Achieving high end-to-end efficiency and broadband quantum memory of squeezed light is crucial for continuousvariable quantum information processing. Existing demonstrations fail to store squeezed states across their full squeezing bandwidth. Here, we present a full-bandwidth quantum memory of squeezed light with up to 24 MHz bandwidth, which is at least 12 times that of previous narrowband resonant memory systems, via a far-off resonant Raman process. We achieve output squeezing as high as 1.0 f 0.29 dB, with fidelity above 92 f 0.5% and a memory efficiency of 80%, corresponding to an end-to-end efficiency of 64.2 f 0.7% when input squeezing is 1.6 f 0.23 dB. The lowest excess noise of 0.025 shot-noise unit in the memory system is estimated by the noisy model, which benefits from optimizing quantum memory performance with a backward-retrieval strategy. Our results show high-performance memory for squeezed states within tens of MHz-level bandwidth, which has potential applications in high-speed quantum information processing. (c) 2026 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

Squeezed light in the audio-frequency band is a key resource for quantum metrology and quantum sensing. However, realizing stable audio-frequency squeezed light on integrated photonic platforms remains challenging due to technical noise and the difficulty of scalable phase referencing. Here, we demonstrate on-chip generation of audio-band two-mode squeezed states down to 60 Hz in a silica microcavity. To enable phase-stable operation without directly locking fragile quantum modes, we develop a coherent-comb control method in which a weak electro-optic reference comb co-propagates with the vacuum at the quantum frequency modes in an orthogonal polarization. This scheme provides quadrature measurement and long-timescale phase stability, thereby enabling covariance-matrix reconstruction. We verify the entanglement with the positive partial transposition criterion, which confirms inseparability via a minimum symplectic eigenvalue of 0.395 (<0.5). Our results establish an experimentally accessible route toward on-chip phase-stable audio-band squeezing and support the scalable framework for continuous-variable quantum information processing with integrated photonics.

Transport equations describe how physical quantities – such as mass, energy, momentum, concentration, probability, or fields – are carried, propagated, or redistributed through space and time, forming a foundational class of partial differential equations across science and engineering. However, high-dimensional partial differential equations are difficult to represent on digital grids because the number of degrees of freedom grows exponentially with dimension. Continuous-variable quantum photonics on the other hand can represent and evolve these large-scale fields without first discretizing space into a discrete grid. We demonstrate a large-scale analog photonic simulator for the constant-coefficient advection equation, a transport equation that is a fundamental benchmark for scientific computing. The solution of a d-variable advection equation is encoded into d optical modes, so that the partial differential equation evolution maps directly to programmable phase-space displacements generated by optical quadrature momenta. Using a time-domain continuous-variable quantum photonic platform, we validate programmable control with 20,000 single-mode squeezed states and 20,000 two-mode squeezed states, and implement transport dynamics on a 20,000-mode cluster-state resource. Homodyne measurements then verifies mode-resolved displacement control, which can provide first and second-order moment information of the solution to the advection equation, with final achievable relative error as low as 0.8% and 0.92% for first and second-order moment observables respectively. Our results establish continuous-variable photonics as a suitable programmable analog platform for large-scale advection equations.

The development of large-scale, high-fidelity quantum processors is a fundamental scientific challenge, essential for exploring the boundaries of classical computation and advancing towards fault-tolerant systems. Gaussian boson sampling not only serves as a prominent model for demonstrating quantum computational advantage1-3 but can also generate bosonic error-correcting codes for fault-tolerant quantum computing4-6. However, its scalability has been hindered by significant photon loss in increasingly large and complex encoding circuits. Here we show a programmable photonic quantum processor, Jiuzhang 4.0, which incorporates 1,024 high-efficiency squeezed states into a hybrid spatial-temporal encoded 8,176-mode circuit. By achieving 92% source efficiency and 51% overall system efficiency, the processor produces samples with detection events up to 3,050 photons, representing an order-of-magnitude increase in scale over previous demonstrations7-10. This architecture realizes a cubic scaling of connectivity (163 = 4, 096), enabling sampling within a Hilbert space of dimension approximately 102,461. The experimental results are rigorously validated against all current classical simulation methods, especially the matrix product state algorithms recently designed to exploit photon loss11. The ability to control thousands of photons in programmable low-loss quantum processors pushes the experimental frontier into a regime far beyond classical tractability and opens a pathway to trillion-qumode three-dimensional cluster states and fault-tolerant photonic quantum hardware.

