We theoretically compare the quantum Fisher information (QFI) for three configurations of absorption spectroscopy with undetected idler photons: an SU(1,1) interferometer with inter-source idler loss, an induced-coherence (IC) setup in which the idler partially seeds a second squeezer together with a vacuum ancilla, and a distributed-loss (DL) scheme with in-medium attenuation. We calculate the QFI as a function of parametric gain for both full and signal-only detection access. For losses below 99% and low to moderate gain, the SU(1,1) configuration provides the largest QFI. At high gain and intermediate loss, the IC scheme performs best, while under extreme attenuation (transmission < 1%) the DL model becomes optimal. These results delineate the measurement regimes in which each architecture is optimal in terms of information theory.

We study theoretically how high-gain effects affect the measurement outcome of visible signal spectra in undetected photon measurement schemes. We consider two interferometric configurations: firstly, the SU(1,1) interferometer where the idler incurs loss and additional dispersion in between two identical, lossless, squeezers; secondly, the induced coherence interferometer where the idler incurs loss and additional dispersion in between two identical, lossless, squeezers and where the second squeezer is seeded by the idler and a vacuum ancilla mode. Furthermore, we consider a distributed loss configuration where the idler incurs loss as it propagates in the nonlinear medium. Motivated by experimental evidence and due to the fact that broadband sources are ideal for these measurement schemes, we use the dispersive data of a third-order dispersion engineered integrated waveguide parametric down conversion (PDC) source presented in New Journal of Physics 26, 123025 (2024) to model the PDC spectra in the three configurations. For each configuration we consider the case of idler-only (i) absorption, (ii) additional dispersion, and (iii) the combined effects. We obtain results which outline the strength and weaknesses of the different configurations at different operation points.

For the ever-growing field of quantum information processing, large-scale, efficient multiport interferometers serving as photonic processors are required. In this context, the suitability of quantum walks as the interferometric base for universal computation has been theoretically proven. In this work, we bridge the gap between theoretical proposals and state-of-the-art experimental capabilities by providing the recipe for the implementation of a universal photonic processor in discrete-time quantum walks. Specifically, we present the protocol for translating arbitrary linear transformations into the coin and step operator of a quantum walk and map these to the experimental parameters of the established time-multiplexed platform [A. Schreiber , Phys. Rev. Lett. , 050502 (2010)]. We show that our interface is highly scalable and resource efficient due to the hybrid encoding consisting of multiple degrees of freedom. Finally, we prove that our system is highly resilient against experimental imperfections and show that it compares favorably against existing architectures.

Simulating vibronic spectra is a central task in physical chemistry, offering insight into important properties of molecules. Recently, it has been experimentally demonstrated that photonic platforms based on Gaussian boson sampling (GBS) are capable of performing these simulations. However, whether an actual GBS approach is required depends on the molecule under investigation. To develop a better understanding on the requirements for simulating vibronic spectra, we explore connections between theoretical approximations in physical chemistry and their photonic counterparts. Mapping these approximations into photonics, we show that for certain molecules the GBS approach is unnecessary. We place special emphasis on the linear coupling approximation, which in photonics corresponds to sampling from multiple coherent states. By implementing this approach in experiments, we demonstrate improved similarities over previously reported GBS results for formic acid and identify the particular attributes that a molecule must exhibit for this, and other approximations, to be valid. These results highlight the importance in forming deeper connections between traditional methods and photonic approaches.

Superconducting nanowire single-photon detectors (SNSPDs) can enable photon-number resolution (PNR) based on accurate measurements of the detector’s response time to few-photon optical pulses. In this work, we investigate the impact of the optical pulse shape and duration on the accuracy of this method. We find that Gaussian temporal pulse shapes yield cleaner arrival-time histograms and, thus, more accurate PNR, compared to bandpass-filtered pulses of equal bandwidth. For low system jitter and an optical pulse duration comparable to the other jitter contributions, photon numbers can be discriminated in our system with a commercial SNSPD. At 60 ps optical pulse duration, photon-number discrimination is significantly reduced. Furthermore, we highlight the importance of using the correct arrival-time histogram model when analyzing photon-number assignment. Using exponentially modified Gaussian distributions, instead of the commonly used Gaussian distributions, we can more accurately determine photon-number misidentification probabilities. Finally, we reconstruct the positive operator-valued measures of the detector, revealing sharp features that indicate the intrinsic PNR capabilities.

