arXiv subjects

Lixiang Chen

Publications and source records attributed to Lixiang Chen.

At least 19 recordsLinked to original sources

arXiv2026

Generic properties of discrete Steklov eigenfunctions

Let $G=(V,E)$ be a finite connected graph with boundary $B$. We prove that for a generic positive edge weight function $w \in \mathbb{R}^{|E|}$, the Steklov eigenvalues of $(G,B,w)$ are simple and every Steklov eigenfunction does not vanish on the boundary. More precisely, the exceptional weights are contained in a zero set of a non-identically zero polynomial and hence form a set of Lebesgue measure zero and Hausdorff dimension at most $|E|-1$. Our results provide a discrete extension of the genericity theorem for the Steklov problem on compact manifolds.

math.CO↗

arXiv2026

Connecting Quantum Contextuality and Nonlocality

Quantum theory departs from classical physics in its treatment of correlations, most prominently through the phenomena of contextuality and nonlocality. Once regarded primarily as foundational curiosities, these effects are now understood as key operational resources for quantum computation, communication, and simulation. Although traditionally investigated in distinct settings, recent theoretical and experimental advances have revealed deep conceptual, mathematical, and operational connections between them. This review presents a unified perspective on these developments based on sheaf-theoretic and graph-theoretic frameworks, which provide theory-independent characterizations of statistical correlations. These approaches clarify the structural relationship between contextuality and nonlocality, facilitate the formulation of experimentally testable inequalities, and guide implementations in realistic physical platforms, with particular emphasis on photonic systems. By bridging abstract theoretical structures and concrete experimental realizations, this review sheds light on the nonclassical foundations of quantum correlations and their emerging role in quantum technologies.

quant-ph↗

arXiv2026

Discord-Enabled Teleportation-Inspired Optical Imaging at a Distance

In quantum teleportation, a pair of entangled photons are prerequisite to serve as the quantum channel for quantum state transfer distantly. Here, we report a new strategy of quantum-teleportation-inspired classical optical imaging, which also works non-locally at a distance; however, only a classically correlated light source is used instead of entanglement. In our experiment, we explore the pseudo-thermal light source to offer the teleportation-like channel and employ the sum-frequency generation to perform the Bell-like state measurement. We successfully demonstrate the teleportation-inspired optical imaging of simple characters, Taiji diagram, and the superposition of orbital angular momentum modes. Moreover, we experimentally observe that a better coherence of pseudo-thermal light will result in a lower contrast of the formed images, and thus revealing that non-zero quantum discord offered by pseudo-thermal light, regardless of zero entanglement, plays the pivotal role in sustaining the teleportation-like channel for imaging at a distance.

physics.optics↗

arXiv2025

Enhanced Detection of Rotational Doppler Shift from Sunlight

The rotational Doppler effect, for which the frequency shift is proportional to the light's orbital angular momentum $\ell$ and the object's rotational speed ($\Delta f \propto\ell \Omega$), has proven to be a powerful tool for detecting the speed of rotational objects. However, the current detection technique is mainly based on coherent laser sources. There is scarce mention of using partially coherent light sources, let alone sunlight. In this work, we collect sunlight and direct it into the laboratory, where it is modulated into a partially coherent probing source and then realize rotational Doppler shift detection. Our study reveals that in low-light conditions, where background noise is stronger than the signal, the superposition of rotational Doppler signals at different wavelengths can significantly enhance the signal strength and improve the signal-to-noise ratio, enabling accurate measurement of the rotational speed of objects. Our research provides experimental validation for the application of sunlight in rotational Doppler shift detection, demonstrating its potential value for passive remote sensing.

physics.optics↗

arXiv2025

The first Steklov eigenvalue bound for graphs of positive genus

Let $G$ be a graph of genus $g$ with boundary $\delta\Omega$. For $g=0$, Lin and Zhao [J. Lond. Math. Soc. 112 (2025), Paper No. e70238] proved an upper bound for the first (non-trivial) Steklov eigenvalue of $(G, \delta\Omega )$, and they posed the problem of determining a corresponding bound for graphs of genus $g>0$. In this paper, we prove an $O\left(\frac{g}{|\delta \Omega|}\right)$ bound for a bounded-degree graph of positive genus $g$. Our result can be regarded as a discrete analogue of Kokarev's bound [Adv. Math. 258 (2014), 191-239], up to a constant factor.

math.CO↗

arXiv2025

Dynamical control of quantum photon-photon interaction with phase change material

