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arXiv:2604.00434

Improvement of entanglement generation rate in frequency-multiplexed quantum repeaters using cavity-enhanced SPDC source

Ryoma Komatsudaira, Tomoyuki Horikiri

quant-phSubmitted Apr 1, 2026• Announced Apr 2, 2026• 0 citations
arXivHTMLPDF

Abstract

High-rate entanglement generation is essential for the realization of practical quantum repeaters. To this end, frequency multiplexing of the photons employed is an effective approach. In particular, schemes using cavity-enhanced spontaneous parametric down-conversion (cSPDC) as a photon-pair source have been proposed. In this study, toward a theoretical performance evaluation of frequency-multiplexed quantum repeaters based on cSPDC, we derive an approximate expression for the quantum state of the frequency-multiplexed photons, where each frequency mode is treated as an independent two-mode squeezed vacuum (TMSV) state. Using this expression, we calculate the heralding probability and fidelity of entanglement generation for several cases in a single-photon interference scheme using frequency multiplexing with cSPDC. Our results demonstrate that by multiplexing approximately 100 modes, the heralding probability improves to approximately 98% for an elementary link distance $L_\mathrm{EL}=25 \mathrm{km}$, even in scenarios where the fidelity exceeds 0.9 across all modes. Furthermore, for $L_\mathrm{EL}=100 \mathrm{km}$, we show that the heralding probability, which was approximately 0.7% in the single-mode case, increases to about 38% under the condition that the fidelity remains 0.9 or higher. These analytical results demonstrate the effectiveness of employing cSPDC as a photon-pair source for quantum repeaters.

