Soliton microcombs have emerged as a promising integrated light source for applications ranging from coherent communications to precision metrology. However, their coherence remains limited by intrinsic and technical noise. While conventional two-point locking techniques can suppress these noises by simultaneously stabilizing both the pump and a sideband comb line, they typically require two external lasers, complicating system integration. In contrast, sideband self-injection locking (SSIL) achieves stabilization with only a single pump laser by feeding a selected comb line back into the cavity. This approach not only narrows the linewidth of the target comb line but also reduces the soliton timing jitter through optical frequency division. However, existing SSIL implementations demand high feedback ratios and suffer from significant insertion loss in the feedback loop, necessitating optical amplifiers and undermining system simplicity. Here, we present a systematic numerical study demonstrating that locking the feedback loop to a dispersive wave (DW) generated via soliton Cherenkov radiation drastically reduces the required feedback ratio by over an order of magnitude. This reduction arises from the DW's enhanced coupling and intracavity power, enabling efficient SSIL with low optical feedback. Consequently, the stringent optical amplifier requirement is eliminated, allowing fully passive stabilization. Our work deepens the understanding of SSIL dynamics in Kerr combs and provides a feasible, power-efficient strategy for stabilizing soliton microcombs in chip-scale systems.

Nonlocal interactions between photonic resonator array and giant atoms have attracted extensive attentions. Optimization and control of quantum states via giant atoms have been shown. We here study the dynamical scattering of a single-photon wave packet by a giant atom coupled to a two-dimensional photonic resonator array via multiple spatial points. Using several iterations of time evolutions, we can prepare an expected wave packet with a stable size and use it as the incident state for the scattering process. We show that spatially symmetric or asymmetric target scattering states of single-photon wave packet can be generated by adjusting the coupling strengths between the giant atom and different lattice sites of the resonator array. Furthermore, the dynamical scattering of the wave packets enables us to study the atomic excitation and propagating properties of the scattering states. We find that the atomic excitation has negligibly small probability during the scattering process. Our study may provide a new way to generate an expected photon state via photon scattering by a giant atom in two-dimensional photonic array.

We study the single-photon scattering process and the single-excitation bound states in a waveguide QED system where a giant atom (GA) couples simultaneously to a one‐dimensional coupled-resonator waveguide and an yttrium iron garnet (YIG) sphere. For a stationary YIG sphere, we demonstrate that the magnon-atom coupling strength provides flexible control over the transmission spectrum, enabling magnon‐driven single‐photon transport and bound states. When the YIG sphere spins, the resulting Barnett effect induces tunable photon routing: Incident photons are fully transmitted (reflected) when the bias magnetic field is parallel to the YIG sphere's angular velocity, whereas they are entirely reflected (transmitted) when the bias magnetic field is antiparallel to the YIG sphere's angular velocity. By increasing the separation between the GA's coupling points, we further realize a single‐photon switch with either broad operational bandwidth or multiple operational frequencies. We also show that large detuning between the GA and the magnon mode suppresses the effect of the magnetically controlled single-photon switch via effective dispersive coupling, and we identify magnon‐controlled bound states that facilitate directional quantum storage. Finally, we simulate the dynamics of single-photon scattering, analyze the time evolution of magnon excitation and the atomic population, and discuss the dependence of magnon excitation on the magnon-atom coupling strength, Barnett frequency shift, and wave vector of the single-photon wave packet. Our work opens a way for realizing a magnon-modulated quantum single-photon switch and has potential applications in quantum engineering and scalable quantum networks.

Stellar rank of quantum state of light quantifies the amount of non-Gaussian resources required for its generation. One popular and practical approach to certification of stellar rank is based on measurement of click statistics with an array of binary detectors that can only distinguish the presence and absence of photons. Specifically, it was shown that measurements with an array of $m+1$ detectors allow one to certify stellar rank $m$ of approximate Fock state $|m\rangle$, even when the state is subjected to losses or certain noise. Here we address the question as to how many click detectors are in principle required to certify stellar ranks higher than one. We show that two click detectors arranged in a Hanbury Brown-Twiss setup suffice. Interestingly, detection of stellar ranks higher than one is greatly facilitated by making the total detection efficiency of the detectors sufficiently low but well calibrated. Losses affect the response of the detection scheme in a way that can be exploited to certify stellar rank of higher Fock states. We explicitly construct the corresponding stellar rank witnesses and discuss dependence of the stellar rank thresholds on parameters of the considered setup. Our results reveal that it is possible to certify stellar ranks higher than 1 even with a minimalistic scheme that provides only very coarse-grained information about the photon number statistics of the characterized state.

We study the quantum statistics of single-mode radiation emitted by an atomic ensemble when the ensemble is initially prepared in a superradiant Dicke state. We show that while the radiation is well approximated by the Glauber coherent state at early times in the evolution, the emission can be truly quantum at later times. In particular, one can observe a large amount of photon-number squeezing in the emission under certain conditions; even a Fock state can be produced. We discuss the quantum statistics of the emission for various parameters, including different initial conditions for the atomic ensemble. To obtain these results, we have developed a formalism where we are able to calculate the quantum statistics of the emission over long time scales even when the number of atoms in the ensemble is quite large.