Broadband bright squeezed states are important quantum resources that play a crucial role in quantum information and quantum measurement. Here, we present the broadband bright pulsed squeezed states generated by a single-pass optical parametric amplification based on a custom-poled potassium titanyl phosphate crystal. By optimizing the spatial mode of the picosecond pump beams, a bright squeezed light with 1.7 dB squeezing and output power of 5 mW is obtained. With a spatial light modulator, the spatial distribution of the bright squeezed light is shaped into perfect vortex beams with topological charges up to , while the squeezing level is 1.4 dB. The presented squeezed states provide essential resources for advanced quantum optics applications. Graphical Abstract

A squeezed state is a key quantum resource for quantum information processing and quantum metrology. It is essential to extend the dimension of the squeezed state for spatially multiplexed large-capacity quantum communication and quantum precision measurements. Here, we report the experimental preparation of a picosecond pulsed squeezed state carrying orbital angular momentum (OAM). By modulating bright pulsed squeezed light with a spatial light modulator, we generate a squeezed state with Laguer re-Gaussian distribution, whose topological charges are up to l = 20 and squeezed noise is 1.22 dB below the shot noise level. The presented bright picosecond pulsed squeezed light carrying high-order OAM provides promising resources for high-dimensional quantum information processing.

As a powerful tool of biological imaging, stimulated Raman scattering (SRS) microscopy enables rapid, label-free imaging with high molecular specificity. In the application of SRS microscopy, it is essential to break the optical diffraction limit and enhance the resolution. Here, we demonstrate an effective method that combines antiphase demodulation with a deconvolution algorithm to achieve super-resolution SRS imaging. By introducing a donut-shaped pump beam with antiphase modulation in SRS microscopy, the signal around the focal center is effectively suppressed, enabling subdiffraction-limited imaging. Followed by a deconvolution algorithm, we obtain a 3.5-fold improvement in spatial resolution using human hair as a test specimen. The result offers a practical method for super-resolution SRS microscopy without significant sample damage, broadening applications in super-resolution, label-free biological imaging.

Photonic integrated circuits provide a controllable and scalable platform for quantum information processing. In particular, continuous-variable integrated photonic quantum devices-which encode quantum information in the quadratures of optical qumodes-provide distinct advantages, although generating multimode entanglement in such systems has remained a key challenge. Here we demonstrate a monolithic integrated quantum photonic circuit that enables the full on-chip generation, manipulation and measurement of continuous-variable multi-qumode cluster-state entanglement. The device incorporates strongly squeezed quantum light sources with wafer-scale scalability, high-fidelity single-qumode and two-qumode entangling gates, and local oscillators and interferometers for balanced homodyne detection-all on a single chip. This co-integration enables the preparation, control and measurement of four-qumode cluster states and individual qumodes with high stability and high fidelity. The monolithic integration of high-performance devices allows rigorous verification of genuine multipartite entanglement with unambiguous cluster-state structures. This work establishes a controllable and scalable platform for optical quantum computing, networking and sensing.

In addition to carrying spin angular momentum (SAM), light can also possess orbital angular momentum (OAM), whose quantum number can, in principle, take any integer value. This property provides a new degree of freedom to expand the capacity of both classical and quantum information. In recent years, generating OAM multiplexed continuous-variable entanglement via four-wave mixing (FWM) has emerged as an effective approach to increasing the capacity of quantum information channels. Consequently, there is a growing demand for precise characterization of the OAM spectrum in such quantum beams. Here we present, to the best of our knowledge, the first experimental demonstration of OAM spectrum measurement in quantum optics using phase-shifting interferometry (PSI). This method enables accurate characterization of the OAM spectrum of both the probe and conjugate beams in OAM multiplexed continuous-variable entanglement generated via the FWM process. These results provide an experimental foundation for the reliable detection and utilization of multiplexed OAM degrees of freedom in quantum communication and quantum information processing.