We report on the first experimental verification of mode-independent entanglement. Commonly, the entanglement of a state is firmly based on pre-defined parties that are correlated, and the state might be disentangled when the definition of the parties is changed. Exceeding this party-dependent concept, we realize a type of quantum entanglement that persists even if the parties, in our case modes, are transformed. This safeguards the performance of entanglement in real-world applications, such as quantum communication settings involving noise and untrusted parties. For the state generation, we present an experimental scheme based on a fully reconfigurable temporally multiplexed interferometer with measurement-induced nonlinearities, which generates heralded two-photon states in two modes that are entangled for all choices of orthonormal mode basis. For the certification process, we utilize a tailored quantum-state tomography, achieving fidelities that validate the presence of mode-independent entanglement as a resilient and operationally advantageous quantum correlation.

Abstract The two-qubit controlled-not (C-NOT) gate is an essential component for gate-based quantum circuits. In fact, its operation, combined with single qubit rotations allows to realise any quantum circuit. Several strategies have been adopted in order to build quantum gates. Among them, photonics offers the dual advantage of excellent isolation from the environment and ease of manipulation at the single qubit level. Here we adopt a scalable time-multiplexed approach in order to build a fully reconfigurable architecture capable of implementing a post-selected C-NOT gate with a fidelity of (93.8 ± 1.4)%. We then show how our time-multiplexed platform can be employed to combine a C-NOT and a single qubit gate in order to generate the four Bell states.

Advancements in photonic platforms have enabled the precise control of light's spectral and temporal degrees of freedom, a capability crucial for the development of scalable quantum information systems. In this work, we address the challenge of implementing spectro-temporal mode-selective non-Gaussian quantum operations, specifically single-photon subtraction (SPS) and addition (SPA), in the telecom wavelength regime. Building on prior experimental demonstrations of mode-selective near-infrared SPS, we present the first design framework for achieving mode-selective SPA and SPS using thin-film lithium niobate nonlinear waveguide platforms. We introduce an inverse-design optimization scheme by modeling the quantum-optical response via the Joint Spectral Amplitude and Transfer Function, in order to identify optimal waveguide and pump parameters that maximize mode selectivity and state purity. This approach is first tested on a metallic waveguide design. We then exploit the dispersion engineering capabilities of thin-film waveguides, which offer enhanced nonlinear interactions through tighter light confinement. Our findings demonstrate that tailored nonlinear processes, particularly parametric down-conversion and frequency up-conversion, can support high-fidelity non-Gaussian operations essential for next-generation quantum photonic networks.

Hybrid quantum photonics seeks to combine the complementary advantages of continuous- and discrete-variable quantum optics. This typically entails photon-counting measurements on entangled states generated by interfering many single-mode squeezed-vacuum (SMSV) states. However, because conventional photon-counting schemes are mode-insensitive, it is critical that the SMSV states occupy a single, well-defined mode. Achieving this requires careful engineering of the process, which determines both the spatial and spectro-temporal properties of the generated state. In addition, the ideal source must be massively scalable, capable of efficiently generating strong squeezing, and remain compatible with existing detection schemes and fiber networks. Although many platforms address one or more of these requirements, satisfying all of them simultaneously remains challenging. Here, we present a source that meets all of these requirements: a single-pass, periodically poled, Type-II potassium titanyl phosphate (KTP) waveguide optimized for scalable hybrid quantum-photonic architectures. The SMSV state produced by the source has a measured effective mode number of 1.24. Furthermore, the source is extremely bright (producing up to 40 000 photons per pulse) and operates at a central wavelength of 1546nm, optimized for fiber-network compatibility and which, in combination with picosecond duration, also enables intrinsic photon-number resolution in superconducting nanowire single-photon detectors. Although this source constitutes an ideal source in a simplified picture, the ultimate limitations of any source will be governed by complex dynamics that arise when the system is driven at high-gain or due to unavoidable loss during state generation. We have therefore developed a complete theoretical framework that enables a comprehensive photon-counting-based characterization of the source.

