arXiv subjects

Ting Gao

Publications and source records attributed to Ting Gao.

At least 55 records · Page 3Linked to original sources

arXiv2024

Momentum shift and on-shell constructible massive amplitudes

We construct tree-level amplitude for massive particles using on-shell recursion relations based on two classes of momentum shifts: an all-line transverse shift that deforms momentum by its transverse polarization vector, and a massive BCFW-type shift. We illustrate that these shifts allow us to correctly calculate four-point and five-point amplitudes in massive QED, without an ambiguity associated with the contact terms that may arise from a simple ''gluing'' of lower-point on-shell amplitudes. We discuss various aspects and applicability of the two shifts, including the large-z behavior and complexity scaling. We show that there exists a ''good'' all-line transverse shift for all possible little group configurations of the external particles, which can be extended to a broader class of theories with massive particles such as massive QCD and theories with massive spin-1 particles. The massive BCFW-type shift enjoys more simplicity, but a ''good'' shift does not exist for all the spin states due to the specific choice of spin axis.

hep-ph↗

arXiv2024

Momentum shift and on-shell recursion relation for electroweak theory

We study the All-Line Transverse (ALT) shift which we developed for on-shell recursion of amplitudes for particles of any mass. We discuss the validity of the shift for general theories of spin $\leq$ 1, and illustrate the connection between Ward identity and constructibility for massive spin-1 amplitude under the ALT shift. We apply the shift to the electroweak theory, and various four-point scattering amplitudes among electroweak gauge bosons and fermions are constructed. We show explicitly that the four-point gauge boson contact terms in massive electroweak theory automatically arise after recursive construction, independent of UV completion, and they automatically cancel the terms growing as (energy)$^4$ at high energy. We explore UV completion of the electroweak theory that cancels the remaining (energy)$^2$ terms and impose unitarity requirements to constrain additional couplings. The ALT shift framework allows consistent treatment in dealing with contact term ambiguities for renormalizable massive and massless theories, which we show can be useful in studying real-world amplitudes with massive spinors.

hep-ph↗

arXiv2024

Strongest quantum nonlocality in $N$-partite systems

A set of orthogonal states possesses the strongest quantum nonlocality if only a trivial orthogonality-preserving positive operator-valued measure (POVM) can be performed for each bipartition of the subsystems. This concept originated from the strong quantum nonlocality proposed by Halder $et~al.$ [Phy. Rev. Lett. $\textbf{122}$, 040403 (2019)], which is a stronger manifestation of nonlocality based on locally indistinguishability and finds more efficient applications in quantum information hiding. However, demonstrating the triviality of orthogonality-preserving local measurements (OPLMs) is not straightforward. In this paper, we present a sufficient and necessary condition for trivial OPLMs in $N$-partite systems under certain conditions. By using our proposed condition, we deduce the minimum size of set with the strongest nonlocality in system $(\mathbb{C}^{3})^{\otimes N}$, where the genuinely entangled sets constructed in Ref. [Phys. Rev. A $\textbf{109}$, 022220 (2024)] achieve this value. As it is known that studying construction involving fewer states with strongest nonlocality contribute to reducing resource consumption in applications. Furthermore, we construct strongest nonlocal genuinely entangled sets in system $(\mathbb{C}^{d})^{\otimes N}~(d\geq4)$, which have a smaller size than the existing strongest nonlocal genuinely entangled sets as $N$ increases. Consequently, our results contribute to a better understanding of strongest nonlocality.

quant-ph↗

arXiv2024

GT-CausIn: a novel causal-based insight for traffic prediction

Traffic forecasting is an important application of spatiotemporal series prediction. Among different methods, graph neural networks have achieved so far the most promising results, learning relations between graph nodes then becomes a crucial task. However, improvement space is very limited when these relations are learned in a node-to-node manner. The challenge stems from (1) obscure temporal dependencies between different stations, (2) difficulties in defining variables beyond the node level, and (3) no ready-made method to validate the learned relations. To confront these challenges, we define legitimate traffic causal variables to discover the causal relation inside the traffic network, which is carefully checked with statistic tools and case analysis. We then present a novel model named Graph Spatial-Temporal Network Based on Causal Insight (GT-CausIn), where prior learned causal information is integrated with graph diffusion layers and temporal convolutional network (TCN) layers. Experiments are carried out on two real-world traffic datasets: PEMS-BAY and METR-LA, which show that GT-CausIn significantly outperforms the state-of-the-art models on mid-term and long-term prediction.