Quantum entanglement and quantum steering, as important quantum resources, are of great significance in the field of quantum information science. Toward practical quantum communication, it is essential to distribute Gaussian entanglement and quantum steering through optical fiber channels. Here, we experimentally demonstrate the distribution of deterministic Einstein-Podolsky-Rosen (EPR) entanglement and EPR steering through fiber channels. By transmitting the EPR entangled light and the local oscillator (LO) over independent fiber channels, the excess noise in the quantum channel is reduced. Utilizing this transmission approach, we extend the transmission distance of continuous-variable (CV) entanglement distribution to 60.26 km and that of CV EPR steering to 10.06 km in fiber channels. Our results take a crucial step toward practical quantum communication with CV entanglement and quantum steering in fiber channels.

Convolution, a cornerstone of signal processing and optical neural networks, has traditionally been implemented by mapping mathematical operations onto complex hardware. Here, we overcome this challenge by revealing that wave dynamics in translation-symmetric lattices intrinsically performs convolution, with the dispersion relation uniquely defining the complex-valued kernel. Leveraging this universal principle, we develop a convolutional architecture of minimal complexity through wave evolution in programmable photonic synthetic lattices, delivering high-throughput, multifunctional capabilities at a rate of 13.5 tera-operations per second (TOPS) for image processing. Beyond convolution acceleration, the kernel's complex nature facilitates the photonic simulation of both irreversible diffusion and reversible unitary quantum dynamics under classical incoherent excitation. Capitalizing on the physics-based reversibility and undetectable phase information, we demonstrate a convolution-driven optical encryption strategy. This work establishes a unified perspective for photonic computing by grounding convolution in wave dynamics, opening avenues toward scalable, multifunctional photonic processors with high integration potential.

Entanglement-assisted quantum communication has substantial advantages in surpassing the power of classical communication by utilizing the entangled state. Up to now, most of entanglement-assisted quantum communications with dense coding are limited to the proof-of-principle experiments. Here, we experimentally demonstrate the deterministic entanglement-assisted quantum communication based on the continuous-variable (CV) entangled state over 20 km commercial fiber channels. We propose a new CV dense coding scheme with improved classical signals and show that the transmission distance of CV entanglement-assisted quantum communication can be extended compared with that using fixed classical signals. By applying the frequency division multiplexing technique, we simultaneously decode 10 classical signals submerged in the shot noise of coherent state with the help of CV entangled state after the transmission through a 20.121 km fiber channel. The results show that around 3 times of channel capacity in classical communication with coherent state are achieved in the CV entanglement-assisted communication with the frequency division multiplexing technique. Our result takes a crucial step towards realizing the deterministic metropolitan entanglement-assisted quantum communication in practical quantum channels.

