Time-resolved certification of frequency-bin entanglement over multi-mode channels
Stephane Vinet, Marco Clementi, Marcello Bacchi, Yujie Zhang, Massimo Giacomin, Luke Neal, Paolo Villoresi, Mattéo Galli, Daniele Bajoni, Thomas D. Jennewein
Abstract Frequency-bin entangled photons can be efficiently produced on-chip which offers a scalable, robust and low-footprint platform for quantum communication, particularly well-suited for resource-constrained settings such as mobile or satellite-based systems. However, analyzing such entangled states typically requires active and lossy components, limiting scalability and multi-mode compatibility. We demonstrate a novel technique for processing frequency-encoded photons using linear interferometry and time-resolved detection. Our approach is fully passive and compatible with spatially multi-mode light, making it suitable for free-space and satellite-to-ground applications. As a proof-of-concept, we utilize frequency-bin entangled photons generated from a high-brightness multi-resonator source integrated on-chip to show the ability to perform arbitrary projective measurements over both single- and multi-mode channels. We report the first measurement of the joint temporal intensity between frequency-bin entangled photons, which allows us to certify entanglement by violating the Clauser-Horne-Shimony-Holt (CHSH) inequality, with a measured value of ∣ S ∣ = 2.32 ± 0.05 over multi-mode fiber. By combining time-resolved detection with energy-correlation measurements, we perform full quantum state tomography, yielding a state fidelity of up to 91%. We further assess our ability to produce non-classical states via a violation of time-energy entropic uncertainty relations and investigate the feasibility of a quantum key distribution protocol. Our work establishes a resource-efficient and scalable approach toward the deployment of robust frequency-bin entanglement over free-space and satellite-based links.
Abstract Frequency-bin entangled photons can be efficiently produced on-chip which offers a scalable, robust and low-footprint platform for quantum communication, particularly well-suited for resource-constrained settings such as mobile or satellite-based systems. However, analyzing such entangled states typically requires active and lossy components, limiting scalability and multi-mode compatibility. We demonstrate a novel technique for processing frequency-encoded photons using linear interferometry and time-resolved detection. Our approach is fully passive and compatible with spatially multi-mode light, making it suitable for free-space and satellite-to-ground applications. As a proof-of-concept, we utilize frequency-bin entangled photons generated from a high-brightness multi-resonator source integrated on-chip to show the ability to perform arbitrary projective measurements over both single- and multi-mode channels. We report the first measurement of the joint temporal intensity between frequency-bin entangled photons, which allows us to certify entanglement by violating the Clauser-Horne-Shimony-Holt (CHSH) inequality, with a measured value of ∣ S ∣ = 2.32 ± 0.05 over multi-mode fiber. By combining time-resolved detection with energy-correlation measurements, we perform full quantum state tomography, yielding a state fidelity of up to 91%. We further assess our ability to produce non-classical states via a violation of time-energy entropic uncertainty relations and investigate the feasibility of a quantum key distribution protocol. Our work establishes a resource-efficient and scalable approach toward the deployment of robust frequency-bin entanglement over free-space and satellite-based links.
We demonstrate a novel, passive method for processing frequency-bin encoded quantum information using linear interferometry and time-resolved detection, eliminating the need for electro-optic modulation or nonlinear optics. This approach is compatible with multimode propagation, a crucial step for free-space quantum communication, and favorable for size, weight, and power (SWaP) requirements. Using a high-brightness multi-resonator source, we generate frequency-bin entangled photons and show the ability to perform arbitrary projective measurements in both single- and multi-mode propagation scenarios. For the first time, we measure the joint temporal amplitude of the generated state, directly linking its entangled nature to the temporal oscillation of non-local correlations. We leverage this to certify entanglement with a Bell curve visibility exceeding 95%. Our technique enables full quantum state tomography, yielding a state fidelity of up to 91% for a maximally entangled state. This work paves the way for robust entanglement deployment over free-space and satellite-based links.
Entanglement, describing the inseparability of a quantum multiparty system, is one of the most intriguing features of quantum mechanics. Violation of Bell inequality, for ruling out the possibility of local hidden variable theories, is commonly used as a strong witness for quantum entanglement. In previous Bell test experiments with photonic entanglement based on two-photon coincidence measurement, the photon temporal wave packets are absorbed completely by the detectors. That is, the photon coherence time is much shorter than the detection time window. Here we demonstrate generation of frequency-bin entangled narrowband biphotons, and for the first time, test the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality |S|<= 2 for their nonlocal temporal correlations with time-resolved detection. We obtain a maximum |S| value of 2.52+/-0.48 that violates the CHSH inequality. Our result will have applications in quantum information processing involving time-frequency entanglement.
