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Cardinality estimation is a critical component and a longstanding challenge in modern data warehouses. ByteHouse, ByteDance's cloud-native engine for extensive data analysis in exabyte-scale environments, serves numerous internal decision-making business scenarios. With the increasing demand for ByteHouse, cardinality estimation becomes the bottleneck for efficiently processing queries. Specifically, the existing query optimizer of ByteHouse uses the traditional Selinger-like cardinality estimator, which can produce substantial estimation errors, resulting in suboptimal query plans. To improve cardinality estimation accuracy while maintaining a practical inference overhead, we develop a framework ByteCard that enables efficient training and integration of learned cardinality estimators. Furthermore, ByteCard adapts recent advances in cardinality estimation to build models that can balance accuracy and practicality (e.g., inference latency, model size, training overhead). We observe significant query processing speed-up in ByteHouse after replacing the existing cardinality estimator with ByteCard for several optimization scenarios. Evaluations on real-world datasets show the integration of ByteCard leads to an improvement of up to 30% in the 99th quantile of latency. At last, we share our valuable experience in engineering advanced cardinality estimators. This experience can help ByteHouse integrate more learning-based solutions on the critical query execution path in the future.

There are two powerful arguments against the possibility of extending quantum mechanics, the violation of Bell inequalities and the Kochen-Specker theorem, but the connection between the two remains confused. Following the distinctive strategy proposed by Cabello [Phys. Rev. Lett. 127, 070401 (2021)], Bell inequalities can be violated by state-independent contextuality sets. However, the experimental realization of such ideas is challenging as it requires high-dimensional entanglement. Orbital angular momentum provides an unlimited state space and the number of effective dimensions can be readily tailored as required. We performed an experimental test of non-locality based on Bell inequalities from contextuality, using orbital angular momentum entanglement in a bipartite photonic system. Our experiment not only shows a new way to produce non-locality but also connects contextuality and non-locality, two fundamental quantum resources that are critical for quantum computation and secure communication tasks.

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.

The $d$-th order Laplacian spectral moment of a $k$-uniform hypergraph is the sum of the $d$-th powers of all eigenvalues of its Laplacian tensor. In this paper, we obtain some expressions of the Laplacian spectral moments for $k$-uniform power hypergraphs, and these expressions can be represented by some parameters of graphs. And we show that some graphs can be determined by their high-order Laplacian spectrum by using the Laplacian spectral moments of power hypergraphs.

It is well-known that the spectral radius of a connected uniform hypergraph is an eigenvalue of the hypergraph. However, its algebraic multiplicity remains unknown. In this paper, we use the Poisson Formula and matching polynomials to determine the algebraic multiplicity of the spectral radius of a uniform hypertree.

The $k$-power hypergraph $G^{(k)}$ is the $k$-uniform hypergraph that is obtained by adding $k-2$ new vertices to each edge of a graph $G$, for $k \geq 3$. A parity-closed walk in $G$ is a closed walk that uses each edge an even number of times. In an earlier paper, we determined the eigenvalues of the adjacency tensor of $G^{(k)}$ using the eigenvalues of signed subgraphs of $G$. Here, we express the entire spectrum (that is, we determine all multiplicities and the characteristic polynomial) of $G^{(k)}$ in terms of parity-closed walks of $G$. Moreover, we give an explicit expression for the multiplicity of the spectral radius of $G^{(k)}$. Our results are mainly obtained by exploiting the so-called trace formula to determine the spectral moments of $G^{(k)}$. As a side result, we show that the number of parity-closed walks of given length is the corresponding spectral moment averaged over all signed graphs with underlying graph $G$. We also extrapolate the characteristic polynomial of $G^{(k)}$ to $k=2$, thereby introducing a pseudo-characteristic function. Among other results, we show that this function is the geometric mean of the characteristic polynomials of all signed graphs on $G$ and characterize when it is a polynomial. This supplements a result by Godsil and Gutman that the arithmetic mean of the characteristic polynomials of all signed graphs on $G$ equals the matching polynomial of $G$.

