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arXiv:2409.16622 · Optics Express

Heralded optical entanglement distribution via lossy quantum channels: a comparative study

Wan Zo, Seungbeom Chin, Yong‐Su Kim

Published Feb 28, 2025• 2 citations
arXivHTMLPDF

Abstract

Quantum entanglement serves as a foundational resource for various quantum technologies. In optical systems, entanglement distribution relies on the indistinguishability and spatial overlap of photons. Heralded schemes play a crucial role in ensuring the reliability of entanglement generation by detecting ancillary photons to signal the creation of desired entangled states. However, photon losses in quantum channels remain a significant challenge, limiting the distance and capacity of entanglement distributions. This study suggests three heralded schemes for distributing multipartite Greenberger-Horne-Zeilinger (GHZ) states via lossy quantum channels. These schemes differ both qualitatively in their network architecture (centralized or decentralized) and photon source requirements (Bell states or single-photons), and quantitatively in their success probabilities and heralding efficiency. Through comprehensive analysis incorporating both practical implementation considerations and theoretical performance metrics, we find that each scheme offers distinct advantages depending on the number of parties, channel distance, and security requirements. The decentralized scheme proves particularly advantageous for networks requiring balanced information distribution, while centralized schemes may offer better performance for smaller networks. This analysis provides insights into designing resilient heralded circuits for quantum information processing over lossy channels, considering both architectural constraints and performance requirements.

