We generate a three-qutrit GHZ state using a deterministic high-dimensional entangling gate—the SUM gate—applied across the time and frequency degrees of freedom of a biphoton frequency comb. The state exhibits high fidelity of F=0.958(10), and we verify its nonlocality by measuring the Mermin operator and observing a clear violation of the classical bound by 59 standard deviations, in a Mermin inequality test.

Mermin's inequality provides a fundamental test to verify the quantum nonlocality of multipartite Greenberger-Horne-Zeilinger (GHZ) states, by also serving as a key resource for measurement-based quantum computing. While the theoretical foundation of Mermin's inequality test is well established for both qubit and qudit systems, the experimental validation for qudits remains elusive. In this work, we perform qudit Mermin's inequality test implemented on a qutrit (i.e., three-level system) GHZ state, where the multipartition is achieved by deterministically entangling the time and frequency bins of a biphoton state via standard fiber-optic components. The direct measurement of Mermin's operator yields an expectation value of 8.612(44), surpassing the bound of 6 for local realism by 59 standard deviations. We demonstrate the potential of the verified GHZ state for high-dimensional quantum computing by utilizing the nonlocality results to compute a ternary logic function through non-adaptive high-dimensional measurement-based quantum computation. Our scheme is readily scalable to higher dimensions without additional loss or modifications to the experimental setup.

We review advances using time and frequency degrees of freedom as complementary, high-dimensional resources for quantum photonics. Fiber synthetic temporal lattices and integrated time-bin platforms enable programmable dynamics and telecom-compatible entanglement. Nonlocal dispersion cancellation via sum-time correlations boosts time-bin resilience for long-distance quantum key distribution.

We demonstrate non-adaptive measurement-based quantum computation using a frequency-time-entangled three-qutrit GHZ state. The findings highlight the effectiveness of qudit GHZ states in quantum computation and reveal the nonlocal characteristics of multipartite high-dimensional entangled systems.

We present a resource-efficient compiled version of Shor's algorithm by employing frequency and time qudits within a single photon and utilizing fiber-optic devices. Our results demonstrate successful factorization of the number 15 with high fidelity.

We employ a coupled fiber-loop system to simulate a synthetic photonic lattice in the temporal domain and control the quantum walk evolution of time-bin entangled states, enabling improved detection efficiency and enhanced coincidence counts.

High-dimensional photon states (qudits) are pivotal to enhance the information capacity, noise robustness, and data rates of quantum communications. Time-bin entangled qudits are promising candidates for implementing high-dimensional quantum communications over optical fiber networks with processing rates approaching those of classical telecommunications. However, their use is hindered by phase instability, timing inaccuracy, and low scalability of interferometric schemes needed for time-bin processing. As well, increasing the number of time bins per photon state typically requires decreasing the repetition rate of the system, affecting in turn the effective qudit rates. Here, we demonstrate a fiber-pigtailed, integrated photonic platform enabling the generation and processing of picosecond-spaced time-bin entangled qudits in the telecommunication C band via an on-chip interferometry system. We experimentally demonstrate the Bennett-Brassard-Mermin 1992 quantum key distribution protocol with time-bin entangled qudits and extend it over a 60 km-long optical fiber link, by showing dimensionality scaling without sacrificing the repetition rate. Our approach enables the manipulation of time-bin entangled qudits at processing speeds typical of standard telecommunications (10 s of GHz) with high quantum information capacity per single frequency channel, representing an important step towards an efficient implementation of high-data rate quantum communications in standard, multi-user optical fiber networks.

We demonstrate a scalable synthetic temporal photonic lattice on a coupled-fiber loop system and utilize it to control the quantum walk evolution of time-bin entangled states. Our system enables enhanced detection efficiency and coincidence counts.

We demonstrate the Bennett-Brassard-Mermin 1992 quantum key distribution protocol with time-bin entangled photonic qudits over a 60-km-long optical fiber link. The on-chip framework utilized therein addresses low effective qudit rates associated with time-bin encoding schemes.