Quantum interference can produce a pivotal effective photon-photon interaction, enabling the exploration of various quantum information technologies that beyond the possibilities of classical physics. While such an effective interaction is fundamentally limited to the bosonic nature of photons and the restricted phase responses from commonly used unitary optical elements, loss-induced nonunitary operation provides an alternative degree of freedom to control the quantum interference. Here, we propose and experimentally demonstrate a concise yet powerful tool to unravel fundamental features of quantum interference based on the phase change material vanadium dioxide. Since the insulator-metal transition in an elaborate vanadium dioxide thin film can create any desired particle exchange phase response, we show its tunability over the effective photon-photon interaction between paired photons that are entangled in the symmetric and anti-symmetric forms, which may introduce sophisticated nonunitary operations and functionalities into programmable optical platforms. These results provide an alternative approach to investigate the quantum light-matter interaction, and facilitate the use of quantum interference for various quantum information processing tasks such as quantum simulation and quantum computation.

quant-ph↗

arXiv2025

SU(2) symmetry of spatiotemporal Gaussian modes propagating in the isotropic dispersive media

The far-field intensity distribution of spatiotemporal Laguerre-Gaussian (STLG) modes propagating in free space exhibits a multi-petal pattern analogous to that observed in tilted Hermite-Gaussian modes. Here, we show that this phenomenon can be explained by the SU(2) symmetry of spatiotemporal Gaussian modes, which can support the irreducible representation of SU(2) group and enable the construction of the spatiotemporal model Poincar\'e sphere. We have also derived analytical expressions for the STLG mode with an arbitrary radial and angular indices propagating in the isotropic media. The propagation dynamics can be understood as a unitary transformation generated by a conserved quantity, where the rotation angle is exactly the intermodal Gouy phase of the spatiotemporal modes in the same order subspace. This spatiotemporal Gouy phase depends on the ellipticity of the wave packets and the group velocity dispersion (GVD) of the media. The phase, as a function of propagation distance, is categorized into three distinct regimes: normal dispersion, anomalous dispersion, and zero dispersion. Interestingly, in the regime of anomalous dispersion, the non-monotonic behavior induces to both distortion and revival of the intensity distribution, thereby establishing a phase-locked mechanism that is analogous to the Talbot effect.

physics.optics↗

arXiv2025

Sunlight-Excited Spontaneous Parametric Down-Conversion for Quantum Imaging

Quantum imaging, which harnesses quantum correlations to achieve imaging with multiple advantages over classical optics, has been in development for several years. Here, we explore sunlight, serving as the pump beam, to excite spontaneous parametric down-conversion to get the quantum correlation of two photons. Remarkably, our investigations disclose that the photon pairs produced from sunlight are well correlated in position such that they can be used for quantum imaging. Consequently, this demonstrates a latent application scenario in which the incoherent beam is harnessed as the pump source for quantum imaging. Our research is of substantial significance as it broadens the scope of available illumination options, such as using scattering light or non-traditional artificial incoherent light sources, for quantum information, a prime potential application being a space-based quantum information mechanism where this approach allows the system to operate independently of a laser.

quant-ph↗

arXiv2025

The characteristic polynomial of sunflowers

A uniform hypergraph is called a sunflower if all of its hyperedges intersect in the same set of vertices. In this paper, we determine the eigenvalues and spectral moments of a sunflower, thereby obtaining an explicit formula for its characteristic polynomial.

math.CO↗

arXiv2025

How gravitational waves change photon orbital angular momentum quantum states

We explore the evolution of vortex light in the presence of gravitational waves (GWs) and demonstrate that the quantized orbital angular momentum (OAM) states can make transitions to other states due to the GWs. The interaction is calculated based on the framework of the wave propagation in linearized gravity theory and canonical quantization of the light field in curved spacetime. It is found that when a photon possessing OAM of $l$ interacts with GWs, the OAM modes of $l\pm1$ and $l\pm2$ may be excited with probabilities of $P_{l\pm1}\sim 10^{-17}$ and $P_{l\pm2}\sim 10^{-20}$, respectively. Higher probabilities of the transitions can be achieved when the photon radial wave vector or the propagation distance is increased, or when the photons encounter GWs with stronger amplitudes or smaller frequencies. Thus, a new GW detection technique is proposed, which may exhibit good performance in a wide range of GW frequencies. Furthermore, the detector is insensitive to seismic noise and is more advantageous for determining the distance of the source compared to current interferometer detectors.

