High-precision optical phase stabilization in quantum networks is fundamentally constrained by the strict photon-flux and duty-cycle limits required to avoid disturbing fragile quantum states. This challenge becomes especially critical when coordinating multiple independent light sources for multistep quantum protocols. Here, we develop an integrated phase-stabilization framework that incorporates a Bayesian phase estimator to optimally extract information from sparse single-photon detection events. This approach outperforms conventional maximum-likelihood estimation and achieves the shot-noise limit under minimal photon flux. The framework enables real-time correction of combined phase noise from both nodal lasers and transmission fibers, facilitating a two-step excitation protocol for heralded entanglement generation between separate trapped-ion nodes via single-photon interference. Operating with a detected photon rate of ∼1 MHz and a duty cycle ≤6.5%, the system maintains interferometric visibility >97% over fiber links of 10 km and 100 km. This phase control yields long-lived ion-ion entanglement with parity contrast exceeding 85%, enabling device-independent quantum key distribution with finite-size security analysis over 10 km and a positive asymptotic key-rate over 100 km. Moreover, the resulting memory-memory entanglement at 10 km survives beyond the average time required to establish it-a fundamental requirement for quantum repeaters. This Letter establishes a robust and scalable foundation for practical long-distance quantum networks.
High-precision optical phase stabilization in quantum networks is fundamentally constrained by the strict photon-flux and duty-cycle limits required to avoid disturbing fragile quantum states. This challenge becomes especially critical when coordinating multiple independent light sources for multistep quantum protocols. Here, we develop an integrated phase-stabilization framework that incorporates a Bayesian phase estimator to optimally extract information from sparse single-photon detection events. This approach outperforms conventional maximum-likelihood estimation and achieves the shot-noise limit under minimal photon flux. The framework enables real-time correction of combined phase noise from both nodal lasers and transmission fibers, facilitating a two-step excitation protocol for heralded entanglement generation between separate trapped-ion nodes via single-photon interference. Operating with a detected photon rate of ∼1 MHz and a duty cycle ≤6.5%, the system maintains interferometric visibility >97% over fiber links of 10 km and 100 km. This phase control yields long-lived ion-ion entanglement with parity contrast exceeding 85%, enabling device-independent quantum key distribution with finite-size security analysis over 10 km and a positive asymptotic key-rate over 100 km. Moreover, the resulting memory-memory entanglement at 10 km survives beyond the average time required to establish it-a fundamental requirement for quantum repeaters. This Letter establishes a robust and scalable foundation for practical long-distance quantum networks.
High-precision optical phase stabilization in quantum networks is fundamentally constrained by the strict photon-flux and duty-cycle limits required to avoid disturbing fragile quantum states. This challenge becomes especially critical when coordinating multiple independent light sources for multi-step quantum protocols. Here, we develop an integrated phase-stabilization framework that incorporates a Bayesian phase estimator to optimally extract information from sparse single-photon detection events. This approach outperforms conventional maximum-likelihood estimation and achieves the shot-noise limit under minimal photon flux. The framework enables real-time correction of combined phase noise from both nodal lasers and transmission fibers, facilitating a two-step excitation protocol for heralded entanglement generation between separate trapped-ion nodes via single-photon interference. Operating with a detected photon rate of approximately 1 MHz and a duty cycle less than 6.5%, the system maintains interferometric visibility greater than 97% over fiber links of 10 km and 100 km. This phase control yields long-lived ion-ion entanglement with parity contrast exceeding 85%, enabling device-independent quantum key distribution with finite-size security analysis over 10 km and a positive asymptotic key-rate over 100 km. Moreover, the resulting memory-memory entanglement at 10 km survives beyond the average time required to establish it, which is a fundamental requirement for quantum repeaters. This work establishes a robust and scalable foundation for practical long-distance quantum networks.
Quantum networks, integrating quantum communication, quantum metrology, and distributed quantum computing, could provide secure and efficient information transfer, high-resolution sensing, and an exponential speed-up in information processing. Deterministic entanglement distribution over long distances is a prerequisite for scalable quantum networks, enabling the utilization of device-independent quantum key distribution (DI-QKD) and quantum teleportation to achieve secure and efficient information transfer. However, the exponential photon loss in optical fibres prohibits efficient and deterministic entanglement distribution. Quantum repeaters, incorporating entanglement swapping and entanglement purification with quantum memories, offer the most promising means to overcome this limitation in fibre-based quantum networks. Despite numerous pioneering efforts toward realizing quantum repeaters, a critical bottleneck remains, as remote memory-memory entanglement suffers from decoherence more rapidly than it can be established and purified over long distances. We overcome this by developing long-lived trapped-ion memories, an efficient telecom interface, and a high-visibility single-photon entanglement protocol. This allows us to establish and maintain memory-memory entanglement over a 10 km fibre within the average entanglement establishment time for the same distance. As a direct application, we demonstrate metropolitan-scale DI-QKD, distilling 1,917 secret keys out of 4.05*10^5 Bell pairs over 10 km. We further report a positive key rate over 101 km in the asymptotic limit, extending the achievable distance by more than two orders of magnitude. Our work provides a critical building block for quantum repeaters and marks an important step toward scalable quantum networks.
