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arXiv:1305.4541 · Journal of Physics B Atomic Molecular and Optical Physics

Security of high-dimensional quantum key distribution protocols using Franson interferometers

Thomas Brougham, Stephen Mark Barnett, Kevin T. McCusker, Paul G. Kwiat, Daniel J. Gauthier

Published May 9, 2013• 66 citations
arXivHTMLPDF

Abstract

Franson interferometers are increasingly being proposed as a means of securing high-dimensional energy–time entanglement-based quantum key distribution (QKD) systems. Heuristic arguments have been proposed that purport to demonstrate the security of these schemes. We show, however, that such systems are vulnerable to attacks that localize the photons to several temporally separate locations. This demonstrates that a single pair of Franson interferometers is not a practical approach to securing high-dimensional energy–time entanglement-based QKD. This observation leads us to investigate the security of modified Franson-based-protocols, where Alice and Bob have two or more Franson interferometers. We show that such setups can improve the sensitivity against attacks that localize the photons to multiple temporal locations. While our results do not constitute a full security proof, they do show that a single pair of Franson interferometers is not secure and that multiple such interferometers could be a promising candidate for experimentally realizable high-dimensional QKD.

DOI
10.1088/0953-4075/46/10/104010

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Franson interferometers are increasingly being proposed as a means of securing high-dimensional energy–time entanglement-based quantum key distribution (QKD) systems. Heuristic arguments have been proposed that purport to demonstrate the security of these schemes. We show, however, that such systems are vulnerable to attacks that localize the photons to several temporally separate locations. This demonstrates that a single pair of Franson interferometers is not a practical approach to securing high-dimensional energy–time entanglement-based QKD. This observation leads us to investigate the security of modified Franson-based-protocols, where Alice and Bob have two or more Franson interferometers. We show that such setups can improve the sensitivity against attacks that localize the photons to multiple temporal locations. While our results do not constitute a full security proof, they do show that a single pair of Franson interferometers is not secure and that multiple such interferometers could be a promising candidate for experimentally realizable high-dimensional QKD.
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.
Abstract High-dimensional quantum key distribution (QKD) offers secure communication with key rates that surpass those of QKD protocols utilizing two-dimensional encoding. However, existing high-dimensional QKD protocols require additional experimental resources, such as multiport interferometers and multiple detectors, thereby increasing the cost of high-dimensional systems and limiting their use. We introduce and analyze a high-dimensional QKD protocol that requires only standard two-dimensional hardware. We provide security analysis against individual and coherent attacks, establishing upper and lower bounds on the secure key rates. We tested our protocol on a standard two-dimensional QKD system over a 40 km fiber link, achieving a twofold increase in secure key rate compared to the standard two-dimensional coherent one-way protocol, without any hardware modifications. This work offers a significant improvement in the performance of already deployed QKD systems through simple software updates and holds broad applicability across various QKD schemes, making high-dimensional QKD practical for widespread use.
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 (QKD) offers the possibility of encoding multiple bits of key on a single entangled photon pair. An experimentally promising approach to realizing this is to use energy–time entanglement. Currently, however, the control of very high-dimensional entangled photons is challenging. We present a simple and experimentally compact approach, which is based on a cavity that allows one to measure two different bases: the time of arrival and another that is approximately mutually unbiased to the arrival time. We quantify the errors in the setup, due both to the approximate nature of the mutually unbiased measurement and as a result of experimental errors. It is shown that the protocol can be adapted using a cut-off so that it is robust against the considered errors, even within the regime of up to 10 bits per photon pair.
High-dimensional time-bin entanglement is known for having high potential for quantum key distribution (QKD) applications, being easily implementable, robust and may offer better keyrates than simple qubit protocols. The temporal encoding, combined with limited clock resolution, however, implies a trade-off: Is it better to send more low-dimensionally encoded photons or few high-dimensional ones? Answering this question presents a hard challenge as it depends on the entire context of the protocol, including the production rates, losses, dark counts, timing jitters and many more. We answer this question for single Franson based interferometers and asymptotic key rate and shared entanglement as main figures of merit. We present a flexible noise model incorporating all relevant parameters and find that there are indeed regions where high-dimensional encoding still outperforms any qubit based version when the pair arrival rate is limited, for instance through loss or limited pump power.