Spontaneous parametric down-conversion (SPDC) is a reliable platform for entanglement generation. Routinely, a coherent laser beam is an essential prerequisite for pumping the nonlinear crystal. Here we break this barrier to generate polarization entangled photon pairs by using a commercial light-emitting diode (LED) source to serve as the pump beam. This effect is counterintuitive, as the LED source is of extremely low spatial coherence, which is transferred during the down-conversion process to the biphoton wavefunction. However, the type-II phase-matching condition naturally filters the specific frequency and wavelength of LED light exclusively to participate in SPDC such that localized polarization Bell states can be generated, regardless of the global incoherence over the full transverse plane. In our experiment, we characterize the degree of LED light-induced polarization entanglement in the standard framework of the violation of Bell inequality. We have achieved the Bell value $S=2.33\pm 0.097$, obviously surpassing the classical bound $S=2$ and thus witnessing the quantum entanglement. Our work can be extended to prepare polarization entanglement by using other natural light sources, such as sunlight and bio-light, which holds promise for electricity-free quantum communications in outer space.

We show how all eigenvalues of a power hypergraph $G^{(k)}$ can be generated from the eigenvalues of signed subgraphs of the underlying graph $G$. This fixes an incorrect statement in the case of power hypergraphs from [Linear Algebra and its Applications, 590:243-257, 2020].

Twisted photons carrying orbital angular momentum (OAM) are competent candidates for future interstellar communications. However, the gravitational fluctuations are ubiquitous in spacetime. Thus a fundamental question arises naturally as to how the gravitational fluctuations affect the coherence and the degree of high-dimensional OAM entanglement when twisted photons travel across the textures of curved spacetime. Here, we consider the covariant scalar Helmholtz equations and the Minkowski metric with fluctuations of Gaussian distribution and formulate analytically the equations describing the motion for twisted light in the Laguerre-Gaussian mode space. It is seen that the OAM cannot remain conserved in the presence of gravitational fluctuations. Furthermore, two-photon density matrices are derived for interstellar OAM quantum entanglement distribution, and the degree of entanglement degradation is characterized by purity and negativity. It is revealed that the higher-dimensional OAM entanglement is more susceptible to spacetime fluctuations. We believe that our findings will be of fundamental importance for the future interstellar quantum communications with twisted photons., Comment: To be published in Physical Review D (4 figures)

Generative adversarial learning is currently one of the most prolific fields in artificial intelligence due to its great performance in a variety of challenging tasks such as photorealistic image and video generation. While a quantum version of generative adversarial learning has emerged that promises exponential advantages over its classical counterpart, its experimental implementation and potential applications with accessible quantum technologies remain explored little. Here, we report an experimental demonstration of quantum generative adversarial learning with the assistance of adaptive feedback that is based on stochastic gradient descent algorithm. Its performance is explored by applying this technique to the adaptive characterization of quantum dynamics and simultaneous estimation of multiple phases. These results indicate the intriguing advantages of quantum generative adversarial learning even in the presence of deleterious noise, and pave the way towards quantum-enhanced information processing applications.

Wiener-Khinchin theorem, the fact that the autocorrelation function of a time process has a spectral decomposition given by its power spectrum intensity, can be used in many disciplines. However, the applications based on a quantum counterpart of Wiener-Khinchin theorem that provides a translation between time-energy degrees of freedom of biphoton wavefunction still remains relatively unexplored. Here, we use a quantum Wiener-Khinchin theorem (QWKT) to state that two-photon joint spectral intensity and the cross-correlation of two-photon temporal signal can be connected by making a Fourier transform. The mathematically-defined QWKT is experimentally demonstrated in frequency-entangled two-photon Hong-Ou-Mandel (HOM) interference with the assistance of spectrally-resolved detection. We apply this method to spectral-domain quantum optical coherence tomography that detects thickness-induced optical delays in a transparent sample, and show that our method suffices to achieve great advantages in measurement precision within a wide dynamic range and capturing time over the conventional HOM interferometric schemes. These results may significantly facilitate the use of QWKT for quantum information processing and quantum interferometric spectroscopy.