cs.LG↗

arXiv2024

A more generalized two-qubit symmetric quantum joint measurement

A standard two-qubit joint measurement is the well-known Bell state measurement (BSM), in which each reduced state (traced out one qubit) is the completely mixed state. Recently, a novel quantum joint measurement named elegant joint measurement (EJM) has been proposed, where the reduced states of the EJM basis have tetrahedral symmetry. In this work, we first suggest a five-parameter entangled state and reveal its inherent symmetry. Based on this, we define a more generalized EJM parameterized by $z$, $φ$ and $θ$, and provide the quantum circuits for preparing and detecting these basis states. There are three main results: (i) the previous single-parameter EJM can be directly obtained by specifying the parameters $z$ and $φ$; (ii) the initial unit vectors related to the four vertices of the regular tetrahedron are not limited to the original choice and not all the unit vectors in cylindrical coordinates are suitable for forming the EJM basis; and (iii) the reduced states of the present EJM basis can always form two mirrorimage tetrahedrons, robustly preserving its elegant properties. We focus on figuring out what kind of states the EJM basis belongs to and providing a method for constructing the more generalized three-parameter EJM, which may contribute to the multi-setting measurement and the potential applications for quantum information processing.

quant-ph↗

arXiv2024

Strong quantum nonlocality without entanglement in every $(n-1)$-partition

Orthogonal product sets that are locally irreducible in every bipartition have the strongest nonlocality while also need a large number of quantum states. In this paper, we construct the orthogonal product sets with strong quantum nonlocality in any possible $n$-partite systems, where $n$ is greater than three. Rigorous proofs show that these sets are locally irreducible in every $(n-1)$-partition. They not only possess stronger properties than nonlocality and fewer quantum states than the strongest nonlocal sets, but also are positive answers to the open question "how to construct different strength nonlocality of orthogonal product states for general multipartite and high-dimensional quantum systems" of Zhang et al. [{Phys. Rev. A \textbf{99}, 062108 (2019)}]. Our results can also enhance one understanding for the nonlocality without entanglement.

quant-ph↗

arXiv2024

G_q-concurrence and entanglement constraints in multiqubit systems

In this paper, we introduce a category of one-parameter bipartite entanglement quantifiers, termed $G_q$-concurrence ($q>1$), and show rigorously that they satisfy all the axiomatic conditions of an entanglement measure and can be considered as a generalization of concurrence. In addition, we establish an analytic formula relating $G_q$-concurrence to concurrence for $1<q\leq2$ in two-qubit systems. Furthermore, the polygamy relation is presented based on the $G_q$-concurrence of assistance in multiqubit systems. As far as $G_q$-concurrence ($1<q\leq2$) itself is concerned, however, it does not obey the monogamy relation, but we prove that the square of $G_q$-concurrence does. By means of this monogamy inequality, we construct a set of entanglement indicators that can detect genuinely multiqubit entangled states even when the tangle loses its efficacy.

quant-ph↗

arXiv2024

Entanglement hierarchies in multipartite scenarios

In this paper, we investigate the hierarchical structure of the $n$-partite quantum states. We present a whole set of hierarchical quantifications as a method of characterizing quantum states, which go beyond genuine multipartite entanglement measures and allow for fine identification among distinct entanglement contributions. This kind of quantifications, termed $k$-GM concurrence, can unambiguously classify entangled states into $(n-1)$ distinct classes from the perspective of $k$-nonseparability with $k$ running from $n$ down to 2, and comply with the axiomatic conditions of an entanglement measure. Compared to $k$-ME concurrence [\href{https://journals.aps.org/pra/abstract/10.1103/PhysRevA.86.062323} {Phys. Rev. A \textbf{86}, 062323 (2012)}], the hierarchical measures proposed by us embody advantages in distinguishing same class entangled state and measuring continuity. In addition, we establish the relation between $k$-ME concurrence and $k$-GM concurrence, and further derive a strong lower bound on the $k$-GM concurrence by exploiting the permutationally invariant part of a quantum state. Furthermore, we parametrize $k$-GM concurrence to obtain two more general and complete categories of quantifications, $q$-$k$-GM concurrence $(q>1)$ and $α$-$k$-GM concurrence $(0\leqα<1)$, which obey the properties enjoyed by $k$-GM concurrence as well. In particular, $α$-$2$-GM concurrence $(0<α<1)$ determines that the GHZ state and the $W$ state belong to the same hierarchy, and it is proven in detail satisfying the requirement that the GHZ state is more entangled than the $W$ state in multiqubit systems.

quant-ph↗

arXiv2024

Chiral properties of the nucleon interpolating current and $θ$-dependent observables

