Bell state measurements, which project bipartite qubit systems onto the maximally entangled Bell basis, are central to a wide range of quantum information processing tasks, including quantum teleportation, entanglement swapping, and fusion-gate quantum computation. In photonic quantum platforms, where information is encoded in optical degrees of freedom, the realization of efficient Bell state measurements is particularly challenging, especially when constrained to linear optical elements. In this review, we provide a comprehensive examination of existing proposals for implementing Bell state measurements, highlighting their fundamental limitations and the strategies developed to overcome them. Additionally, we survey recent advances in Bell state measurements for high-dimensional systems, an area of growing interest due to its relevance in scalable quantum networks and high-capacity quantum communication.

Quantum technologies play a central role in establishing new ways of quantum-secured communication. This work investigates free-space quantum communication and explores the advantage of implementing quantum key distribution (QKD) with weak coherent states produced by a light source in the mid-infrared (). Time-bin encoded quantum key distribution is simulated, and it is demonstrated that a free-space QKD link operating in the mid-infrared outperforms configurations based on conventional near-infrared wavelengths under various weather scenarios, with a particular significance in adverse meteorological conditions.

Quantum Key Distribution (QKD) protocols require Information-Theoretically Secure (ITS) authentication of the classical channel to preserve the unconditional security of the distilled key. Standard ITS schemes are based on one-time keys: once a key is used to authenticate a message, it must be discarded. Since QKD requires mutual authentication, two independent one-time keys are typically consumed per round, imposing a non-trivial overhead on the net secure key rate. In this work, we present the authentication-with-response scheme, a novel ITS authentication scheme based on ε-Almost Strongly Universal_2 (ε-ASU_2) functions, whose IT security can be established in the Universal Composability (UC) framework. The scheme achieves mutual authentication consuming a single one-time key per QKD round, halving key consumption compared to the state-of-the-art.

Quantum key distribution (QKD) can provide secret keys with security rooted in quantum mechanics, but operation alongside high-capacity classical traffic remains limited by the excess-noise budget of weak quantum states in conventional solid-core fiber. Here, we combine ultralow-loss anti-resonant hollow-core fiber with residual-carrier-assisted discrete-modulation continuous-variable QKD (DM-CV-QKD) to address both propagation-induced coexistence noise and low-SNR phase recovery. Over a 24.3-km hollow-core link with 3.3-dB end-to-end loss, a dual-polarization 15-Gbaud DM-CV-QKD channel achieves an average asymptotic secret-key rate (SKR) of 153.22 Mb/s and a finite-size SKR of 149.99 Mb/s, while 39 coherent wavelength-division-multiplexed channels deliver an aggregate data rate of 7.6 Tb/s and a net data rate of 7.2 Tb/s. The system can even sustain a positive SKR under a high classical launch power of up to 15 dBm, without an optical bandpass filter (BPF). Finite-size analysis against collective attacks further yields a projected positive secret-key rate at a 100-km-equivalent condition. These results show that an anti-resonant hollow-core fiber, combined with carrier-assisted phase recovery, can greatly extend the operating regime of shared-fiber quantum-secured coherent links, pointing to a promising approach for integrating high-rate CV-QKD with high-capacity optical networks.

Long-range quantum entanglement is essential for building large-scale quantum networks and unconditionally secure cryptographic systems based on quantum key distribution (QKD). While photonic integrated circuits offer a highly scalable platform, the fragility of phase coherence between spatial modes has prevented the distribution of path-encoded entanglement over long distances. Here, we report chip-to-chip distribution of path-encoded entangled states over 80 km between fully integrated silicon photonic transmitter and receiver chips. Telecom-band entangled photon pairs are generated via spontaneous four-wave mixing in on-chip spiral waveguides and distributed between chips over a dual-core, actively stabilized fiber link. Upon distribution, we measure a Bell state fidelity of 85.7 ± 0.2 %. Implementing the BBM92 protocol with the same source, we obtain a secure key rate of 2.03 bit/s in the infinite-key regime. These results establish silicon photonic chips as a viable platform for long-distance path-encoded entanglement-based quantum key distribution, paving the way toward scalable, device-independent quantum networks.

High-visibility Franson interference at telecom C-band wavelengths is achieved using a cascaded periodically poled lithium niobate (PPLN) waveguide photon-pair source combined with fully passive, path-imbalanced Mach-Zehnder interferometers implemented on photonic integrated circuits (PICs). The interferometers require neither on-chip phase shifters nor active stabilization; instead, the phase is scanned via thermal tuning of the chip. By employing a narrow-linewidth continuous-wave (CW) pump and dense wavelength-division multiplexing (DWDM) filtering, energy-time entangled photon pairs with high spectral indistinguishability are generated. We achieve a 4.8