The concept of quantum entanglement and hyper-entanglement, lying at the heart of quantum information science and technologies, is physically counter-intuitive and mathematically elusive. We design a polarization-encoded ghost imaging system based on the frame of Hardy nonlocality paradox to visualize the evidence of quantum hyper-entanglement by capturing purely nonlocal photonic events. In two-photon polarization-spatial-mode hyper-entangled state, spatial entanglement con-veys the ghost images while polarization entanglement encodes the imaging channels. Then whether imaging the single ghost image of a skull-shape object or not can be a direct yet intuitive signature to support or defy quantum mechanics. We use the contrast-to-noise ratio of ghost images to macroscopically characterize the degree of the violation of locality. We also showcase the nonlocal behavior of violating the locality with a reasonable confidence level of 75%, microscopically at the single-pixel level. Our strategy not only sheds new light on the fundamental issue of quantum mechanics, but also holds promise for developing hyper-entanglement-based quantum imaging technology., Comment: 9pages,5 figures

Quantum teleportation, lying at the heart of a variety of quantum technologies, has inspired a widespread of research activities, most of which focused on 2-dimensional qubit states. Multilevel systems, qudits, promise to upgrade and inspire new technical developments in high-dimensional Hilbert space. Whereas, for high-dimensional teleportation, it routinely necessitates several ancillary photons in linear optical schemes. A fundamental open challenge remains as to whether we can teleport qudit states with bipartite entanglement only. Here we demonstrate such a high-dimensional teleportation using photonic orbital angular momentum (OAM). The so-called "perfect vortices" are exploited both for conducting the prerequisite entanglement concentration to prepare high-dimensional yet maximal OAM entanglement, and for performing faithful high-dimensional Bell sate measurements (HDBSM) based on sum-frequency generation. We experimentally achieve the average teleportation fidelity 0.8788$\pm$0.048 for a complete set of 3-dimensional mutually unbiased bases, for instance, conditional on three specific HDBSM results. More importantly, we succeed in realizing the first quantum teleportation of optical images by exploring full transverse spatial entanglement. From the multi-pixel field of view in the teleported images recorded by the ICCD camera, we estimate the effective channel capacity up to \k{appa} > 100. Our scheme holds promise for future high-volume quantum image transmission.

Two-photon excitation spectroscopy is a nonlinear technique that has gained rapidly in interest and significance for studying the complex energy-level structure and transition probabilities of materials. While the conventional spectroscopy based on tunable classical light has been long established, quantum light provides an alternative way towards excitation spectroscopy with potential advantages in temporal and spectral resolution, as well as reduced photon fluxes. By using a quantum Fourier transform that connects the sum-frequency intensity and N00N-state temporal interference, we present an approach for quantum interferometric two-photon excitation spectroscopy. Our proposed protocol overcomes the difficulties of engineering two-photon joint spectral intensities and fine-tuned absorption-frequency selection. These results may significantly facilitate the use of quantum interferometric spectroscopy for extracting the information about the electronic structure of the two-photon excited-state manifold of atoms or molecules, in a "single-shot" measurement. This may be particularly relevant for photon-sensitive biological and chemical samples., Comment: 6 pages, 4 figures

The spectrum of the $k$-power hypergraph of a graph $G$ is called the $k$-ordered spectrum of $G$.If graphs $G_1$ and $G_2$ have same $k$-ordered spectrum for all positive integer $k\geq2$, $G_1$ and $G_2$ are said to be high-ordered cospectral. If all graphs who are high-ordered cospectral with the graph $G$ are isomorphic to $G$, we say that $G$ is determined by the high-ordered spectrum.In this paper, we use the high-ordered spectrum of graphs to study graph isomorphism and show that all Smith's graphs are determined by the high-ordered spectrum.And we give infinitely many pairs of trees with same spectrum but different high-ordered spectrum by high-ordered cospectral invariants of trees,it means that we can determine that these cospectral trees are not isomorphism by the high-ordered spectrum.