Significance Quantum communication is an important research direction in quantum technology and is moving toward practical quantum communication systems and quantum networks. Entanglement-assisted quantum communication can complete quantum communication tasks that classical communication systems cannot accomplish and has yielded significant advances in recent years. Continuous-variable quantum communication systems based on quantum optical fields have advantages such as deterministic generation of quantum entanglement and high compatibility with classical optical communication systems, holding important application prospects in quantum communication. We briefly introduce the basic principles and progress of three key communication protocols in continuous-variable entanglement-assisted quantum communication, including quantum key distribution, quantum dense coding, and quantum teleportation, and discuss the problems and challenges facing continuous-variable entanglement-assisted quantum communication. Progress The research team at Shanxi University proposed the two-way quantum key distribution scheme based on continuous-variable entangled states in 2006, and subsequently experimentally realized continuous-variable quantum key distribution based on Einstein?Podolsky?Rosen (EPR) entangled states without signal modulation. Madsen et al. achieved the proof-of-principle verification of continuous-variable quantum key distribution based on modulated entangled states, and the transmission distance was extended over 50 km by Shanxi University's research team. Pirandola et al. extended the continuous-variable two-way quantum key distribution protocol that enhances the security threshold via bidirectional quantum communication. Furthermore, Mele et al. examined the tolerable excess noise limit in continuous-variable two-way quantum key distribution and determined the maximum transmission loss sustainable by continuous-variable quantum key distribution without the utilization of relays. Recently, it has been proven that by relaxing the trust premise on a subset of devices, when one party's device is untrusted, the security of quantum key distribution can still be guaranteed, which is known as one-sided device-independent quantum key distribution. Gehring et al. achieved proof-of-principle verification of continuous-variable one-sided device-independent quantum key distribution based on the EPR entangled state, and Walk et al. compared the performance of six kinds of one-sided device-independent quantum key distribution protocols. The concept of quantum dense coding was first proposed by Bennett and Wiesner. Zhang and Braunstein et al. extended quantum dense coding to the continuous-variable domain. Ralph et al. further studied the unconditional continuous-variable quantum dense coding and established the relationship between the channel capacity of dense coding (when different quantum states are employed) and the average photon number. In the aspect of experimental research, a series of significant progress has been made in continuous-variable quantum dense coding. The research teams at Shanxi University and the University of Tokyo verified the advantage of quantum dense coding in enhancing the channel capacity respectively. To further enhance the channel capacity of continuous-variable quantum dense coding, many teams have conducted experimental studies on multiplexed quantum dense coding. Currently, experimental verification of continuous-variable quantum dense coding based on two-component entangled optical fields has been achieved. However, the demonstration of quantum dense coding is limited to the proof-of-principle experiment, and it is urgent to verify the feasibility of quantum dense coding in practical quantum channels. Since the quantum teleportation scheme was first proposed by Bennett et al., it has caught extensive attention. In the theoretical research on continuous-variable quantum teleportation, researchers have established a comprehensive theoretical framework for quantum teleportation. In terms of experimental research, continuous-variable quantum teleportation has achieved a series of breakthroughs. Quantum teleportation of various quantum states, such as coherent states, squeezed states, entangled states, optical cat states, and optical qubits, has all been experimentally realized. In recent years, the fidelity of continuous-variable quantum teleportation has been improved with the advancement of experimental techniques, and it is gradually moving toward practical applications. The research teams at Shanxi University experimentally implemented continuous-variable quantum teleportation over 6 km and 10 km commercial fibers respectively, verifying the feasibility of continuous-variable quantum teleportation in fiber channels. Furthermore, to expand the bandwidth and channel capacity of quantum teleportation, the research team at East China Normal University realized all-optical quantum teleportation. Conclusions and Prospects We briefly introduce the basic principles and research progress of entanglement-assisted quantum communication based on continuous-variable entangled states, including entanglement-assisted continuous-variable quantum key distribution, quantum dense coding, and quantum teleportation. Currently, entanglement-assisted quantum communication is advancing toward quantum networks and practical application. In multi-user quantum communication based on multipartite entanglement, communication parties need the assistance of other users to complete communication tasks. Therefore, quantum communication based on multipartite entanglement usually manifests as controlled quantum communication. Additionally, the development of fiber-channel-based continuous-variable entanglement-assisted quantum communication is a crucial step for continuous-variable quantum communication to move toward practical applications.

The pulsed squeezed state plays a pivotal role in quantum information processing and precision measurement. In the detection of the pulsed squeezed state, the high noise power at its repetition rate prevents the achievement of a high signal-to-noise ratio (SNR). Therefore, a high-SNR detector that can suppress the high noise power of the repetition rate of pulsed light is very crucial. In this paper, we present a high-SNR resonant balanced photodetector that filters out the noise power of the repetition rate by introducing an LC series notch filter. A 24.37 dB attenuation is obtained at the 80 MHz repetition rate by finely adjusting the capacitance of the LC series notch filter. Consequently, the photodetector's maximum SNR is improved to 19.60 dB, which is 5 dB higher than previous studies. Our work provides a key detection tool for the measurement of the pulsed squeezed state.

Hybrid continuous-variable (CV) and discrete-variable (DV) entanglement is an essential quantum resource of hybrid quantum information processing, which enables one to overcome the intrinsic limitations of CV and DV quantum protocols. Besides CV and DV quantum variables, introducing more degrees of freedom provides a feasible approach to increase the information carried by the entangled state. Among all the degrees of freedom of photons, orbital angular momentum (OAM) has potential applications in enhancing the communication capacity of quantum communication and precision of quantum measurement. Here, we present the experimental preparation of hybrid entanglement carrying OAM, which involves three degrees of freedom including polarization, cat states, and OAM. By converting the wavefront of optical cat states with a q-plate, the OAM degree of freedom is introduced into the prepared hybrid entanglement between a polarization-encoded DV qubit and a cat-encoded CV qubit. Based on the measured topological charges l = 0, +1, +2 and reconstructed Wigner functions of the output states, the hybrid entangled states carrying OAM with l = 0, +1, +2 are confirmed with non-zero logarithmic negativities, respectively. Our work takes a crucial step towards extending the degree of freedom for hybrid entanglement, which provides a new quantum resource for hybrid quantum information processing.