DOI
10.1364/oe.542222

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Quantum entanglement serves as a foundational resource for various quantum technologies. In optical systems, entanglement distribution relies on the indistinguishability and spatial overlap of photons. Heralded schemes play a crucial role in ensuring the reliability of entanglement generation by detecting ancillary photons to signal the creation of desired entangled states. However, photon losses in quantum channels remain a significant challenge, limiting the distance and capacity of entanglement distributions. This study suggests three heralded schemes for distributing multipartite Greenberger-Horne-Zeilinger (GHZ) states via lossy quantum channels. These schemes differ both qualitatively in their network architecture (centralized or decentralized) and photon source requirements (Bell states or single-photons), and quantitatively in their success probabilities and heralding efficiency. Through comprehensive analysis incorporating both practical implementation considerations and theoretical performance metrics, we find that each scheme offers distinct advantages depending on the number of parties, channel distance, and security requirements. The decentralized scheme proves particularly advantageous for networks requiring balanced information distribution, while centralized schemes may offer better performance for smaller networks. This analysis provides insights into designing resilient heralded circuits for quantum information processing over lossy channels, considering both architectural constraints and performance requirements.
Abstract One of the most important resources for quantum optical experiments and applications are on-demand highly entangled multiphoton quantum states. A promising way of generating them is heralding entanglement generation at a high rate from letting independent photons interfere. However, such schemes often work for a specific internal degree of freedom of the interfering photons only. Going to higher numbers of entangled photons, the success probabilities decrease while the number of necessary resources, e.g. auxiliary photons and optical elements, increases. To make probabilistic schemes feasible also for larger quantum states, it is therefore important to find resource-efficient generation schemes with high success probabilities. In this work, we introduce easily implementable schemes to herald qubit Greenberger–Horne–Zeilinger (GHZ) states, higher-dimensional Bell states and higher-dimensional three-party GHZ states. Our schemes solely rely on multiphoton interference, i.e. they can be adjusted to work for arbitrary degrees of freedom. Furthermore, they demonstrate high success probabilities and need comparably few auxiliary photons.
Entanglement distribution is essential for unlocking the potential of distributed quantum information processing. We consider an N-partite network where entanglement is distributed via a central source over lossy channels, and network participants cooperate to establish entanglement between any two chosen parties under local operations and classical communication (LOCC). We develop a general mathematical framework to assess the average bipartite entanglement shared in a lossy distribution, and introduce a tractable lower bound by optimizing over a subset of single-parameter LOCC transformations. Our results show that probabilistically extracting Bell pairs from W states is more advantageous than deterministically extracting them from GHZ-like states in lossy networks, with this advantage increasing with network size. We further extend our analysis analytically, proving that W states remain more effective in large-scale networks. These findings offer valuable insights into the practical deployment of near-term networks, and corroborate a trade-off relationship between the success conversion probability of entanglement distribution protocols and their robustness to loss.
High-dimensional multipartite entanglement plays a crucial role in quantum information science. However, existing schemes for generating such entanglement become complex and costly as the dimension of quantum units increases. In this Letter, we overcome the limitation by proposing a significantly enhanced linear optical heralded scheme that generates the d-level N-partite Greenberger-Horne-Zeilinger (GHZ) state with single-photon sources and linear operations. Our scheme requires dN photons, which is the minimal required photon number, with substantially improved success probability from previous schemes. It employs linear optical logic gates compatible with any qudit encoding system and can generate generalized GHZ states with installments of beam splitters. With efficient generations of high-dimensional resource states, our work opens avenues for further exploration in high-dimensional quantum information processing.
Abstract Efficient long-distance entanglement distribution is a key requirement for a global quantum internet. Quantum repeaters overcome photon loss in optical fibers, offering a route to long-distance entanglement distribution. Here, we study heralded quantum repeater architectures that are based on two-photon interference and integrate local or remote swapping. We derive an analytical expression for the entanglement distribution time as a function of transmission distance for both heralded local-swapping and remote-swapping schemes. This expression provides physical insight into how repeaters overcome channel loss in long-haul fibers. Considering a realistic quantum memory, we present theoretical curves showing the effect of finite memory lifetime on the entanglement distribution time. By comparing optimal distribution times over distances up to thousands of kilometers, we determine the optimal nesting architectures for the single-repeater channel in each scheme and compare the optimal distribution rates and entanglement fidelities of these schemes at various distances. Finally, by examining the limiting cases of zero channel loss, zero device loss, and lossless repeater systems, we find fundamental performance bounds for quantum repeaters. These results provide practical design principles for scalable quantum repeater networks and pave the way toward continent-scale quantum communication.
Generating large multiphoton entangled states is of main interest due to enabling universal photonic quantum computing and all-optical quantum repeater nodes. These applications exploit measurement-based quantum computation using cluster states. Remarkably, it was shown that photonic cluster states of arbitrary size can be generated by using feasible heralded linear optics fusion gates that act on heralded three-photon Greenberger-Horne-Zeilinger (GHZ) states as the initial resource state. Thus, the capability of generating heralded GHZ states is of great importance for scaling up photonic quantum computing. Here, we experimentally demonstrate this required building block by reporting a polarisation-encoded heralded GHZ state of three photons, for which we build a high-rate six-photon source (547±2 Hz) from a solid-state quantum emitter and a stable polarization-based interferometer. The detection of three ancillary photons heralds the generation of three-photon GHZ states among the remaining particles with fidelities up to F=0.7278±0.0106. Our results initiate a path for scalable entangling operations using heralded linear-optics implementations.
High-quality entangled states of photons underlie quantum information science (QIS) applications across communication, sensing, and computing. In many discrete-variable photonic QIS architectures, large application-ready states (e.g., cluster states, repeater graph states) are constructed via fusion measurements on small entangled seed states, of which Bell states are the fundamental example. The quality of seed-state generation therefore sets a baseline for application performance, making it crucial to understand this process under realistic error mechanisms, particularly in integrated photonics experiments. In this work, we analyze five heralded schemes for generating event-ready photonic Bell states, contrasting their heralding probabilities, fidelities, and error robustness. We develop a hierarchy of error models, progressing from an analytically tractable lumped-loss model to realistic heralded single-photon sources with multiphoton emission errors and finally to integrated frequency-bin implementations with architecture-dependent loss. Across these models, we find that schemes based on higher-order multiphoton interference provide superior fidelity robustness in low-loss implementations, while lower-photon-number schemes can be preferable when probabilistic sources or lossy beamsplitters dominate the resource cost. Our results provide design guidance for integrated discrete-variable quantum photonics, with particular relevance for frequency-bin architectures where active beamsplitter loss can determine the optimal resource-state-generation strategy.