We present a semi-device-independent quantum random number generator (QRNG) based on the violation of a contextuality inequality, implemented by the integration of two silicon photonic chips. Our system combines a heralded single-photon source with a reconfigurable interferometric mesh to implement qutrit state preparation, transformations, and measurements suitable for testing a KCBS contextuality inequality. This architecture enables the generation of random numbers from the intrinsic randomness of single-photon interference in a complex optical network, while simultaneously allowing a quantitative certification of their security without requiring entanglement. We observe a contextuality violation exceeding the classical bound by more than 10σ, unambiguously confirming non-classical behavior. From this violation, we certify a conditional min-entropy per experimental round of Hmin = 0.077 +- 0.002, derived via a tailored semidefinite-programming-based security analysis. Each measurement outcome therefore contains at least 0.077 +- 0.002 bits of extractable genuine randomness, corresponding to an asymptotic generation rate of 21.7 +- 0.5 bits/s. These results establish a viable route towards general-purpose, untrusted quantum random number generators compatible with practical integrated photonic quantum networks.

Privacy of a quantum metrological protocol concerns the extent to which single parameters can be kept inaccessible to an observer or to other users of the network. In this work, an information geometric framework is developed to quantify privacy and accessibility of functions of parameters effectively, that is, up to a finite accuracy in state discrimination. Both quantities are defined by measuring volumes in the parameter space induced by the underlying quantum states. This construction subsumes previous definitions of privacy based on the degeneracy of quantum Fisher information, naturally encompassing imperfect implementations. Using extended-GHZ states as a representative example of a quantum network scenario, privacy and accessibility are characterized by quantum correlations and accuracy, providing scaling laws depending on imperfect measurements and entanglement.

This perspective paper explores quantum-safe networks as the convergence of technology innovation and regulatory frameworks. With cryptographically relevant quantum computers potentially arriving within a decade, organizations face immediate risks from harvest-now-decrypt-later attacks. The paper presents a dual-technology approach combining Quantum Key Distribution and Post-Quantum Cryptography, analyzes global regulatory timelines converging on 2030-2035 migration deadlines, and provides concrete use cases across finance, government, healthcare, telecommunications, and critical infrastructure sectors.

Quantum technologies are rapidly emerging as a foundation for next-generation information processing, communication, and sensing. In particular, optical platforms stand out as a promising avenue for scalable and efficient architectures. Here, information can be encoded either in discrete variables (DV)—such as polarization, path, frequency, or angular momentum—or in continuous variables (CV) of the optical field, such as quadratures. We develope a new formalism for the joint description of multiphoton and multimode light undergoing Gaussian transformations, and we use it to explore two DV-CV hybrid protocols. The first unifies and extends distinct forms of boson sampling, merging DV scattershot boson sampling with CV Gaussian boson sampling, thereby enabling quantum advantage demonstrations with squeezed photons. The second protocol deals with the Bell state measurement (BSM) for qudits, which are a higher-dimensional generalization of the qubit. Bell measurements play a key role in fusion-based quantum computation entanglement distribution and secret key sharing. We therefore introduce high-dimensional BSMs through linear interferometry combined with multiple single-mode squeezers, outperforming state-of-the-art theoretical methods in linear optics without using auxiliary states. This result shows how bridging the DV and CV paradigms provides a framework in which their combined strengths can outperform their standalone applications and overcome their individual limitations.

The development of wireless communication systems has reached even more ambitious goals through the years, one of this being the attempt to exchange information by using optical signals in the underwater domain. To do so, there is the need to overcome the intrinsic challenges of this environment, represented by the strong attenuations and temporal variations caused by the optical properties of the underwater medium. Hence, the feasibility of an underwater communication system necessarily passes through the ability to model the underwater channel and design a system that is resilient to this environment. In particular, the main task is to characterize the turbulence and the channel impulse response, having both a major impact on the power fading and waveform distortions experienced by the transmitted signal during the packet communication. In this work, we propose a comprehensive model for the attenuation of the underwater medium focusing on the effect of turbulence and scattering within the marine environment and their impact on the temporal response of the whole system. Then, we summarize these results in the turbulence random process model and the channel impulse response. We also analyze the performances of the system using the most important figures of merit, such as the average bit error rate (BER), ergodic capacity, outage probability and capacity, and analyze the temporal distortion of the received waveforms, using the scatter plots and the eye diagrams. The analysis is carried out using several uncoded modulation formats, without error correction and other impairments, by means of numerical simulations.

Information reconciliation is a critical component of quantum key distribution, ensuring that mismatches between Alice's and Bob's keys are corrected. In this study, we analyse, simulate, optimise and compare the performance of two prevalent algorithms used for information reconciliation: Cascade and LDPC codes in combination with the blind protocol. We focus on their applicability in practical and industrial settings, operating in realistic and application-close conditions. The results are further validated through evaluation on a live industrial QKD system.