The generation of large-scale entangled states is crucial for quantum technologies, such as quantum computation1, communication2 and metrology3. Integrated quantum photonics that enables on-chip encoding, processing and detection of quantum light states offers a promising platform for the generation and manipulation of large-scale entangled states4,5. Generating entanglement between qubits encoded in discrete variables within single photons is challenging, owing to the difficulty of making single photons interact on photonic chips6–11. Devices that operate with continuous variables are more promising, as they enable the deterministic generation and entanglement of qumodes, in which information is encoded in light quadratures. Demonstrations so far have been limited to entanglement between two qumodes12–20. Here we report the deterministic generation of a continuous-variable eight-mode entanglement on an integrated optical chip. The chip delivers a quantum microcomb that produces multimode squeezed-vacuum optical frequency combs below the threshold. We verify the inseparability of our eight-mode state and demonstrate supermode multipartite entanglement over hundreds of megahertz sideband frequencies through violation of the van Loock–Furusawa criteria. By measuring the full matrices of nullifier correlations with sufficiently low off-diagonal noises, we characterize multipartite entanglement structures, which are approximate to the expected cluster-type structures for finite squeezing. This work shows the potential of continuous-variable integrated photonic quantum devices for facilitating quantum computing, networking and sensing. Deterministic generation of a continuous-variable eight-mode entanglement on an integrated optical chip is reported.

The creation of large-scale, high-fidelity quantum computers is not only a fundamental scientific endeavour in itself, but also provides increasingly robust proofs of quantum computational advantage (QCA) in the pres- ence of unavoidable noise and the dynamic competition with classical algorithm improvements. To overcome the biggest challenge of photon-based QCA experiments, photon loss, we report new Gaussian boson sampling (GBS) experiments with 1024 high-efficiency squeezed states injected into a hybrid spatial-temporal encoded, 8176-mode, programmable photonic quantum processor, Jiuzhang 4.0, which produces up to 3050 photon de- tection events. Our experimental results outperform all classical spoofing algorithms, particularly the matrix product state (MPS) method, which was recently proposed to utilise photon loss to reduce the classical simula- tion complexity of the GBS. Using the state-of-the-art MPS algorithm on the most powerful supercomputer EI Capitan, it would take > 1042 years to construct the required tensor network for simulation, while our Jiuzhang 4.0 quantum computer takes 25.6 μs to produce a sample. This work establishes a new frontier of QCA and paves the way to fault-tolerant photonic quantum computing hardware.

In continuous-variable quantum information processing, it is crucial to develop high-efficiency and broadband quantum memory of squeezed light, which enables the storage of full-bandwidth information. Here, we present a quantum memory of squeezed light with up to 24 MHz bandwidth, which is at least 12 times that of previous narrowband resonant memory systems, via a far-off resonant Raman process. We achieve output squeezing of as high as 1.0 dB with fidelity above 92 end-to-end efficiency of 64.2 excess noise of 0.025 shot-noise-unit in the memory system is estimated by the noisy channel model which is benefited from optimizing quantum memory performance with a backward retrieval strategy. Our results represent a breakthrough in high-performance memory for squeezed states within tens of MHz-level bandwidth, which has potential applications in high-speed quantum information processing.

An intensity-differential squeezed state optical field prepared via four-wave mixing in a cesium atomic ensemble offers advantages such as wavelength matching with cesium atomic transition lines and a spatial multimode structure. This renders it valuable for quantum information applications. However, achieving high-compression-state optical fields through four-wave mixing in cesium atoms typically requires high pump light power and atomic pool temperature, thereby limiting its practicality. This study combines a six-mirror ring optical resonant cavity and a cesium atomic ensemble to achieve a single resonance of the pump light within the cavity while allowing the probe and conjugate lights to pass through in a single pass. This configuration improves pump light utilization and achieves cavity-enhanced cesium atomic four-wave mixing. Consequently, the required pump light power and atomic pool temperature are considerably reduced. Experimental results show that at an intensity-difference compression degree of-6 dB, compared to cavity-free four-wave mixing, the cavity-enhanced four-wave mixing reduces the required pump light power from 600 mW to 340 mW and the atomic cell temperature from 109 degrees C to 98 degrees C . These findings offer a new solution for developing low-power, spatially multimode quantum light sources. Further, they are crucial for advancing the application of four-wave mixing in atomic ensembles.