arXiv subjects

Ting Gao

Publications and source records attributed to Ting Gao.

At least 91 records · Page 5Linked to original sources

arXiv2022

A $(k+1)$-partite entanglement measure of $N$-partite quantum states

The concept of \textquotedblleft the permutationally invariant part of a density matrx\textquotedblright constitutes an important tool for entanglement characterization of multiqubit systems. In this paper, we first present $(k+1)$-partite entanglement measure of $N$-partite quantum system, which possesses desirable properties of an entanglement measure. Moreover, we give strong bounds on this measure by considering the permutationally invariant part of a multipartite state. We give two definitions of efficient measurable degree of $(k+1)$-partite entanglement. Finally, several concrete examples are given to illustrate the effectiveness of our results.

quant-ph↗

arXiv2022

Neural network stochastic differential equation models with applications to financial data forecasting

In this article, we employ a collection of stochastic differential equations with drift and diffusion coefficients approximated by neural networks to predict the trend of chaotic time series which has big jump properties. Our contributions are, first, we propose a model called Lévy induced stochastic differential equation network, which explores compounded stochastic differential equations with $α$-stable Lévy motion to model complex time series data and solve the problem through neural network approximation. Second, we theoretically prove that the numerical solution through our algorithm converges in probability to the solution of corresponding stochastic differential equation, without curse of dimensionality. Finally, we illustrate our method by applying it to real financial time series data and find the accuracy increases through the use of non-Gaussian Lévy processes. We also present detailed comparisons in terms of data patterns, various models, different shapes of Lévy motion and the prediction lengths.

cs.LG↗

arXiv2022

Methods of constructing superposition measures

The resource theory of quantum superposition is an extension of the quantum coherent theory, in which linear independence relaxes the requirement of orthogonality. It can be used to quantify the nonclassical in superposition of finite number of optical coherent states. Based on convex roof extended, state transformation and weight, we give three methods of constructing superposition measures of quantum states, respectively. We also generalize the superposition resource theory from two perspectives.

quant-ph↗

arXiv2022

Tighter sum uncertainty relations via metric-adjusted skew information

In this paper, we first provide three general norm inequalities, which are used to give new uncertainty relations of any finite observables and quantum channels via metric-adjusted skew information. The results are applicable to its special cases as Wigner-Yanase-Dyson skew information. In quantifying the uncertainty of channels, we discuss two types of lower bounds and compare the tightness between them, meanwhile, a tight lower bound is given. The uncertainty relations obtained by us are stronger than the existing ones. To illustrate our results, we give several specific examples.

quant-ph↗

arXiv2022

Quantum properties in the four-node network

There are different preparable quantum states in different network structures. The four nodes as a whole has two situations: one is the four nodes in a plane, the other is the four nodes in the space. In this paper, we obtain some properties of the quantum states that can be prepared in four-node network structures. These include the properties of entropy, entanglement measure, rank and multipartite entangled states. These properties also mean that the network structures impose some constraints on the states that can be prepared in a four-node quantum network. In order to obtain these properties we also define $n$-partite mutual information of the quantum system, which satisfies symmetry requirement.

quant-ph↗

arXiv2022

Reevaluation of heavy-fermion-induced electron EDM at three loops

Motivated by improved limits on electric dipole moments (EDMs), we revisit the three-loop light-by-light mechanism that transmits $CP$ violation from a heavy fermion to a light one. Applying it to the electron EDM induced by EDMs of heavier flavors, we find additional contributions at the order $ m_e/m_μ$ or $m_e/m_τ$ that were missing before and that make the result 1.4 times larger. Consequently we improve bounds on the tau EDM, and update indirect limits on the muon EDM as well as charm and bottom quark color EDMs.

hep-ph↗

arXiv2022

An end-to-end deep learning approach for extracting stochastic dynamical systems with $α$-stable Lévy noise

Recently, extracting data-driven governing laws of dynamical systems through deep learning frameworks has gained a lot of attention in various fields. Moreover, a growing amount of research work tends to transfer deterministic dynamical systems to stochastic dynamical systems, especially those driven by non-Gaussian multiplicative noise. However, lots of log-likelihood based algorithms that work well for Gaussian cases cannot be directly extended to non-Gaussian scenarios which could have high error and low convergence issues. In this work, we overcome some of these challenges and identify stochastic dynamical systems driven by $α$-stable Lévy noise from only random pairwise data. Our innovations include: (1) designing a deep learning approach to learn both drift and diffusion coefficients for Lévy induced noise with $α$ across all values, (2) learning complex multiplicative noise without restrictions on small noise intensity, (3) proposing an end-to-end complete framework for stochastic systems identification under a general input data assumption, that is, $α$-stable random variable. Finally, numerical experiments and comparisons with the non-local Kramers-Moyal formulas with moment generating function confirm the effectiveness of our method.

stat.ML↗

arXiv2022

Stock Trading Optimization through Model-based Reinforcement Learning with Resistance Support Relative Strength