High-dimensional time-bin analyzers are essential for characterizing quantum states in photonic systems. We present advancements in fiber- and chip-based platforms for generating and analyzing time-bin entanglement, emphasizing ultrastable fiber architectures, scalable quantum key distribution, and post-selection-free measurements, enabling robust and scalable quantum communication and processing.

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.

We present a framework describing dispersion’s impact on time-bin entangled photon pairs, identifying a new regime resilient to dispersion. This low-loss approach enables secure communication across dispersive links, without using lossy dispersion-compensating elements.

Encoding quantum information via time-bin entangled states has had a profound impact on the development of quantum communications. However, dispersive propagation limits their achievable transmission distances. Here we describe a regime for nonlocal dispersion cancellation where the sum of arrival times of photons undergoing identical dispersion remains highly correlated. We exploit this effect to mitigate dispersive effects in a quantum key distribution fiber link, allowing an increase in the secret key rate by over a factor of 5 after 80 km of optical fiber dispersion.

The development of integrated and programmable photonic devices has significantly affected modern communications and signal processing in both the classical and quantum domains. However, achieving the required performance for new smart applications presents challenges in terms of design, fabrication, and control over multiple parameters. Optimization methods that leverage metaheuristic algorithms, machine learning, and artificial neural networks offer efficient solutions for the complex design of photonic devices, enabling new and desired functionalities. This comprehensive review explores the use of these methods to enhance the fabrication of innovative devices for smart photonic applications in next-generation communication and signal processing. We begin by introducing the mathematical frameworks of these optimization methods. We then investigate how they enable customization, optimization, and new device functionalities. Ultimately, we present our conclusions and discuss future prospects, emphasizing the potential of optimization methods in promoting revolutionary advancements in photonics.

Time-entanglement is a promising resource for the implementation of quantum communications over standard fiber networks. In particular, photonic qudits can enhance the performance of quantum communication, including quantum key distribution, in terms of noise robustness, quantum information content, distance reach, as well as security and secret key rates. However, time-entangled photonic qudits are not ready yet to be fully exploited for quantum communications in fiber networks that are fully compatible with standard telecommunication architecture. Here, we demonstrate the implementation of telecommunication-compatible quantum communications based on picosecond-spaced time-entangled qudits. To this end, we make use of an integrated photonic chip comprising a cascade of programmable interferometers and a spiral waveguide. We use entangled qudits to implement high-speed quantum key distribution, chip-to-chip entanglement distribution, and quantum state propagation over 60 km of standard fiber. Our results show the potential of time-entangled qudits for high-speed quantum communications in telecommunication-compatible architecture.

We present a generalized description of the effect of dispersion on time-bin entangled photon pairs. Leveraging this framework, we identify a new regime that is resilient to dispersion, allowing for secure communication across dispersive links with low loss by avoiding the use of dispersion-compensating elements.

Encoding information in photonic time bin enables quantum technologies compatible with both integrated and fiber frameworks. Here, we demonstrate time-bin entangled qudits in a programmable photonic chip and in a fully fibered coupled loop system.

Indistinguishability of identical particles is a resource for quantum information processing and has been utilized to generate entanglement from independent particles that spatially overlap only at the detection stage. Here we provide a general controllable scheme capable of generating, from a pure product state of $N$ qubits, a comprehensive class of multipartite entangled states, including W, Dicke, GHZ, and cluster states with both bosonic and fermionic statistics within the framework of spatially localized operations and classical communication (sLOCC). Using graph-based representations of the sLOCC framework, we translate the generation schemes of specific entangled states into colored, complex, and weighted digraphs, each corresponding to a given experimental setup. This graph-theoretical approach allows for precise targeting of particular multipartite states, exploration of diverse generation schemes, and optimization of generation efficiency. Our results demonstrate that the indistinguishability of identical graph nodes in quantum networks offers useful perspectives for photonic technology.