gr-qc↗

arXiv2025

AQETuner: Reliable Query-level Configuration Tuning for Analytical Query Engines

Modern analytical query engines (AQEs) are essential for large-scale data analysis and processing. These systems usually provide numerous query-level tunable knobs that significantly affect individual query performance. While several studies have explored automatic DBMS configuration tuning, they have several limitations to handle query-level tuning. Firstly, they fail to capture how knobs influence query plans, which directly affect query performance. Secondly, they overlook query failures during the tuning processing, resulting in low tuning efficiency. Thirdly, they struggle with cold-start problems for new queries, leading to prolonged tuning time. To address these challenges, we propose AQETuner, a novel Bayesian Optimization-based system tailored for reliable query-level knob tuning in AQEs. AQETuner first applies the attention mechanisms to jointly encode the knobs and plan query, effectively identifying the impact of knobs on plan nodes. Then, AQETuner employs a dual-task Neural Process to predict both query performance and failures, leveraging their interactions to guide the tuning process. Furthermore, AQETuner utilizes Particle Swarm Optimization to efficiently generate high-quality samples in parallel during the initial tuning stage for the new queries. Experimental results show that AQETuner significantly outperforms existing methods, reducing query latency by up to 23.7% and query failures by up to 51.2%.

cs.DB↗

arXiv2025

Learning from the Past: Adaptive Parallelism Tuning for Stream Processing Systems

Distributed stream processing systems rely on the dataflow model to define and execute streaming jobs, organizing computations as Directed Acyclic Graphs (DAGs) of operators. Adjusting the parallelism of these operators is crucial to handling fluctuating workloads efficiently while balancing resource usage and processing performance. However, existing methods often fail to effectively utilize execution histories or fully exploit DAG structures, limiting their ability to identity bottlenecks and determine the optimal parallelism. In this paper, we propose StreamTune, a novel approach for adaptive paralelism tuning in stream processing systems. StreamTune incorporates a pre-training and fine-tuning framework that leverages global knowledge from historical execution data for job-specific parallelism tuning. In the pre-training phase, Stream Tune clusters the historical data with Graph Edit Distance and pre-trains a Graph Neural Networkbased encoder per cluster to capture the correlation between the operator parallelism, DAG structures, and the identified operator-level bottlenecks. In the online tuning phase, StreamTune iteratively refines operator parallelism recommendations using an operator-level bottleneck prediction model enforced with a monotonic constraint, which aligns with the observed system performance behavior. Evaluation results demonstrate that StreamTune reduces reconfigurations by up to 29.6% and parallelism degrees by up to 30.8% in Apache Flink under a synthetic workload. In Timely Dataflow, StreamTune achieves up to an 83.3% reduction in parallelism degrees while maintaining comparable processing performance under the Nexmark benchmark, when compared to the state-of-the-art methods.

cs.DC↗

arXiv2025

On the second-largest modulus among the eigenvalues of a power hypergraph

It is well known that the algebraic multiplicity of an eigenvalue of a graph (or real symmetric matrix) is equal to the dimension of its corresponding linear eigen-subspace, also known as the geometric multiplicity. However, for hypergraphs, the relationship between these two multiplicities remains an open problem. For a graph $G=(V,E)$ and $k \geq 3$, the $k$-power hypergraph $G^{(k)}$ is a $k$-uniform hypergraph obtained by adding $k-2$ new vertices to each edge of $G$, who always has non-real eigenvalues. In this paper, we determine the second-largest modulus $\Lambda$ among the eigenvalues of $G^{(k)}$, which is indeed an eigenvalue of $G^{(k)}$. The projective eigenvariety $\mathbb{V}_{\Lambda}$ associated with $\Lambda$ is the set of the eigenvectors of $G^{(k)}$ corresponding to $\Lambda$ considered in the complex projective space. We show that the dimension of $\mathbb{V}_{\Lambda}$ is zero, i.e, there are finitely many eigenvectors corresponding to $\Lambda$ up to a scalar. We give both the algebraic multiplicity of $\Lambda$ and the total multiplicity of the eigenvector in $\mathbb{V}_{\Lambda}$ in terms of the number of the weakest edges of $G$. Our result show that these two multiplicities are equal.

math.CO↗

arXiv2025

Orbital Angular Momentum Experimental Bound on the Maximum Predictive Power of Physical Theories in Multi-Dimensional Systems