We revisit the chiral properties of nucleon interpolating currents, and show that of the two leading order currents $j_1$ and $j_2$, only two linear combinations $j_1\pm j_2$ transform covariantly under the anomalous $U(1)_A$ symmetry. As a result, calculations of quantities which vanish by symmetry in the chiral limit may produce unphysical results if carried out with different linear combinations of the currents. This includes observables such as electric dipole moments, induced by the QCD parameter $θ$, and the $θ$-dependence of the nucleon mass. For completeness, we also exhibit the leading order results for nucleon electric dipole moments ($d_{n,p}$) induced by $θ$, and the nucleon magnetic moments ($μ_{n,p}$), when calculated using QCD sum rules for both the covariant choices of the nucleon interpolating current. The results in each channel, conveniently expressed as the ratios, $d_{n,p}/μ_{n,p}$, are numerically consistent, and reflect the required physical dependence on $θ$.

hep-ph↗

arXiv2024

Quantifying multipartite quantum states by ($k+1$)-partite entanglement measures

In this paper, we investigate how to quantify the quantum states of $n$-particles from the point of $(k+1)$-partite entanglement $(1\leq k\leq n-1)$, which plays an instrumental role in quantum nonlocality and quantum metrology. We put forward two families of entanglement measures termed $q$-$(k+1)$-PE concurrence $(q>1)$ and $α$-$(k+1)$-PE concurrence $(0\leqα<1)$, respectively. As far as the pure state is concerned, they are defined based on the minimum in entanglement. Meanwhile, rigorous proofs showing that both types of quantifications fulfill all the requirements of an entanglement measure are provided. In addition, we also propose two alternative kinds of entanglement measures, named $q$-$(k+1)$-GPE concurrence $(q>1)$ and $α$-$(k+1)$-GPE concurrence $(0\leqα<1)$, respectively, where the quantifications of any pure state are given by taking the geometric mean of entanglement under all partitions satisfying preconditions. Besides, the lower bounds of these measures are presented by means of the entanglement of permutationally invariant (PI) part of quantum states and the connections of these measures are offered. Moreover, we compare these measures and explain the similarities and differences among them. Furthermore, for computational convenience, we consider enhanced versions of the above quantifications that can be utilized to distinguish whether a multipartite state is genuinely strong $k$-producible.

quant-ph↗

arXiv2024

Early warning indicators via latent stochastic dynamical systems

Detecting early warning indicators for abrupt dynamical transitions in complex systems or high-dimensional observation data is essential in many real-world applications, such as brain diseases, natural disasters, and engineering reliability. To this end, we develop a novel approach: the directed anisotropic diffusion map that captures the latent evolutionary dynamics in the low-dimensional manifold. Then three effective warning signals (Onsager-Machlup Indicator, Sample Entropy Indicator, and Transition Probability Indicator) are derived through the latent coordinates and the latent stochastic dynamical systems. To validate our framework, we apply this methodology to authentic electroencephalogram (EEG) data. We find that our early warning indicators are capable of detecting the tipping point during state transition. This framework not only bridges the latent dynamics with real-world data but also shows the potential ability for automatic labeling on complex high-dimensional time series.

stat.ML↗

arXiv2024

$(n,m,p)$-type quantum network configuration and its nonlocality

A quantum network shared entangled sources among distant nodes enables us to distribute entanglement along the network by suitable measurements. Network nonlocality means that it does not admit a network model involving local variables emitted from independent sources. In this work, we construct an $(n,m,p)$-type quantum network configuration and then derive the corresponding $n$-local correlation inequalities based on the assumption of independent sources. As a universal acyclic network configuration, it can cover most of the existing network models, such as the typical chain-network and star-network, and admit both centerless and asymmetric configurations. Then we demonstrate the non-$n$-locality of the present network by calculating the violation of the $n$-local inequality with bipartite entangled sources and Pauli measurements.

quant-ph↗

arXiv2024

Planar two-region multi-partite maximally entangled states

In entanglement theory, there are different methods to consider one state being more entangled than another. The "maximally" entangled states in a multipartite system can be defined from an axiomatic perspective. According to different criteria for selection, there are many specific types of quantum maximally entangled states, such as absolutely maximally entangled state, planar maximally entangled state and so on. In this paper we propose a new type of maximally entangled states, the planar two-region multipartite maximally entangled state. The requirement condition of this maximally entangled state is weak than that of the absolutely maximally entangled state and different from that of the planar maximally entangled state. We show that there are the two-region four-partite maximally entangled states in 4-qubit and 7-qubit planar systems, although there is no absolutely maximally entangled state in these systems. It is proved that there are the planar two-region four-partite maximally entangled states in both even particle quantum systems and odd particle quantum systems. Additionally, based on some planar two-region four-partite maximally entangled states, the new planar two-region four-partite maximally entangled states are generated. We also provide some important examples of the planar two-region multi-partite maximally entangled states.