High-dimensional quantum entanglement is currently one of the most prolific fields in quantum information processing due to its high information capacity and error resilience. A versatile method for harnessing high-dimensional entanglement has long been hailed as an absolute necessity in the exploration of quantum science and technologies. Here we exploit Hong-Ou-Mandel interference to manipulate discrete frequency entanglement in arbitrary-dimensional Hilbert space. The generation and characterization of two-, four- and six-dimensional frequency entangled qudits are theoretically and experimentally investigated, allowing for the estimation of entanglement dimensionality in the whole state space. Additionally, our strategy can be generalized to engineer higher-dimensional entanglement in other photonic degrees of freedom. Our results may provide a more comprehensive understanding of frequency shaping and interference phenomena, and pave the way to more complex high-dimensional quantum information processing protocols.

The Bell basis, a set of maximally entangled biphoton state, is a critical prerequisite towards quantum information processing, and many quantum applications have highlighted the requirement for the manipulation of high-dimensional Bell basis. While the Bell states can be created by using ingenious single-photon quantum gates, its implementation complexity in higher dimensions is significantly increased. Here we present an elaborate approach to show that the adaptive pump modulation enable the efficient preparation of Bell basis in arbitrary-dimensional Hilbert space. A complete set of four-dimensional orbital angular momentum Bell states are experimentally created, yielding high fidelities for certifying the entanglement dimensionality. Our strategy can be simply generalized to prepare more complex forms of quantum states even exploiting other physical degrees of freedom. Also, it can facilitate the use of high-dimensional entanglement in a variety of quantum protocols, in particular those requiring quantum dense coding.

Characterizing high-dimensional entangled states is of crucial importance in quantum information science and technology. Recent theoretical progress has been made to extend the Hardy's paradox into a general scenario with multisetting multidimensional systems, which can surpass the bound limited by the original version. Hitherto, no experimental verification has been conducted to verify such a Hardy's paradox, as most of previous experimental efforts were restricted to two-dimensional systems. Here, based on two-photon high-dimensional orbital angular momentum (OAM) entanglement, we report the first experiment to demonstrate the Hardy's paradox for multiple settings and multiple outcomes. We demonstrate the paradox for two-setting higher-dimensional OAM subspaces up to d = 7, which reveals that the nonlocal events increase with the dimension. Furthermore, we showcase the nonlocality with an experimentally recording probability of 36.77% for five-setting three-dimensional OAM subspace via entanglement concentration, and thus showing a sharper contradiction between quantum mechanics and classical theory., Comment: 10 pages, 3 figures

Entanglement and quantum interference are key ingredients in a variety of quantum information processing tasks. Harnessing the generation and characterization of entanglement in high-dimensional state spaces is a necessary prerequisite towards practical quantum protocols. Here, we use quantum interference on a beam splitter to engineer hyperentanglement in polarization and discrete frequency degrees of freedom (DOF). We show how independent measurements of polarization and frequency DOF allow for the verification of high-dimensional entanglement in the combined state space. These results may indicate new paths towards practical exploitation of entanglement stored in multiple degrees of freedom, in particular in the context of high-dimensional quantum information processing protocols.

Based on two-photon entanglement, quantum remote sensing enables the measurement and detection to be done non-locally and remotely. However, little attention has been paid to implement a noncontact way to sense a real objects angular rotation, which is a key step towards the practical applications of precise measurements with entangled twisted photons. Here, we use photon pairs entangled in orbital angular momentum (OAM) to show that a real object's angular rotation can be measured non-locally. Our experiment reveals that the angular sensitivity of the object encoded with idler photons is proportional to the measured OAM values of signal photons. It suggests potential applications in developing a noncontact way for angle remote sensing of an object with customized measurement resolution. Moreover, this feature may provide potential application in sensing of some light-sensitive specimens when the entangled photon pairs, which have significantly different wavelengths, are used, such as one photon is infrared but the other one is visible., Comment: second revision in APS journal

Strong correlations in two conjugate variables are the signature of quantum entanglement and have played a key role in the development of modern physics. Entangled photons have become a standard tool in quantum information and foundations. An impressive example is position-momentum entanglement of photon pairs, explained heuristically through the correlations implied by a common birth zone and momentum conservation. However, these arguments entirely neglect the importance of the `quantumness', i.e. coherence, of the driving force behind the generation mechanism. We study theoretically and experimentally how the correlations depend on the coherence of the pump of nonlinear down-conversion. In the extreme case - a truly incoherent pump - only position correlations exist. By increasing the pump's coherence, correlations in momenta emerge until their strength is sufficient to produce entanglement. Our results shed light on entanglement generation and can be applied to adjust the entanglement for quantum information applications., Comment: 6 pages, 4 figures

In this paper, we give a reduced formula of the characteristic polynomial of $k$-uniform hypergraphs with a pendant edge. And the explicit characteristic polynomial and all distinct eigenvalues of $k$-uniform hyperpath are given.