A physics-constrained neural network is presented for predicting the optical response of metasurfaces. Our approach incorporates physical laws directly into the neural network architecture and loss function, addressing critical challenges in the modeling of metasurfaces. Unlike methods that require specialized weighting strategies or separate architectural branches to handle different data regimes and phase wrapping discontinuities, this unified approach effectively addresses phase discontinuities, energy conservation constraints, and complex gap-dependent behavior. We implement sine-cosine phase representation with Euclidean normalization as a non-trainable layer within the network, enabling the model to account for the periodic nature of phase while enforcing the mathematical constraint sin^2 ϕ+ cos^2 ϕ= 1. A Euclidean distance-based loss function in the sine-cosine space ensures a physically meaningful error metric while preventing discontinuity issues. The model achieves good, consistent performance (e.g., coefficient of determinations above 0.9) with small, imbalanced datasets of 580 and 1075 data points, compared to several thousand typically required by alternative approaches. This physics-informed approach preserves physical interpretability while reducing reliance on large datasets and could be extended to systems involving periodic or wrapped quantities.

Bell measurements, entailing the projection onto one of the Bell states, play a key role in quantum information and communication, where the outcome of a variety of protocols crucially depends on the success probability of such measurements. Although in the case of qubit systems, Bell measurements can be implemented using only linear optical components, the same result is no longer true for qudits, where at least the use of ancillary photons is required. In order to circumvent this limitation, one possibility is to introduce nonlinear effects. In this work, we adopt the latter approach and propose a scalable Bell measurement scheme for high-dimensional states, exploiting multiple squeezer devices applied to a linear optical circuit for discriminating the different Bell states. Our approach does not require ancillary photons, is not limited by the dimension of the quantum states, and is experimentally scalable, thus paving the way toward the realization of an effective high-dimensional Bell measurement.

Quantum networks have been a reality for several years, with quantum key distribution as their primary application. However, several factors still limit their widespread adoption as a user-ready technology. In this work, we present four real-world experiments that demonstrate concrete progress toward the deployment of quantum networks. These field trials showcase the ability to interconnect different countries, interface diverse infrastructures, and exploit quantum properties and innovative technologies to boost key rates and enable coexistence with classical communication channels. Together, they highlight a viable path toward scalable, interoperable, and high-performance quantum-secured communication.

We demonstrate the BBM92 quantum key distribution protocol using frequency-bin entangled photon pairs generated by two independent, high-finesse, ring resonators on a silicon photonic chip.

Boson sampling is a key candidate for demonstrating quantum advantage and has already yielded significant advances in quantum simulation, machine learning, and graph theory. In this work, a unification and extension of distinct forms of boson sampling is developed. The devised protocol merges discrete-variable scattershot boson sampling with continuous-variable Gaussian boson sampling. Therefore, it is rendered possible to harness the complexity of more interesting states, such as squeezed photons, in advanced sampling protocols. A generating function formalism is developed for the joint description of multiphoton and multimode light undergoing Gaussian transformations. The resulting analytical tools enable one to explore interfaces of different photonic quantum-information-processing platforms. A numerical simulation of unified sampling is carried out, benchmarking its performance, complexity, and scalability. Entanglement is characterized to exemplify the generation of quantum correlations from the nonlinear interactions of a unified sampler.

The reliable distribution of high-dimensional entangled quantum states, an important resource in quantum technologies, through optical fibre networks is challenging due to the need to maintain coherence across multiple modes. Here we demonstrate the distribution of four-dimensional path-encoded entangled quantum states between photonic chips, enabled by a novel multimode phase stabilisation algorithm. The algorithm utilises the reconfigurability of the integrated photonic circuits to complete one iteration of phase stabilisation in just two measurement rounds for an arbitrary number of modes, and requires no additional hardware to the quantum measurements it enables. As a result, we are able to perform complete quantum state tomography across two chips using the minimum number of local projective measurements to verify the fidelity of the distributed entangled state to be 86% (compared to 8.1% without the phase stabilisation) with an entanglement entropy of 0.995±0.002.

Quantum key distribution (QKD) is a secure communication method for sharing symmetric cryptographic keys based on the principles of quantum physics. Its integration into the fiber-optic network infrastructure is important for ensuring privacy in optical communications. Multi-core fibers (MCFs), the likely building blocks of future high-capacity optical networks, offer new opportunities for such integration. Here, we experimentally demonstrate, for the first time, the coexistence of discrete-variable QKD and high-throughput classical communication in the C-band over a field-deployed MCF with industry standard cladding diameter of 125 μm. Specifically, we demonstrate successful secure-key establishment in one core of a 25.2-km uncoupled-core MCF, while simultaneously loading the remaining three cores with full C-band counter-propagating classical traffic at an aggregate net rate of 110.8 Tb/s. By proposing and experimentally validating an improved analytical model for inter-core spontaneous Raman scattering noise, we find that this configuration is optimal for our deployed MCF link as it is immune to four-wave mixing, that becomes relevant when the quantum and classical signals are propagating in the same direction. Our findings make an important step forward in demonstrating the integration of QKD and classical transmission in uncoupled-core multi-core fibers for next-generation optical communication networks. The world’s first integration of quantum key distribution and high-speed classical communications over field-deployed multi-core fiber.