We provide experimental validation of tight entropic uncertainty relations for the Shannon entropies of observables with mutually unbiased eigenstates in high dimensions. In particular, we address the cases of dimensions d = 3, 4 and 5 and consider from 2 to d+1 mutually unbiased bases. The experiment is based on pulsed frequency bins measured with a multi-output quantum pulse gate, which can perform projective measurements on a complete high-dimensional basis in the time-frequency domain. Our results fit the theoretical predictions: the bound on the sum of the entropies is never violated and is saturated by the states that minimize the uncertainty relations.

Precise measurements of both the arrival time and carrier frequency of light pulses are essential for time-frequencyencoded quantum technologies. Quantum mechanics, however, imposes fundamental limits on the simultaneous determination of these quantities. In this work, we derive and experimentally verify the quantum uncertainty bounds governing joint time-frequency measurements. We show that when detection is restricted to finite time windows, the problem is naturally described by a quantum rotor, rendering the commonly used Heisenberg uncertainty relation inapplicable. We further propose an optimal detection scheme that saturates these fundamental limits. By sampling the Q-function, we demonstrate the reconstruction of the Wigner function beyond the harmonic oscillator. Using an experimental implementation based on a quantum pulse gate, we confirm that the proposed scheme approaches the ultimate quantum limit for simultaneous time-frequency measurements. These results provide a framework for joint time-frequency detection with direct implications for precision measurements and quantum information processing. (c) 2026 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

We introduce a method for determining the sensitivity of any given Entangled Two-Photon Absorption (ETPA) measurement. By modeling all signal and noise contributions to the measurement, we derive a single numerical value that describes the sensitivity of the ETPA measurement in Göppert-Mayer units. This allows us to directly compare vastly different experimental approaches and, determine whether ETPA will be detectable under the given conditions. Therefore, we can quantify the effect of any change to a given experimental apparatus and identify the ideal optimization pathway.

In this work, we demonstrate a quantum pulse gate (QPG) in thin-film lithium niobate. QPGs enable the selective manipulation and detection of temporal modes of quantum light and form the basis of numerous applications in photonic quantum technologies. To date, their widespread adaption is held back by two main limitations: restricted wavelength and polarization combinations of the involved fields and low normalized conversion efficiencies. We overcome these limitations through developing a QPG in thin-film lithium niobate. We design a waveguide geometry that provides the required dispersion properties for a highly efficient type-0 sum-frequency generation.We verify our design through mapping of the phase matching intensity, and demonstrate high-quality QPG operation by measuring a temporal-mode selectivity of (96.8±1.7)

Spectrally pure and indistinguishable single photons are essential for quantum network platforms, where high-visibility interference underpins many quantum information protocols. However, most practical single-photon sources emit spectrally multimode states with reduced purity. Conventional spectral intensity filtering can partially improve purity but cannot select a well-defined temporal mode (TM). Here, we demonstrate coherent temporal filtering of a multimode parametric down-conversion (PDC) source using a quantum pulse gate (QPG) and benchmark its performance against conventional intensity filtering. The generated PDC photons exhibit strong spectral correlations, rendering extraction of pure heralded photons from the pair a challenge. We demonstrate that QPG filtering consistently generates heralded photons with purities above 0.90 regardless of the filter shape. Contrariwise, using spectral intensity filters yields mixed photons. Photon purities are probed with chronocyclic Q-function tomography. Furthermore, we demonstrate the versatility of QPG filtering by extracting structured TMs, including superposition of picosecond time bins. These results establish the QPG as a practical coherent filtering tool for quantum network applications.

The field of high-dimensional quantum photonics involves the use of multimode photonic degrees-of-freedom such as the spatial, temporal, or spectral structure of light to encode multi-level quantum states. Recent years have seen rapid progress in the development of methods to generate, manipulate, and distribute such quantum states of light and their use in a range of quantum technology applications that offer practical advantages over conventional qubit-based approaches. High-dimensional quantum states of light encoded in photonic time-bins, frequency-bins, transverse-spatial modes, waveguide paths, and temporal modes have enabled noise-robust fundamental tests of quantum mechanics, error-resilient and high-capacity quantum communication protocols, andas well as efficient approaches for quantum information processing, to name just a few examples. However, research in this field has progressed fairly independently, with little exchange across different photonic degrees-of-freedom or between experiment and theory and no comprehensive comparison between degrees-of-freedom. This roadmap aims to bridge this gap by surveying progress in each area and identifying shared challenges and opportunities that cut across two or more photonic degrees-of-freedoms. We review early work and state-of-the-art experimental techniques under development for high-dimensional quantum states encoded in single and entangled photons, as well as theoretical tools for their measurement and certification. We outline the main outstanding challenges for theory and each experimental degree-of-freedom, identifying promising future directions of research that may enable these to be overcome. We end by discussing interconnections and shared challenges centered around their distribution, measurement, and manipulation, with a view towards their integration into next-generation quantum technology platforms and applications.

