gaussian attacks is provided by a high-visibility Franson interferometer. We achieve unprecedented key capacity and throughput for an entanglement-based QKD system because 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 efficient WSi superconducting nanowire single-photon detectors. The secure key capacity yields as much as 8.7 bits per coincidence. When optimized for throughput we observe a secure key rate of 2.7 Mbit s−1 after 20 km fiber transmission with a key capacity of 6.9 bits per photon coincidence. Our results demonstrate a viable approach to high-rate QKD using practical photonic entanglement and single-photon detection technologies.
High-dimensional quantum key distribution (HDQKD) offers the possibility of high secure-key rate with high photon-information efficiency. We consider HDQKD based on the time-energy entanglement produced by spontaneous parametric down-conversion and show that it is secure against collective attacks. Its security rests upon visibility data-obtained from Franson and conjugate-Franson interferometers-that probe photon-pair frequency correlations and arrival-time correlations. From these measurements, an upper bound can be established on the eavesdropper's Holevo information by translating the Gaussian-state security analysis for continuous-variable quantum key distribution so that it applies to our protocol. We show that visibility data from just the Franson interferometer provides a weaker, but nonetheless useful, secure-key rate lower bound. To handle multiple-pair emissions, we incorporate the decoy-state approach into our protocol. Our results show that over a 200-km transmission distance in optical fiber, time-energy entanglement HDQKD could permit a 700-bit/sec secure-key rate and a photon information efficiency of 2 secure-key bits per photon coincidence in the key-generation phase using receivers with a 15% system efficiency.
Higher Dimensional Quantum Key Distribution (HD-QKD) improves information capacity and security compared to binary QKD systems. Previous HD-QKD implementations have required d+1 (d refers to encoding dimension) single-photon detectors, limiting large-scale implementation. In contrast, another HD-QKD implementation using coherent one-way (COW) protocol hardware with two detectors achieved a secret key rate (SKR) of 155 kbps for an 8-D system and 2.7% QBER tolerance for a 16-D system with qubit scrambling across a time window. In this paper, we theoretically simulate and experimentally demonstrate time-bin encoded HD-QKD using COW protocol hardware with two single-photon detectors operating at standard telecom wavelengths, achieving a remarkable maximum encoding of 6 bits per photon (i.e., 56-d system). Our HD-QKD system incorporates a practical decoy-state technique to counter the photon number splitting attack, allowing greater flexibility in choosing higher mean photon number thereby achieving higher SKR and distances. This implementation demonstrates a remarkable ninefold increase in SKR for a 16-d system (210 kbps over 25 km of standard single-mode fiber) compared to qubit-based systems, with a QBER tolerance of 13.5% for d = 16. Notably, we achieved positive key rates for emulated loss up to 131 km of fiber length for d = 8. By optimizing detector deadtime and mean photon number using our theoretical model, we achieve enhanced key rates and security. Our findings highlight the superiority of our approach and lay the foundation for high throughput HD-QKD implementation, offering a secure and efficient method for transmitting sensitive information.
Abstract Quantum key distribution (QKD) has established itself as a groundbreaking technology, showcasing inherent security features that are fundamentally proven. Qubit-based QKD protocols that rely on binary encoding encounter an inherent constraint related to the secret key capacity. This limitation restricts the maximum secret key capacity to one bit per photon. On the other hand, qudit-based QKD protocols have their advantages in scenarios where photons are scarce and noise is present, as they enable the transmission of more than one secret bit per photon. While proof-of-principle entangled-based qudit QKD systems have been successfully demonstrated over the years, the current limitation lies in the maximum distribution distance, which remains at 20 km fiber distance. Moreover, in these entangled high-dimensional QKD systems, the witness and distribution of quantum steering have not been shown before. Here we present a high-dimensional time-bin QKD protocol based on energy-time entanglement that generates a secure finite-length key capacity of 2.39 bit/coincidences and secure cryptographic finite-length keys at 0.24 Mbits s −1 in a 50 km optical fiber link. Our system is built entirely using readily available commercial off-the-shelf components, and secured by nonlocal dispersion cancellation technique against collective Gaussian attacks. Furthermore, we set new records for witnessing both energy-time entanglement and quantum steering over different fiber distances. When operating with a quantum channel loss of 39 dB, our system retains its inherent characteristic of utilizing large-alphabet. This enables us to achieve a secure key rate of 0.30 kbits s −1 and a secure key capacity of 1.10 bit/coincidences, considering finite-key effects. Our experimental results closely match the theoretical upper bound limit of secure cryptographic keys in high-dimensional time-bin QKD protocols (Mower et al 2013 Phys. Rev. A 87 062322; Zhang et al 2014 Phys. Rev. Lett. 112 120506), and outperform recent state-of-the-art qubit-based QKD protocols in terms of secure key throughput using commercial single-photon detectors (Wengerowsky et al 2019 Proc. Natl Acad. Sci. 116 6684; Wengerowsky et al 2020 npj Quantum Inf. 6 5; Zhang et al 2014 Phys. Rev. Lett. 112 120506; Zhang et al 2019 Nat. Photon. 13 839; Liu et al 2019 Phys. Rev. Lett. 122 160501; Zhang et al 2020 Phys. Rev. Lett. 125 010502; Wei et al 2020 Phys. Rev. X 10 031030). The simple and robust entanglement-based high-dimensional time-bin protocol presented here provides potential for practical long-distance quantum steering and QKD with multiple secure bits-per-coincidence, and higher secure cryptographic keys compared to mature qubit-based QKD protocols.
The binary (one-bit-per-photon) encoding that most existing quantum key distribution (QKD) protocols employ puts a fundamental limit on their achievable key rates, especially under high channel loss conditions associated with long-distance fiber-optic or satellite-to-ground links. Inspired by the pulse-position-modulation (PPM) approach to photon-starved classical communications, we design and demonstrate the first PPM-QKD, whose security against collective attacks is established through continuous-variable entanglement measurements that also enable a novel decoy-state protocol performed conveniently in post processing. We achieve a throughput of 8.0 Mbit/s (2.5 Mbit/s for loss equivalent to 25 km of fiber) and secret-key capacity up to 4.0 bits per detected photon, thus demonstrating the significant enhancement afforded by high-dimensional encoding. These results point to a new avenue for realizing high-throughput satellite-based or long-haul fiber-optic quantum communications beyond their photon-reception-rate limits.
The security of conventional cryptography systems is threatened in the forthcoming era of quantum computers. Quantum key distribution (QKD) features fundamentally proven security and offers a promising option for quantum-proof cryptography solution. Although prototype QKD systems over optical fiber have been demonstrated over the years, the key generation rates remain several orders of magnitude lower than current classical communication systems. In an effort toward a commercially viable QKD system with improved key generation rates, we developed a discrete-variable QKD system based on time-bin quantum photonic states that can generate provably secure cryptographic keys at megabit-per-second rates over metropolitan distances. We use high-dimensional quantum states that transmit more than one secret bit per received photon, alleviating detector saturation effects in the superconducting nanowire single-photon detectors used in our system that feature very high detection efficiency (of more than 70%) and low timing jitter (of less than 40 ps). Our system is constructed using commercial off-the-shelf components, and the adopted protocol can be readily extended to free-space quantum channels. The security analysis adopted to distill the keys ensures that the demonstrated protocol is robust against coherent attacks, finite-size effects, and a broad class of experimental imperfections identified in our system.