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22 pages, 14 figures

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High-rate entanglement generation is essential for the realization of practical quantum repeaters. To this end, frequency multiplexing of the photons employed is an effective approach. In particular, schemes using cavity-enhanced spontaneous parametric down-conversion (cSPDC) as a photon-pair source have been proposed. In this study, toward a theoretical performance evaluation of frequency-multiplexed quantum repeaters based on cSPDC, we derive an approximate expression for the quantum state of the frequency-multiplexed photons, where each frequency mode is treated as an independent two-mode squeezed vacuum (TMSV) state. Using this expression, we calculate the heralding probability and fidelity of entanglement generation for several cases in a single-photon interference scheme using frequency multiplexing with cSPDC. Our results demonstrate that by multiplexing approximately 100 modes, the heralding probability improves to approximately 98% for an elementary link distance LEL=25kmL_\mathrm{EL}=25 \mathrm{km}LEL​=25km, even in scenarios where the fidelity exceeds 0.9 across all modes. Furthermore, for LEL=100kmL_\mathrm{EL}=100 \mathrm{km}LEL​=100km, we show that the heralding probability, which was approximately 0.7% in the single-mode case, increases to about 38% under the condition that the fidelity remains 0.9 or higher. These analytical results demonstrate the effectiveness of employing cSPDC as a photon-pair source for quantum repeaters.
Cavity-enhanced spontaneous parametric down-conversion (SPDC) can be used to implement heralded single-photon sources with narrow bandwidth down to tens of megahertz, thus compatible with atom-based quantum memories. In this work, we propose and study the cavities that are either singly resonant at the frequency of only one of the generated photons or doubly resonant at the frequency of one generated photon and for the pump field. We derive analytical expressions for the generation rate and the spectral brightness as a function of the main structure parameters. Our analysis shows that by exploiting counterpropagating SPDC inside a cavity with properly designed distributed Bragg reflectors, pure narrow-band heralded single photons can be generated. In particular, when a pulsed pump illuminates a 1-mm-long singly resonant cavity, the bandwidth of the resonant and the nonresonant photons will be 120 MHz and 5.7 GHz, respectively, with heralded single-photon purity as high as 0.993. Due to its small absorption probability inside the cavity, the heralding efficiency can approach unity if the nonresonant partner is used as a heralded single photon. Finally, we also show that continuous-wave excitation of a 1-cm-long cavity resonant for the pump and copropagating fields can provide photon pairs in a narrow bandwidth of 10 MHz with spectral brightness as high as $2\ifmmode\times\else\texttimes\fi{}{10}^{6}$ $({\text{s}\phantom{\rule{4.pt}{0ex}}\text{mW}\phantom{\rule{4.pt}{0ex}}\text{MHz})}^{\ensuremath{-}1}$. This source can efficiently couple with quantum memories and can find applications in quantum information processing and communication.
Abstract In long-distance quantum communication using quantum repeaters with quantum memories, entangled photons at telecommunication wavelengths that can be coupled to quantum memory with high efficiency are required. Typically, entangled photons are generated via spontaneous parametric down conversion (SPDC). However, the phase-matching bandwidth of SPDC is more than 100 GHz, which is much broader than the bandwidth of a Pr 3+ :Y 2 SiO 5 quantum memory (with overall bandwidth of ∼10 GHz while the bandwidth of each frequency channel is ∼10 MHz) suitable for frequency-multiplexed quantum repeaters. In this study, nondegenerate SPDC (1550 nm and 995 nm) inside an optical cavity is used to obtain a narrow linewidth and cluster width of SPDC to match the Pr 3+ :Y 2 SiO 5 bandwidth. We also developed a cavity control mechanism that can fulfill the doubly resonant condition. The developed two-photon source can maximize the coupling efficiency with Pr 3+ :Y 2 SiO 5 by introducing wavelength conversion and is promising for use in a quantum repeater.
Frequency-multiplexed entangled photon pair sources with narrow bandwidths and high pair generation efficiency are a key enabling technology for quantum networking. We present a simulation-based design study of an integrated photonic racetrack resonator source for spontaneous parametric down-conversion (SPDC) that simultaneously achieves all three properties. The central result is a simulated set of 90 doubly resonant signal/idler frequency-mode pairs with an effective Schmidt number of 89.62, average bandwidths of 1.08 GHz, a mean free spectral range of 51.9 GHz, and a total internal pair-generation-rate efficiency of 1.16 GHz/mW. Under deterministic wavelength-based splitting, the accessible frequency-state Schmidt number is reduced to 44.93. To support these predictions, we derive a closed-form analytical connection between classical cavity parameters (resonant frequencies, decay rates, coupling coefficients) and the quantum joint spectral amplitude and pair generation rate, extending the dispersive-medium quantization formalism of Raymer to the nonlinear optical cavity case. We demonstrate how classical electromagnetic field simulations can be combined with this analytical framework to predict quantum figures of merit for an integrated photonic source prior to fabrication. Fabrication and experimental validation are left for future work.
This thesis presents experimental progress towards highly efficient generation of cavity- enhanced, narrow-band multiphotons using spontaneous parametric downconversion. It also suggests theoretical proposals for new applications of multiphoton sources in quantum information technology. Photons prepared in Fock states, with a well-defined number of particles, are the essence of the quantum nature of light, and their unique nonclassical properties help us to develop quantum information technology. The generation of Fock states has been most commonly achieved by using spontaneous parametric down-conversion (SPDC) through the χ(2) nonlinearity in bulk crystals. During the SPDC process the nonlinear crystal emits photon-number correlated modes, and a photon-number- resolving measurement in one mode heralds the preparation of the other mode in a Fock state. The fidelity and the success rate of Fock state generation is limited by the multimode nature of SPDC emission. In this thesis, I will investigate the use of cavity-enhanced SPDC modes for higher fidelity photon pair generation, in which the well defined mode of the cavity is enhanced and results in the narrow-band source of the heralded single-photons with up to 80% heralding efficiency. The heralding efficiency is defined as the ratio between number of coincidences and single events on the heralding mode. The photon-number-resolving ability of high-quantum-efficiency transition edge sensors is used for the heralding and detection. We further discuss the feasibility of Fock state generation with higher photon numbers upon improving the data acquisition and analysis techniques. We also demonstrate and implement an interferometry scheme that exploit the phase of the photon and is capable of reading boundless bits of digital information using a single photon. This thesis also introduces new theoretical proposals for using Fock states to obtain quantum advantages for various quantum information applications, here to increase the efficiency in reading out information stored in a classical digital memory and to discriminate optical phases with lower error rates than is feasible with classical protocols.
Deterministic sources of high-fidelity entangled qubit pairs encoded in the dual-rail photonic basis, i.e., presence of a single photon in one of two orthogonal modes, are a key enabling technology of many applications of quantum information processing, including high-rate, high-fidelity quantum communications over long distances. The most popular and mature sources of such photonic entanglement, e.g., those that leverage spontaneous parametric down-conversion (SPDC) or spontaneous four-wave mixing, generate an entangled (so-called continuous-variable) quantum state that contains contributions from high-order photon terms that lie outside the span of the dual-rail basis, which is detrimental to most applications. One often uses low pump power to mitigate the effects of those high-order terms. However, that reduces the pair generation rate, and the source becomes inherently probabilistic. We investigate a cascaded source that performs a linear-optical entanglement swap between two SPDC sources, to generate a heralded photonic entangled state that has a higher fidelity (to the ideal Bell state) compared to a free-running SPDC source. Furthermore, with the Bell swap providing a heralding trigger, we show how to build a multiplexed source, which despite reasonable switching losses and detector loss and noise, yields a fidelity versus success probability trade-off of a high-efficiency source of high-fidelity dual-rail photonic entanglement. We find, however, that there is a threshold of 1.51.51.5 dB of loss per switch, beyond which multiplexing hurts the fidelity versus success probability trade-off.
Summary form only given. An efficient resource of entanglement in atom-photon-based quantum networks are polarization-entangled photon pairs generated by type-II spontaneous parametric down-conversion (SPDC). Compatibility in frequency and bandwidth between such photons and a single trapped40Ca+-ion was first shown in [1]. The best SPDC entanglement values so far have been achieved by single-pass conversion in Sagnac configuration [2]. On the other hand, the highest pair rates are reported in cavity-enhanced sources [3]. The latter, however, tend to suffer from reduced state purity due to increasing probability of generating double pairs, and thermal effects in the crystal.