We present a detailed theoretical treatment of four-wave mixing (FWM) in a quantized paraxial framework, capturing the multi-spatial-mode nature of the biphoton state generated in the process. By analyzing the biphoton state in both position and momentum representations, we identify the conditions under which these descriptions become equivalent. We also highlight formal and physical similarities between FWM and spontaneous parametric down-conversion, showing that the transfer of pump structure to the spatial coincidence profile, an important and well-known characteristic of the biphoton state, carries over naturally to FWM. In addition, our treatment captures the transition from position correlations in the near field to momentum correlations in the far field, reflecting the underlying spatial entanglement. The measures of entanglement, including the spiral bandwidth and the Schmidt rank, are discussed. Our work consolidates known and new results on spatial correlations in FWM and provides a theoretical framework to support future studies in nonlinear and quantum optics with structured light.

Quantum state tomography (QST) is crucial for understanding and characterizing quantum systems through measurement data. Traditional QST methods face scalability challenges, requiring $\mathcal{O}\left(d^2\right)$ measurements for a general $d$-dimensional state. This complexity can be substantially reduced to $\mathcal{O}\left(d\right)$ in pure state tomography, indicating that full measurements are unnecessary for pure states. In this paper, we investigate the conditions under which a given pure state can be uniquely determined by a subset of full measurements, focusing on the concepts of uniquely determined among pure states (UDP) and uniquely determined among aall states (UDA). The UDP determination inherently involves nonconvexity challenges, while the UDA determination, though convex, becomes computationally intensive for high-dimensional systems. To address these issues, we develop a unified framework based on the mugmented Lagrangian ethod (ALM). Specifically, our theorem on the existence of low-rank solutions in QST allows us to reformulate the UDA problem with low-rank constraints, thereby reducing the number of variables involved. Our approach entails parametrizing quantum states and employing ALM to handle the constrained nonconvex optimization tasks associated with UDP and low-rank UDA determinations. Numerical experiments conducted on qutrit systems, generalized Greenberger-Horne-Zeilinger states and four-qubit symmetric states not only validate theoretical findings but also reveal the complete distribution of quantum states across three uniqueness categories: (a) UDA, (b) UDP but not UDA, and (c) neither UDP nor UDA. This work provides a practical approach for determining state uniqueness, advancing our understanding of quantum state reconstruction.

Most existing studies of quantum walk focus on unitary closed systems, while the nonunitary counterpart, relevant to open quantum systems, remains relatively unexplored. This paper analyzes the position distribution and variance of quantum walk under the specific nonunitary evolution operator. Our results reveal that the variance exhibits distinct dynamical behavior depending on angular parameters, spatial dimensions, and initial states. In particular, for the one-dimensional non-Hermitian two-band lattice model, we demonstrate that the variance grows quadratically with time steps in the short-time regime, indicating faster diffusion than classical random walk. Leveraging this acceleration, we further propose a teleportation protocol based on nonunitary quantum walk, which eliminates the need for entangled state preparation and thereby reduces resource overhead while enhancing information transfer efficiency.

Physics-informed neural networks (PINNs) have emerged as powerful tools for solving partial differential equations (PDEs) in computational physics. However, most existing approaches rely on problem-specific architectures or require retraining for each new equation or boundary condition. In this work, we present an energy-embedded PINN framework for solving the one-dimensional time-independent Schrödinger equation, capable of obtaining both ground- and excited-state wave functions and energy eigenvalues within a unified, parameter-free architecture. By treating energy as a continuous input and incorporating an embedding layer, the network efficiently learns the entire quantum spectrum without training separate models for each eigenstate. Numerical results show that this method achieves a high precision across various potentials—including infinite wells, harmonic oscillators, Woods-Saxon, and double-well potentials—with minimal errors in both energies and wave functions, where orthogonality emerges naturally during training. As a general-purpose, structure-free approach, the method reported in this study provides an alternative strategy for analyzing quantum observables and for scanning energy spectra under arbitrary one-dimensional interaction potentials. Its successful extension to the radial Coulomb problem demonstrates its adaptability to broader classes of Schrödinger-type systems and may open new paths toward solving quantum many-body and nuclear problems in the future.

We present a method for describing the time evolution of many-body controlled quantum systems using matrix product operators (MPOs). Existing techniques for solving the time-dependent Schrödinger equation with an MPO Hamiltonian often rely on time discretization. In contrast, our approach uses the Magnus expansion and Chebyshev polynomials to model the time evolution and the MPO representation to efficiently encode the system's dynamics. This results in a scalable method that can be used efficiently for many-body controlled quantum systems. We apply this technique to quantum optimal control, specifically for a gate synthesis problem, demonstrating that it can be used for large-scale optimization problems that are otherwise impractical to formulate in a dense matrix representation.

