arXiv subjects

Maggie Cheng

Publications and source records attributed to Maggie Cheng.

5 recordsLinked to original sources

arXiv2024

SLOCC and LU classification of black holes with eight electric and magnetic charges

In \cite{Linde}, Kallosh and Linde discussed the SLOCC classification of black holes. However, the criteria for the SLOCC classification of black holes have not been given. In addition, the LU classification of black holes has not been studied in the past. In this paper we will consider both SLOCC and LU classification of the STU black holes with four integer electric charges $q_{i} $ and four integer magnetic charges $p^{i}$, $i=0,1,2,3$. Two STU black holes with eight charges are considered SLOCC (LU) equivalent if and only if their corresponding states of three qubits are SLOCC (LU) equivalent. Under this definition, we give criteria for the classification of the eight-charge STU black holes under SLOCC and under LU, respectively. We will study the classification of the black holes via the classification of SLOCC and LU entanglement of three qubits. We then identify a set of black holes corresponding to the state W of three qubits, which is of interest since it has the maximal average von Neumann entropy of entanglement. Via von Neumann entanglement entropy, we partition the STU black holes corresponding to pure states of GHZ SLOCC class into five families under LU.

gr-qc↗

arXiv2024

Fast Orthogonal Matching Pursuit through Successive Regression

Orthogonal Matching Pursuit (OMP) has been a powerful method in sparse signal recovery and approximation. However, OMP suffers computational issues when the signal has a large number of non-zeros. This paper advances OMP and its extension called generalized OMP (gOMP) by offering fast algorithms for the orthogonal projection of the input signal at each iteration. The proposed modifications directly reduce the computational complexity of OMP and gOMP. Experiment results verified the improvement in computation time. This paper also provides sufficient conditions for exact signal recovery. For general signals with additive noise, the approximation error is at the same order as OMP (gOMP), but is obtained within much less time.

cs.CV↗

arXiv2024

Learning Domain-Independent Green's Function For Elliptic Partial Differential Equations

Green's function characterizes a partial differential equation (PDE) and maps its solution in the entire domain as integrals. Finding the analytical form of Green's function is a non-trivial exercise, especially for a PDE defined on a complex domain or a PDE with variable coefficients. In this paper, we propose a novel boundary integral network to learn the domain-independent Green's function, referred to as BIN-G. We evaluate the Green's function in the BIN-G using a radial basis function (RBF) kernel-based neural network. We train the BIN-G by minimizing the residual of the PDE and the mean squared errors of the solutions to the boundary integral equations for prescribed test functions. By leveraging the symmetry of the Green's function and controlling refinements of the RBF kernel near the singularity of the Green function, we demonstrate that our numerical scheme enables fast training and accurate evaluation of the Green's function for PDEs with variable coefficients. The learned Green's function is independent of the domain geometries, forcing terms, and boundary conditions in the boundary integral formulation. Numerical experiments verify the desired properties of the method and the expected accuracy for the two-dimensional Poisson and Helmholtz equations with variable coefficients.

physics.comp-ph↗

arXiv2022

Classification of "large" black holes into seven families

The black-hole--qubit correspondence has been proven to be ``useful for obtaining additional insight into one of the string black hole theory and quantum information theory by exploiting approaches of the other"[Phys. Rev. D 82, 026003 (2010)]. Though different classes of stringy black holes can be related to the well-known stochastic local operations and classical communication (SLOCC) entanglement classes of pure states, the string theory requires a more detailed classification than the SLOCC classification of three qubits. In this paper, we derive the entanglement family of three qubits under local unitary operations (LU), and use the black-hole--qubit correspondence to classify \textquotedblleft large\textquotedblright\ black holes into seven inequivalent families. In particular, we show that two black holes with 4 non-vanishing charges ($q_{0}$, $p^{1}$, $p^{2}$, and $p^{3}$) are LU equivalent if their difference is only in the signs of charges. Thus, the classification of black holes is independent of the signs of charges and is only related to the ratio of the absolute values of charges. This observation simplifies the classification task, as one would only need to consider either the classification of non-BPS black holes or the classification of BPS black holes, but not both. Moreover, through the LU classification, the physical basis for this black-hole--qubit correspondence can be observed, and a relation between the black-hole entropy and the von Neumann entanglement entropy is revealed. Therefore, the LU classification offers a more straightforward physical connection than the SLOCC classification. Based on the LU classification, we further study the properties of von Neumann entanglement entropy for each of the seven families, and find the black holes with the maximal von Neumann entanglement entropy.

quant-ph↗

arXiv2022

A relation among tangle, 3-tangle, and von Neumann entropy of entanglement for three qubits

In this paper, we derive a general formula of the tangle for pure states of three qubits, and present three explicit local unitary (LU) polynomial invariants. Our result goes beyond the classical work of tangle, 3-tangle and von Neumann entropy of entanglement for Ac\'{\i}n et al.' Schmidt decomposition (ASD) of three qubits by connecting the tangle, 3-tangle, and von Neumann entropy for ASD with Ac\'{\i}n et al.'s LU invariants. In particular, our result reveals a general relation among tangle, 3-tangle, and von Neumann entropy, together with a relation among their averages. The relations can help us find the entangled states satisfying distinct requirements for tangle, 3-tangle, and von Neumann entropy. Moreover, we obtain all the states of three qubits of which tangles, concurrence, 3-tangle and von Neumann entropy don't vanish and these states are endurable when one of three qubits is traced out. We indicate that for the three-qubit W state, its average von Neumann entropy is maximal only within the W SLOCC class, and that under ASD the three-qubit GHZ state is the unique state of which the reduced density operator obtained by tracing any two qubits has the maximal von Neumann entropy.

quant-ph↗