Reinforcement learning (RL) is gaining attention by more and more researchers in quantitative finance as the agent-environment interaction framework is aligned with decision making process in many business problems. Most of the current financial applications using RL algorithms are based on model-free method, which still faces stability and adaptivity challenges. As lots of cutting-edge model-based reinforcement learning (MBRL) algorithms mature in applications such as video games or robotics, we design a new approach that leverages resistance and support (RS) level as regularization terms for action in MBRL, to improve the algorithm's efficiency and stability. From the experiment results, we can see RS level, as a market timing technique, enhances the performance of pure MBRL models in terms of various measurements and obtains better profit gain with less riskiness. Besides, our proposed method even resists big drop (less maximum drawdown) during COVID-19 pandemic period when the financial market got unpredictable crisis. Explanations on why control of resistance and support level can boost MBRL is also investigated through numerical experiments, such as loss of actor-critic network and prediction error of the transition dynamical model. It shows that RS indicators indeed help the MBRL algorithms to converge faster at early stage and obtain smaller critic loss as training episodes increase.

q-fin.MF↗

arXiv2022

Tighter monogamy relations in multiparty quantum systems

We investigate tight monogamy relations of multiparty quantum entanglement for any quantum state in this paper. First, we obtain a class of lower bounds for multiparty quantum systems which improve the previous results. Next, we establish a class of tighter monogamy relations in tripartite quantum systems by means of the new inequality. Furthermore, we generalize this relations to multiparty quantum systems. And then we prove the lower bounds we obtained are larger than the existing ones. Detailed examples are provided at last.

quant-ph↗

arXiv2022

Improved indirect limits on charm and bottom quark EDMs

We derive indirect limits on the charm and bottom quark electric dipole moments (EDMs) from paramagnetic AMO and neutron EDM experiments. The charm and bottom quark EDMs generate $CP$-odd photon-gluon operators and light quark EDMs at the $c$- and $b$-quark mass thresholds. These $CP$-odd operators induce the $CP$-odd semi-leptonic operator $C_S$ and the neutron EDM below the QCD scale that are probed by the paramagnetic and neutron EDM experiments, respectively. The bound from $C_S$ is $\vert d_c \vert < 1.3\times 10^{-20}\,e\,\mathrm{cm}$ for the charm quark and $\vert d_b \vert < 7.6\times 10^{-19}\,e\,\mathrm{cm}$ for the bottom quark, with its uncertainty estimated as 10%. The neutron EDM provides a stronger bound, $\vert d_c \vert < 6\times 10^{-22}\,e\,\mathrm{cm}$ and $\vert d_b \vert < 2\times 10^{-20}\,e\,\mathrm{cm}$, though with a larger hadronic uncertainty.

hep-ph↗

arXiv2022

Learning the temporal evolution of multivariate densities via normalizing flows

In this work, we propose a method to learn multivariate probability distributions using sample path data from stochastic differential equations. Specifically, we consider temporally evolving probability distributions (e.g., those produced by integrating local or nonlocal Fokker-Planck equations). We analyze this evolution through machine learning assisted construction of a time-dependent mapping that takes a reference distribution (say, a Gaussian) to each and every instance of our evolving distribution. If the reference distribution is the initial condition of a Fokker-Planck equation, what we learn is the time-T map of the corresponding solution. Specifically, the learned map is a multivariate normalizing flow that deforms the support of the reference density to the support of each and every density snapshot in time. We demonstrate that this approach can approximate probability density function evolutions in time from observed sampled data for systems driven by both Brownian and Lévy noise. We present examples with two- and three-dimensional, uni- and multimodal distributions to validate the method.

stat.ML↗

arXiv2022

Improved indirect limits on muon EDM

Given current discrepancy in muon $g-2$ and future dedicated efforts to measure muon electric dipole moment (EDM) $d_μ$, we assess the indirect constraints imposed on $d_μ$ by the EDM measurements performed with heavy atoms and molecules. We notice that the dominant muon EDM effect arises via the muon-loop induced "light-by-light" $CP$-odd amplitude $\propto{\bf B}{\bf E}^3$, and in the vicinity of a large nucleus the corresponding parameter of expansion can be significant, $eE_{\rm nucl}/m_μ^2 \sim 0.04$. We compute the $d_μ$-induced Schiff moment of the $^{199}$Hg nucleus, and the linear combination of $d_e$ and semileptonic $C_S$ operator (dominant in this case) that determine the $CP$-odd effects in ThO molecule. The results, $d_μ(^{199}{\rm Hg}) < 6\times 10^{-20}e$cm and $d_μ({\rm ThO}) < 2\times 10^{-20}e$cm, constitute approximately three- and nine-fold improvements over the limits on $d_μ$ extracted from the BNL muon beam experiment.