Nonlinear optical generation has been a well-established way to realize frequency conversion in nonlinear optics, whereas previous studies were just focusing on the scalar light fields. Here we report a concise yet efficient experiment to realize frequency conversion from vector fields to vector fields based on the vectorial nonlinear optical process, e.g., the second-harmonic generation. Our scheme is based on two cascading type-I phase-matching BBO crystals, whose fast axes are configured elaborately to be perpendicular to each other. Without loss of generality, we take the full Poincar\'e beams as the vectorial light fields in our experiment, and visualize the structured features of vectorial second-harmonic fields by using Stokes polarimetry. The interesting doubling effect of polarization topological index, i.e., a low-order full Poincar\'e beam is converted to a high-order one are demonstrated. However, polarization singularities of both C-points and L-lines are found to keep invariant during the SHG process. Our scheme can be straightforwardly generalized to other nonlinear optical effects. Our scheme can offer a deeper understanding on the interaction of vectorial light with media and may find important applications in optical imaging, optical communication and quantum information science.

The correlation properties of the pump field in spontaneous parametric down-conversion are crucial in determining the degree of entanglement of generated signal and idler photons. We find theoretically that continuous-variable entanglement of the transverse positions and momenta of these photons can be achieved only if the coherence of the pump beam is sufficiently high. The positions of signal and idler photons are found to be correlated, even for an incoherent pump. However, the momenta of the signal and idler photons are not anti-correlated, even though transverse momentum is conserved., Comment: 9 pages, 4 figures, author's original

The rotational Doppler effect associated with light's orbital angular momentum (OAM) has been found as a powerful tool to detect rotating bodies. However, this method was only demonstrated experimentally on the laboratory scale under well controlled conditions so far. And its real potential lies at the practical applications in the field of remote sensing. We have established a 120-meter long free-space link between the rooftops of two buildings and show that both the rotation speed and the rotational symmetry of objects can be identified from the detected rotational Doppler frequency shift signal at photon count level. Effects of possible slight misalignments and atmospheric turbulences are quantitatively analyzed in terms of mode power spreading to the adjacent modes as well as the transfer of rotational frequency shifts. Moreover, our results demonstrate that with the preknowledge of the object's rotational symmetry one may always deduce the rotation speed no matter how strong the coupling to neighboring modes is. Without any information of the rotating object, the deduction of the object's symmetry and rotational speed may still be obtained as long as the mode spreading efficiency does not exceed 50 %. Our work supports the feasibility of a practical sensor to remotely detect both the speed and symmetry of rotating bodies.

Twisted light has recently gained enormous interest in communication systems. Thus far, twisted light has not yet been utilized for visible light communication to transmit data. Here, by exploiting the color and orbital angular momentum (OAM) degrees of freedom simultaneously, we construct a much higher-dimensional space spanned by their hybrid mode basis, which further increases the information capacity of twisted light. We build a new visible light communication system using a white light emitting diode, with red, green and blue (RGB) colors serving as independent channels and with OAM superposition states encoding the information. We connect our conceptually new RGB-OAM hybrid coding with the specially designed two-dimensional holographic gratings based on theta-modulation. After indoor free-space transmission, we decode the color information with an Xcube prism and subsequently decode the OAM superposition states with a pattern recognition method based on supervised machine learning. We succeed in demonstrating the transmission of color images and a piece of audio with the fidelity over 96%. Our point-to-point scheme with hybrid RGB-OAM encoding, not only increases significantly the information capacity of twisted light, but also offers additional security that supplements the traditional broadcasting visible light communications, e.g., Li-Fi.