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arXiv:2609.35488

Temporal trade-offs in high-dimensional entanglement: a comprehensive noise model for optimal time-bin QKD protocols

Alexandra E. Bergmayr-Mann, Gláucia Murta, Marcus Huber

quant-phSubmitted Sep 28, 2026• Announced Sep 29, 2026• 0 citations
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Abstract

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.

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23 + 12 pages, 6 figures, 8 tables

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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.
High-dimensional entanglement is considered to hold great potential for quantum key distribution (QKD) in high-loss and -noise scenarios. To harness its robustness, we construct a source for high-dimensional time-bin entangled photons optimized for high brightness, low complexity, and long-term stability. We certify the generated high-dimensional entanglement with a new witness employing nested Franson interferometry. Finally, we obtain key rates using a novel, noise-resilient QKD protocol. Our flexible evaluation method, centered around discretizations of the time stream, enables the same dataset to be processed while varying parameters such as state dimensionality and time bin length, allowing optimization of performance under given environmental conditions. Our results indicate regions within the accessible parameter space where high key rates per time are achievable for dimensionalities larger than two.
High-dimensional entanglement is an important physical resource for quantum communication. A basic issue for any communication scheme is how many shared bits two parties can extract subject to experimental noise. We determine the shared information that can be extracted from time-bin entangled photons using frame encoding. We consider photons generated by a general down-conversion source and also model losses, dark counts and the effects of multiple photons within each frame. Furthermore, we describe a procedure for including other imperfections such as after-pulsing, detector dead-times and jitter. The results are illustrated by deriving analytic expressions for the maximum information that can be extracted from high-dimensional time-bin entangled photons generated by down conversion. A key finding is that under realistic conditions and using standard SPAD detectors one can still choose the frame size so as to extract over 10 bits per photon. These results are thus useful for experiments on high-dimensional quantum-key distribution systems, but are not limited to such systems. For example, the results are also useful for determining the limits of fibre arrays or within time-multiplexing schemes.
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 photonic entanglement holds significant promise for advancing quantum communication, computation, and metrology. For example, large-alphabet quantum communication protocols are known to benefit from enhanced noise resilience and information capacity via multi-bit time-bin encoding. Yet, characterizing high-dimensional entangled states is challenging, as full state tomography becomes prohibitively costly and often requires unrealizable measurements. Here, we demonstrate a scan-free method to characterize high-dimensional entanglement in the time-frequency domain. Our reconstruction achieves a record 5.70±0.075.70\pm0.075.70±0.07 ebits and a fidelity of 65.4±0.4%65.4\pm0.4\%65.4±0.4% with the maximally entangled state of local dimension 102110211021, certifying the presence of 668668668-dimensional entanglement. We further prove the attainability of a secure key rate of 15.615.615.6 kB/s in a composable finite-size, entanglement-based protocol, and show that in continuous operation, the setup can quickly approach asymptotic key rates. Using commercial telecom components and state-of-the-art low-jitter single-photon detectors, our scalable architecture offers a practical path towards high-rate, noise-resilient quantum communication testbeds.
Many quantum communication protocols rely on the distribution of entanglement between the different participating parties. One example is quantum key distribution (QKD), an application that has matured to commercial use in recent years. However, difficulties remain, especially with noise resilience and channel capacity in long-distance communication. One way to overcome these problems is to use high-dimensional entanglement, which has been shown to be more robust to noise and enables higher secret-key rates. It is therefore important to have access to certifiable high-dimensional entanglement sources to confidently implement these advanced QKD protocols. Here we develop a method for certifying high-dimensional time-bin entanglement in fiber-loop systems. In these systems, entanglement creation and detection can utilize the same physical components, and the number of time bins, and thus the entanglement dimension, can be adapted without making physical changes to the setup. Our certification method builds on previous proposals for the certification of angular-momentum entanglement in photon pairs. In particular, measurements in only two experimentally accessible bases are sufficient to obtain a lower bound on the entanglement dimension for both two- and multiphoton quantum states. Numerical simulations show that the method is robust against typical experimental noise effects and works well even with limited measurement statistics, thus establishing time-bin encoded photons as a promising platform for high-dimensional quantum-communication protocols.
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.