The development of integrated photonic systems, both on-chip and fiber-based, has transformed quantum photonics by replacing bulky, fragile free-space optical setups with compact, efficient, and robust circuits. Photonic platforms incorporating fiber-connected sources of correlated and entangled photon pairs offer practical advantages, such as operation at room temperature, efficient integration with telecom infrastructure, and compatibility with mature and efficient semiconductor fabrication processes for cost-effective and large-scale optical circuits. The stability and scalability of integrated quantum photonics platforms have facilitated the generation and processing of quantum information in the temporal domain within a single spatial mode. Time-bin encoded states, known for their robustness against decoherence and compatibility with existing fiber-optic infrastructure, have shown to be an efficient paradigm for advanced applications like quantum secure communication, information processing, spectroscopy, imaging, and sensing. This review examines recent advancements in fiber- and chip-based platforms for generating non-classical states and their applications as quantum state processors in the time domain. We discuss the generation of pulsed quantum frequency combs using microring resonators and intra-cavity mode-locked laser schemes, enabling co- and cross-polarized quantum photonic states. Additionally, the versatility of these resonator chips for entanglement generation is emphasized, including two- and multi-photon time-bin entangled schemes. We highlight the development of time-bin entanglement analyzers in fiber architectures, featuring ultrahigh stability and post-selection-free capabilities, which enable precise and efficient characterization of two- and higher-dimensional time-bin entanglement. We also review scalable on-chip schemes for quantum key distribution, demonstrating low quantum bit error rates and compatibility with higher-dimensional quantum communication protocols. Further, methods for enhancing temporal resolution in detection schemes, crucial for time-bin encoding, are presented, such as the time-stretch sampling technique using electro-optic modulation. These innovations, relying on readily available, telecom-based fiber-optic components, provide practical, scalable, and cost-effective solutions for advancing quantum photonic technologies. Looking forward, time-bin encoding is expected to play a pivotal role in the advancement of quantum repeaters, distributed quantum networks, and hybrid light-matter systems, advancing the realization of globally scalable quantum technologies.
Encoding quantum information in photonic time-bin states is typically considered impractical for moving free-space quantum communication due to the difficulties with phase stabilization of distant quantum time-bin interferometers and turbulence of free-space channels. We demonstrate a novel approach using reference frame independent time-bin quantum key distribution that completely avoids the need for active relative phase stabilization while simultaneously overcoming a highly multi-mode channel without any active mode filtering. This scheme enables passive, self-compensating time-bin quantum communication without any mode filtering, mode sorting, adaptive optics, active basis selection, or active phase alignment. We realize a proof-of-concept demonstration using hybrid polarization and time-bin entangled photons that demonstrates a sustained asymptotic secure key rate greater than 0.07 bits/coincidence over a 15 m multi-mode fiber optical channel and showing entanglement correlations over a moving 38.5 dB loss free-space channel, including system losses. The scheme simplifies the use of time-bin encoding and can be readily applied over various spatially multi-mode and fluctuating channels involving rapidly moving platforms, including airborne and satellite systems.
We demonstrate the first-time frequency-bin-encoded entanglement-based quantum key distribution (EBQKD) between two users, and a flexible entanglement distribution over long optical fiber links. Dynamic and resource-efficient solutions are crucial to realizing large-scale photonic quantum networks capable of accommodating a growing number of users over large distances and at the same time facilitating a reliable performance at a maintained security level. Here, we adopt the frequency-bin encoding approach for defining three frequency channels, namely, CH1, CH2, and CH3, from highly correlated signal and idler photon pairs from pulsed-excited spontaneous parametric down-conversion (SPDC) process. The adaptive frequency de/multiplexing capability of our approach facilitates dynamic allocation of multiple frequency channels to additional users without increasing the hardware overhead. We developed a frequency-bin-basis analyzer module (see Figure. 1 a & b) composed of a programmable filter (PF), a frequency mixer (FM) based on electro-optic phase modulation (EOPM), a fiber Bragg grating (FBG) for the frequency-to-time mapping (FTM), and a superconducting nanowire single photon detector (SNSPD) of high timing resolution. Through a fine-tuned frequency mixing, passive random projection measurements are realized in two mutually unbiased basis (MUB; hereZ={∣0⟩,∣1⟩}andX={∣+⟩,∣−⟩}). The FTM technique applied on the frequency-mixed spectrum of each frequency channel allows for a time-resolved access to the projection measurement results in four basis states using only a single SNSPD. Remarkably, we showcase the capability of our approach for time-resolved detection of the four projection states corresponding to CH1, CH2, and CH3 using a single SNSPD per user. The performance metrics of the BBM92 protocol are shown in Figure. 1 c-e under different optical attenuations, at maximum 15.6 dB (equivalent to a 73 km fiber link). The qubit error ratio (QBER) was obtained for all channels well below the 11% upper threshold [1]. The maximum asymptotic secret key lengthlAof 310-bits, 283-bits, and 149-bits were obtained for channels CH1, CH2, and CH3, respectively. From the finite key analysis, a positive non-zero secret key rate was obtained for less than 15.6 dB attenuation. The capability of the system was also assessed in preserving high quality frequency-insenstive entanglement for distribution across remote fiber links (see Figure.1 f-h). Overall, the presented approach enables passive random projection measurements in two MUB by each user and benefits from frequency-multiplexing capability for adaptive multi-user operations. A single SNSPD per user renders this approach resource-efficient compared to conventional implementation schemes requiring 4×N detectors corresponding to N channels [2]. A single SNSPD means a reduced vulnerability to detector side channel attacks, a minimized dark count contribution, and a diminished imbalance arising from detection probability mismatch. Our approach thus enables a resource-efficient and a scalable implementation of EBQKD required for the future large-scale quantum networks.
Time-bin encoded photonic qubits are robust against decoherence in birefringent media such as optical fibers, which has led to many successful quantum communication demonstrations, including a Mach-Zehnder interferometer-based system, plug-and-play quantum key distribution (QKD), differential phase shift (DPS) and coherent one-way (COW) protocols, quantum teleportation, and elements of quantum repeaters. Despite these successes, time-bin encoding is considered impractical for turbulent free-space or multimode fiber channels, because spatial and temporal mode distortions hinder the interference required for analysis of time-bin superposition states. Here we present an efficient time-bin qubit analyzer, assisted by passive relay optics, that matches the spatial mode of the interfering paths. Our system demonstrates interference visibility of 89 %, even for strongly distorted optical input modes emerging from multimode fiber under variable angles of incidence. We measure a high level of entanglement between a time-bin qubit and a separate polarization qubit, thereby demonstrating the feasibility of time-bin based quantum communication over optical multimodal links.