hep-ph↗

arXiv2022

Standard Model prediction for paramagnetic EDMs

Standard Model $CP$ violation associated with the phase of the Cabibbo-Kobayashi-Maskawa quark mixing matrix is known to give small answers for the EDM observables. Moreover, predictions for the EDMs of neutrons and diamagnetic atoms suffer from considerable uncertainties. We point out that the $CP$-violating observables associated with the electron spin (paramagnetic EDMs) are dominated by the combination of the electroweak penguin diagrams and $ΔI =1/2$ weak transitions in the baryon sector, and are calculable within chiral perturbation theory. The predicted size of the semileptonic operator $C_S$ is $7\times 10^{-16}$ which corresponds to the equivalent electron EDM $d_e^{\rm eq} = 1.0 \times 10^{-35}e\,{\rm cm}$. While still far from the current observational limits, this result is three orders of magnitude larger than previously believed.

hep-ph↗

arXiv2022

On coherence of quantum operations by using Choi-Jamiołkowski isomorphism

In quantum information, most information processing processes involve quantum channels. One manifestation of a quantum channel is quantum operation acting on quantum states. The coherence of quantum operations can be considered as a quantum resource, which can be exploited to perform certain quantum tasks. From the viewpoint of Choi-Jamiołkowski isomorphism, we study the coherence of quantum operations in the framework of resource theory. We define the phase-out superoperation and give the operation which transforms the Choi-Jamiołkowski state of a quantum operation to the Choi-Jamiołkowski state of the another quantum operation obtained by using the phase-out superoperation to act on the quantum operation. The set of maximally incoherent superoperations, the set of nonactivating coherent superoperations and the set of de-phase incoherent superoperations are defined and we prove that these sets are closed to compound operation and convex combination of quantum superoperations. Further, we introduce the fidelity coherence measure of quantum operations and obtain the exact form of the fidelity coherence measure of the unitary operations on the single qubit.

quant-ph↗

arXiv2021

A scalable tripartite Wigner's friend scenario

Wigner's friend thought experiment is intended to reveal the inherent tension between unitary evolution and measurement collapse. On the basis of Wigner's friend experiment, Brukner derives a no-go theorem for observer-independent facts. We construct an extended Wigner's friend scenario including three laboratories, namely, Alice's laboratory, Bob's laboratory and Charlie's laboratory, where Alice, Bob and Charlie are standing outside the laboratories while their friends are placed inside their own laboratories. We consider quantum simulation via Q\# quantum programming and also realize the primary quantum circuits using IBM quantum computers. Then, we calculate the probabilities and corresponding statistical uncertainties. It has been shown that the results of quantum simulation are clearly consistent with theoretical values, while it has a slightly higher error rates for the experimental results of quantum computers mainly because of a series of quantum gates, especially CNOT gates.

quant-ph↗

arXiv2021

The block-coherence measures and the coherence measures based on positive-operator-valued measures

We mainly study the block-coherence measures based on resource theory of block-coherence and the coherence measures based on positive-operator-valued measures (POVM). Several block-coherence measures including a block-coherence measure based on maximum relative entropy, the one-shot block coherence cost under the maximally block-incoherent operations, and a coherence measure based on coherent rank have been introduced and the relationships between these block-coherence measures have been obtained. We also give the definition of the maximally block-coherent state and describe the deterministic coherence dilution process by constructing block-incoherent operations. Based on the POVM coherence resource theory, we propose a POVM-based coherence measure by using the known scheme of building POVM-based coherence measures from block-coherence measures, and the one-shot block coherence cost under the maximally POVM-incoherent operations. The relationship between the POVM-based coherence measure and the one-shot block coherence cost under the maximally POVM-incoherent operations is analysed.

quant-ph↗

arXiv2021

Optimal convex approximations of quantum states based on fidelity

We investigate the problem of optimally approximating a desired state by the convex mixing of a set of available states. The problem is recasted as finding the optimal state with the minimum distance from target state in a convex set of usable states. Based on the fidelity, we define the optimal convex approximation of an expected state and present the complete exact solutions with respect to an arbitrary qubit state. We find that the optimal state based on fidelity is closer to the target state than the optimal state based on trace norm in many ranges. Finally, we analyze the geometrical properties of the target states which can be completely represented by a set of practicable states. Using the feature of convex combination, we express this class of target states in terms of three available states.

quant-ph↗

arXiv2021

Entanglement resource theory of quantum channel

Quantum channels can represent dynamic resources, which are indispensable elements in many physical scenarios. To describe certain facets of nonclassicality of the channels, it is necessary to quantify their properties. In the framework of resource theory of quantum channel, we show two general ways of constructing entanglement measure of channels. We also present several entanglement measures of channels based on the Choi relative entropy of channels, concurrence and $k$-ME concurrence and give some specific examples. These entanglement measures of channels can deepen the cognizing about channel and advance the research on the transformation between coherent resources and entangled resources. In addition, we prove that these measures satisfy the properties including nonnegativity, monotonicity, convexity and so on.

quant-ph↗