The completeness of quantum mechanics in predictive power is a central question in its foundational study. While most investigations focus on two-dimensional systems, high-dimensional systems are more general and widely applicable. Building on the non-extensibility theorem by Colbeck and Renner [Phys. Rev. Lett. 101, 050403 (2008)], which established that no higher theory can enhance the predictive power of quantum mechanics for two-dimensional systems, we extend this result to arbitrarily dimensional systems. We connect maximum potential predictive power achievable by any alternative theory to experimentally observable correlations, and establish optimal experimental bounds across varying dimensions by exploiting two-photon orbital angular momentum entangled states with entanglement concentration. These bounds falsify a broader class of alternative theories, including Bell's and Leggett's models, and those that remain theoretically ambiguous or experimentally unverified. Our findings not only deepen the foundational understanding of quantum mechanics but also hold significant potential for high-dimensional quantum cryptography.

quant-ph↗

arXiv2025

Crypto-nonlocality in arbitrarily dimensional systems

According to Bell's theorem, any model based on local variables cannot reproduce certain quantum correlations. A critical question is whether one could devise an alternative framework, based on nonlocal variables, to reproduce quantum correlations while adhering to fundamental principles. Leggett proposed a nonlocal model, termed crypto-nonlocality, rooted in considerations of the reality of photon polarization, but this property restricted it to being bi-dimensional. In this Letter, we extend the crypto-nonlocal model to higher dimensions and develop a framework for constructing experimentally testable Leggett-type inequalities for arbitrary dimensions. Our investigation into models that yield specific predictions exceeding those of quantum mechanics is intriguing from an information-theoretic perspective and is expected to deepen our understanding of quantum correlations.

quant-ph↗

arXiv2024

Harnessing high-dimensional symmetric and anti-symmetric Bell states through quantum interference

High-dimensional quantum entanglement is an essential resource in quantum technology since it provides benefits in increasing the information capacity and processing speed. Thus, the controlled harnessing of high-dimensional entanglement has long been hailed as a necessary prerequisite towards practical quantum applications. By using a deterministic quantum state filter that implemented through quantum interference, we present a generalised formulation for the complete high-dimensional symmetric and anti-symmetric Bell basis, and experimentally prepare four-dimensional orbital angular momentum Bell states that provide the well-behaved symmetric or anti-symmetric properties. Additionally, we use a concise yet efficient scan of temporal delay to directly observe high-dimensional two-photon interference effects in spatial modes. These results provide an alternative way for harnessing high-dimensional entanglement, and may facilitate the use of quantum interference for more complex quantum information processing tasks that beyond qubits.

quant-ph↗

arXiv2024

Sorting light's radial momentum and orbital angular momentum with a parabola-like lens

The orbital angular momentum and radial momentum both describe the transverse momentum of a light field. Efficient discriminating and sorting the two kinds of momentum lies at the heart of further application. Here, we propose a parabola-like lens that can transform the orbital angular momentum and the radial momentum into different positions in the parabolas. We experimentally characterize the performance of our implementation by separating individual angular and radial momentum as well as the multiple superposition states. The reported scheme can achieve two kinds of transverse momentum identification and thus provide a possible way to complete the characterization of the full transverse momentum of an optical field. The proposed device can readily be used in multiplexing and demultiplexing of optical information, and in principle, achieve unit efficiency, and thus can be suitable for applications that involve quantum states of light.

physics.optics↗

arXiv2024

Orbital angular momentum spectrum and entanglement in a rotating accelerated reference frame

The particle definition varies across different theories. The quantum field theory in curved spacetime shows that from the perspective of a linearly accelerated observer, an inertial empty space may be full of thermal particles. This effect is known as the Unruh effect. When the degrees of freedom of orbital angular momentum (OAM) are considered, all OAM modes share the same expected particle number. Here, we examine the OAM spectrum in a rotating accelerated reference frame to see how the spectrum differs from the linear accelerated case. When the observer starts to rotate, not all OAM modes are allowed and some negative energy modes show up. To understand how a rotating accelerated observer actually perceives these particles, the Unruh-DeWitt detector and its detailed balance are studied. This relation is studied both in the comoving inertial frame and in the rest frame. Based on these results, the OAM entanglement degradation is explored in two-dimensional and high-dimensional cases, respectively. The results indicate that the entanglement dimension and the highest order of OAM modes are mainly related to the acceleration and the rotation, respectively. It is then demonstrated that these results can be generalized to all stationary trajectories.

gr-qc↗