Optical phase stabilization, tracking, and locking in long fiber links are pivotal for the functionality of many communication protocols and distributed sensors. However, conventional phase stabilization methods use strong optical probe signals that may contaminate and destroy fragile quantum signals propagating in the same fiber link. Here, we experimentally demonstrate phase locking of fiber spools up to 100 km and over 120 km deployed optical communication link using faint coherent states with an average of just photons per second detected at the receiving detector as a probe signal. The power spectral density of phase noise, integrated from 1 Hz to 50 kHz, yields an excess rms phase noise of 110 mrad (corresponding to timing jitter below 0.09 fs) for a 100 km fiber spool and 140 mrad (corresponding to rms timing jitter below 0.12 fs) for deployed fiber. The displacement-enhanced measurement protocol that we employ for phase stabilization yields Fisher information that is greater than that of homodyne and heterodyne measurement protocols for fiber links longer than 100 m and, therefore, exceeds the canonical shot noise limit of accuracy. By implementing this stabilization strategy with a 50% duty cycle, we enable time-division multiplexed faint light and quantum payloads to coexist within the same communication channel.
Originally envisioned as a solution for the capacity crunch in telecommunications networks, multicore fibers (MCFs) are contributing to scientific fields beyond telecom, such as sensing and metrology. Confined within the same cladding, the cores of MCF have a high degree of noise correlation, which can be harnessed for a variety of applications. Here, we investigate MCF as a solution to the challenging problem of quantum and classical light co-existence in phase-stabilized quantum networks by operating the quantum and stabilization light in separate but highly correlated cores of a 7-core MCF. Over 40 km of spooled fiber, we achieved 100 attosecond integrated jitter on one core by using phase information derived from another core. This allows for 100% duty cycle on a quantum channel while maintaining a low spurious photon rate from optical crosstalk. With cycle-slip-free stabilization over 6 hours, frequency detuning between designated stabilization and quantum channels, and an additional 40 dB rejection of noise photons provided by the low optical crosstalk between cores, we achieved a Raman scattering-induced spurious photon rate of only 0.01 photons/s in 100 GHz bandwidth. Our results with MCF demonstrate a promising approach to ultra-stable quantum networks with 100% duty cycle on the quantum channel.
Establishing phase-stable links over long-distance fiber infrastructure is crucial for phase-sensitive networking protocols. Faint-light and quantum networking present an additional challenge of keeping the payload channel dark. In this work, we present a scalable solution for phase stabilization of dark metropolitan-scale fiber links using wavelength-division-multiplexing (WDM). We implement a combined feed-back and feed-forward phase stabilization for a target channel by combining error signals from two separate reference channels over a 120 km deployed aerial fiber link. Residual phase noise in the dark target channel is reduced by two orders of magnitude compared to a WDM feedback-only strategy and reaches subfemtosecond root-mean-square (RMS) values. Observed cross-talk photon noise is ≈500 photons per second. Potentially, several dark target channels can be phase-stabilized without injecting additional reference channels. This solution is a major step toward scalable metropolitan-distance quantum networking applications, including single-rail entanglement distribution, quantum key distribution, coherent clock transfer, and coherent optical communication.
The quantum statistical fluctuations of electromagnetic fields establish a limit, known as the shot-noise limit, on the sensitivity of optical measurements performed with classical technologies. However, quantum technologies are not constrained by this shot-noise limit. In this regard, the possibility of using every photon produced by quantum sources of light to estimate small physical parameters, beyond the shot-noise limit, constitutes one of the main goals of quantum optics. Here, we experimentally demonstrate a scalable protocol for quantum-enhanced optical phase estimation across a broad range of phases, with neither pre- nor post-selected measurements. This is achieved through the efficient design of a source of spontaneous parametric downconversion in combination with photon-number-resolving detection. The robustness of two-mode squeezed vacuum states against loss allows us to outperform schemes based on N00N states, in which the loss of a single photon is enough to remove all phase information from a quantum state. In contrast to other schemes that rely on N00N states or conditional measurements, the sensitivity of our technique could be improved through the generation and detection of high-order photon pairs. This unique feature of our protocol makes it scalable. Our work is important for quantum technologies that rely on multiphoton interference such as quantum imaging, boson sampling, and quantum networks.