Discrete modulation continuous-variable quantum key distribution protocols are compatible with modern coherent optical communication technologies and devices. As a key part of the protocol, the performance of information reconciliation directly affects the secret key rate and transmission distance. Herein, we propose a reconciliation scheme for hard-decision strategy–based discrete modulation continuous-variable quantum key distribution protocol with eight-phase shift keying by combining slice reconciliation and raptor-like low-density parity-check (RL-LDPC) codes. We design the optimal binary sequence encoding of the discretized values of the receiver and sender, which reduce both the number of levels of error correction and the reconciliation complexity. In order to reduce the frame error rate, both the degree distribution and the size of the base matrix of RL-LDPC code is optimized. Simulation results show that the proposed scheme can reach reconciliation efficiencies of 92.05% and 93% with frame error rates of 6.2% and 11.7% at the signal-to-noise ratio of 0.15, respectively. At these points, the key rates can reach 0.0193 and 0.0195 bits/pulse, respectively.

The rigorous quantum-electrodynamic (QED) approach is employed to calculate the energies of the $2p2p{}^3{P}_{0,1,2}$, $2p2p{}^1{D}_2$, and $2p2p{}^1{S}_0$ states of selected Be-like highly charged ions over a wide range of nuclear-charge numbers, $18⩽Z⩽92$. Combined with the previously reported energies of the $2s2p{}^3{P}_{0,1,2}$ and $2s2p{}^1{P}_1$ states [A. V. Malyshev et al., Phys. Rev. A 110, 062824 (2024)], the obtained results are used to study various intra-$L$-shell transition energies. Strong level mixing, caused by the proximity of states with the same symmetry, is overcome by means of the QED perturbation theory for quasidegenerate levels. The applied approach merges a rigorous perturbative QED treatment up to the second order with the consideration of electron-electron correlation contributions of the third and higher orders evaluated within the Breit approximation. The higher-order screened QED effects are estimated using the model-QED-operator approach. The nuclear-recoil and nuclear-polarization effects are also taken into account. The obtained predictions represent the most accurate theoretical description of the electronic structure of Be-like ions to date and demonstrate good agreement with available experimental data.

We introduce a non-Hermitian photonic filter that harnesses dissipation to selectively isolate a desired topological state. In science and engineering, dissipation is often used to filter incoherent waves, producing a pure coherent output. Here, we apply this principle to topological states, creating a linear filter that effectively isolates a specific topological state regardless of the initial input's coherence properties. This approach creates a dissipation-free topological subspace, where the desired states are preserved and their topological protection is enhanced. Our work provides a versatile and simple method for topological state selection, opening the door to new applications in integrated topological photonics.

Current models of quantum interference experiments in external gravitational fields lack a common framework: while matter-wave interferometers are commonly described using the Schrödinger equation with a Newtonian potential, gravitational effects in quantum optics are modeled using either post-Newtonian metrics or highly symmetric exact solutions to Einstein's field equations such as those of Schwarzschild and Kerr. To coherently describe both kinds of experiments, this paper develops a unified framework for modeling quantum interferometers in general stationary space-times. This model provides a rigorous description and coherent interpretation of the effects of classical gravity on quantum probes.

Quantum entanglement systems based on qudits dilate high-dimensional (HD) state spaces and enhance resistance to loss in quantum information processing (QIP). To fully exploit this potential, effective schemes for generating HD entanglement are crucial. In this paper, we propose a flexible heralded scheme generating random four-dimensional (4D) two-qudit maximal entanglement for a hybrid photon-emitter system by entering different input ports. This approach can be further extended to prepare 4D $n$-qudit $(n\ge 3)$ maximal entanglement utilizing the 4D single-qudit $Z^m(m=1,2,3)$ gate for the first qudit and $X^m$ gate for the other qudits (except the second qudit). For the hybrid system, the first 4D qudit is encoded on the hybrid polarization-path states of a flying photon, while the second and subsequent 4D qudits are represented by two stationary emitters coupled to the respective 1D waveguide. The qudit-encoded hybrid HD entanglement offers advantages over economizing quantum resource without any auxiliary qudits and obtaining robust fidelities of various HD entanglement by the error-detected mechanism of the emitter-waveguide systems. Moreover, the proposed protocol can be spread to generate $d\mathrm{D}$ $n$-qudit $(d\ge 2^{p+1},$ $n,p=2,3,\cdots )$ entangled states, further broadening its applicability in HD QIP.

In this article, we present quantum algorithms for estimating von Neumann entropy and Renyi entropy, which are crucial physical and information-theoretical properties of a given quantum state $\rho$. Although there have been existing works that have achieved the same goal, some prior developments assume the unitary that prepares the purification to the target state $\rho$. Here, we consider an alternative setting where only copies of $\rho$ are given and we construct a quantum algorithm that estimates the desired entropy. Our framework completes the given task by measuring a small number of ancilla qubits without directly measuring the system, and it achieves significant improvement over prior relevant developments. For example, for the Renyi entropy of the order of nonintegral $\alpha$, our method achieves almost a power-of-2 improvement in sample complexity with respect to the rank of the given state and almost a power-of-2 improvement in error tolerance compared with the work by Wang et al. [Y. Wang, B. Zhao, and X. Wang, Phys. Rev. Appl. 19, 044041 (2023)].