quant-ph↗

arXiv2024

Multi-task Meta Label Correction for Time Series Prediction

Time series classification faces two unavoidable problems. One is partial feature information and the other is poor label quality, which may affect model performance. To address the above issues, we create a label correction method to time series data with meta-learning under a multi-task framework. There are three main contributions. First, we train the label correction model with a two-branch neural network in the outer loop. While in the model-agnostic inner loop, we use pre-existing classification models in a multi-task way and jointly update the meta-knowledge so as to help us achieve adaptive labeling on complex time series. Second, we devise new data visualization methods for both image patterns of the historical data and data in the prediction horizon. Finally, we test our method with various financial datasets, including XOM, S\&P500, and SZ50. Results show that our method is more effective and accurate than some existing label correction techniques.

cs.LG↗

arXiv2024

Quantum teleportation based on the elegant joint measurement

As a generalization of the well-known Bell state measurement (BSM), the elegant joint measurement (EJM) is a kind of novel two-qubit joint measurement, parameterized by a subtle phase factor $θ\in [0,π/2]$. We explore quantum teleportation based on the EJM, inspired by Gisin's idea that quantum entanglement not only provides quantum channel and also quantum joint measurement for quantum teleportation. It is a probabilistic teleportation caused by undesired nonunitary quantum evolution. There are two interesting features in the present scenario. First, it goes beyond the conventional teleportation scenario, which can be included in the present scenario. Second, different from the BSM being single input and four outcomes, it can provide an adjustable input setting or even multiple measurement settings for the sender (or the controller). Moreover, we show in detail the feasible quantum circuits to realize the present scenario, where a few unitary operations and a nonunitary quantum gate are being utilized.

quant-ph↗

arXiv2024

Early Warning Prediction with Automatic Labeling in Epilepsy Patients

Early warning for epilepsy patients is crucial for their safety and well-being, in particular to prevent or minimize the severity of seizures. Through the patients' EEG data, we propose a meta learning framework to improve the prediction of early ictal signals. The proposed bi-level optimization framework can help automatically label noisy data at the early ictal stage, as well as optimize the training accuracy of the backbone model. To validate our approach, we conduct a series of experiments to predict seizure onset in various long-term windows, with LSTM and ResNet implemented as the baseline models. Our study demonstrates that not only the ictal prediction accuracy obtained by meta learning is significantly improved, but also the resulting model captures some intrinsic patterns of the noisy data that a single backbone model could not learn. As a result, the predicted probability generated by the meta network serves as a highly effective early warning indicator.

cs.LG↗

arXiv2024

Fourier neural operator based fluid-structure interaction for predicting the vesicle dynamics

Solving complex fluid-structure interaction (FSI) problems, characterized by nonlinear partial differential equations, is crucial in various scientific and engineering applications. Traditional computational fluid dynamics (CFD) solvers are insufficient to meet the growing requirements for large-scale and long-period simulations. Fortunately, the rapid advancement in neural networks, especially neural operator learning mappings between function spaces, has introduced novel approaches to tackle these challenges via data-driven modeling. In this paper, we propose a Fourier neural operator-based fluid-structure interaction solver (FNO-based FSI solver) for efficient simulation of FSI problems, where the solid solver based on the finite difference method is seamlessly integrated with the Fourier neural operator to predict incompressible flow using the immersed boundary method. We analyze the performance of the FNO-based FSI solver in the following three situations: training data with or without the steady state, training method with one-step label or multi-step labels, and prediction in interpolation or extrapolation. We find that the best performance for interpolation is achieved by training the operator with multi-step labels using steady-state data. Finally, we train the FNO-based FSI solver using this optimal training method and apply it to vesicle dynamics. The results show that the FNO-based FSI solver is capable of capturing the variations in the fluid and the vesicle.

math.DS↗

arXiv2023

Learning effective dynamics from data-driven stochastic systems

Multiscale stochastic dynamical systems have been widely adopted to a variety of scientific and engineering problems due to their capability of depicting complex phenomena in many real world applications. This work is devoted to investigating the effective dynamics for slow-fast stochastic dynamical systems. Given observation data on a short-term period satisfying some unknown slow-fast stochastic systems, we propose a novel algorithm including a neural network called Auto-SDE to learn invariant slow manifold. Our approach captures the evolutionary nature of a series of time-dependent autoencoder neural networks with the loss constructed from a discretized stochastic differential equation. Our algorithm is also validated to be accurate, stable and effective through numerical experiments under various evaluation metrics.

stat.ML↗