Photon counting is a cornerstone of quantum optics. Here, we demonstrate precisely counting from 0 to over 9000 photons, beating the Poisson noise limit by at least 4.1 dB across this range. We achieve sub-single-photon precision up to 276 photons per pulse. To do so, we multiplex eight intrinsically photon-number-resolving superconducting nanowire single-photon detectors across 128 temporal modes. We use a model-informed characterization of each of the 1024 detection bins, for optimal precision. We perform quantum detector tomography to reconstruct the positive operator valued measures (POVMs) of the complete device, which consists of 1.38·10^8 matrix elements. At the repetition rate of our experiment of 80 kHz, we can precisely count photons corresponding to an optical power of approximately 71 pW, bridging the gap from single-photon measurements to high-sensitivity optical power meters. A photon-number-resolving detector of this size, and the tools used to analyze it, will become increasingly important to characterize large quantum states, as well as tasks in precision metrology and optical power standards.

The development of practical sensors for optical coherence tomography (OCT) with undetected photons requires miniaturization via integration. To be practical, these sensors must exhibit a large spectral bandwidth and a high brightness, which are linked to a high axial resolution and a sufficient signal-to-noise ratio, respectively. Here, we combine these requirements in a scheme for OCT measurements with undetected photons based on nonlinear Ti:LiNbO3 waveguides. We investigate the performance benchmarks of the commonly used SU(1,1) scheme in comparison to an induced-coherence scheme and find that the latter is actually better suited when implementing measurements with undetected photons in integrated systems. In both schemes, we perform pump-gain optimization and OCT measurements with undetected photons with an axial resolution as low as 28 & micro;m.

The characterization of the complex spectral amplitude, that is, the spectrum and spectral phase, of single-photon-level light fields is a crucial capability for modern photonic quantum technologies. Since established pulse characterization techniques are not applicable at low intensities, alternative approaches are required. Here, we demonstrate the retrieval of the complex spectral amplitude of single-photon-level light pulses through measuring their chronocyclic Q -function. Our approach draws inspiration from quantum state tomography by exploiting the analogy between quadrature phase space and time-frequency phase space. In the experiment, we perform time-frequency projections with a quantum pulse gate (QPG), which directly yield the chronocyclic Q -function. We evaluate the complex spectral amplitude from the measured chronocyclic Q -function data with maximum likelihood estimation (MLE), which is the established technique for quantum state tomography. The MLE yields not only an unambigious estimate of the complex spectral amplitude of the state under test that does not require any a priori information, but also allows for, in principle, estimating the spectral-temporal coherence properties of the state. Our method accurately recovers features such as jumps in the spectral phase and is resistant against regions with zero spectral intensity, which makes it immediately beneficial for classical pulse characterization problems.

Ultrafast single-photon pulses with tailored time-frequency properties are highly attractive for quantum information science, offering high-dimensional encoding and compatibility with integrated optics platforms. However, accurate characterization of such pulses, including spectral coherence, remains challenging because current methods require substantial experimental resources and complex reconstruction algorithms. Here, we introduce frequency-bin interferometry for reconstructing electric fields with low intensity (FIREFLY), a technique that directly provides spectral amplitude, phase, and coherence profiles of single-photon pulses without requiring intensive reconstruction algorithms. Our approach measures the two-point spectral correlation function of the pulse by interfering its different frequency components using a quantum pulse gate (QPG) driven by a reference pump pulse. We demonstrate its compatibility with quantum light by characterizing partially coherent pulses generated by a type-0 parametric down-conversion process. We also overcome this requirement of a known pump pulse by introducing spectral shear into our interferometric scheme using a multi-output QPG (mQPG). This enables simultaneous characterization of a single-photon-level input pulse alongside an unknown pump pulse. Notably, our method achieves theory-experiment similarity above 95% across all retrieved profiles, which demonstrates the reliability of this scheme for quantum information applications based on time-frequency encodings.