arXiv subjects

Lijun Liu

Publications and source records attributed to Lijun Liu.

32 records · Page 2Linked to original sources

arXiv2024

The polygon relation and subadditivity of entropic measures for discrete and continuous multipartite entanglement

In a recent work [Ge {\it et al.}, arXiv: 2312. 17496 (2023)], we have derived the polygon relation of bipartite entanglement measures that is useful to reveal the entanglement properties of discrete, continuous, and even hybrid multipartite quantum systems. In this work, with the information-theoretical measures of Rényi and Tsallis entropies, we study the relationship between the polygon relation and the subadditivity of entropy. In particular, the entropy-polygon relations are derived for pure multi-qubit states and generalized to multi-mode Gaussian states, by utilizing the known results from the quantum marginal problem. Moreover, the equivalence between the polygon relation and subadditivity is established, in the sense that for all discrete or continuous multipartite states, the polygon relation holds if and only if the underlying entropy is subadditive. As byproduct, the subadditivity of Rényi and Tsallis entropies is proven for all bipartite Gaussian states. Finally, the difference between polygon relations and monogamy relations is clarified, and generalizations of our results are discussed. Our work provides a better understanding of the rich structure of multipartite states, and hence is expected to be helpful for the study of multipartite entanglement.

quant-ph↗

arXiv2024

Faithful geometric measures for genuine tripartite entanglement

We present a faithful geometric picture for genuine tripartite entanglement of discrete, continuous, and hybrid quantum systems. We first find that the triangle relation $\mathcal{E}^α_{i|jk}\leq \mathcal{E}^α_{j|ik}+\mathcal{E}^α_{k|ij}$ holds for all subadditive bipartite entanglement measure $\mathcal{E}$, all permutations under parties $i, j, k$, all $α\in [0, 1]$, and all pure tripartite states. It provides a geometric interpretation that bipartition entanglement, measured by $\mathcal{E}^α$, corresponds to the side of a triangle, of which the area with $α\in (0, 1)$ is nonzero if and only if the underlying state is genuinely entangled. Then, we rigorously prove the non-obtuse triangle area with $0<α\leq 1/2$ is a measure for genuine tripartite entanglement. Useful lower and upper bounds for these measures are obtained, and generalizations of our results are also presented. Finally, it is significantly strengthened for qubits that, given a set of subadditive and non-additive measures, some state is always found to violate the triangle relation for any $α>1$, and the triangle area is not a measure for any $α>1/2$. Hence, our results are expected to aid significant progress in studying both discrete and continuous multipartite entanglement.

quant-ph↗

arXiv2024

Efficient factored gradient descent algorithm for quantum state tomography

Reconstructing the state of quantum many-body systems is of fundamental importance in quantum information tasks, but extremely challenging due to the curse of dimensionality. In this work, we present an efficient quantum tomography protocol that combines the state-factored with eigenvalue mapping to address the rank-deficient issue and incorporates a momentum-accelerated gradient descent algorithm to speed up the optimization process. We implement extensive numerical experiments to demonstrate that our factored gradient descent algorithm efficiently mitigates the rank-deficient problem and admits orders of magnitude better tomography accuracy and faster convergence. We also find that our method can accomplish the full-state tomography of random 11-qubit mixed states within one minute.

quant-ph↗

arXiv2024

AAVDiff: Experimental Validation of Enhanced Viability and Diversity in Recombinant Adeno-Associated Virus (AAV) Capsids through Diffusion Generation

Recombinant adeno-associated virus (rAAV) vectors have revolutionized gene therapy, but their broad tropism and suboptimal transduction efficiency limit their clinical applications. To overcome these limitations, researchers have focused on designing and screening capsid libraries to identify improved vectors. However, the large sequence space and limited resources present challenges in identifying viable capsid variants. In this study, we propose an end-to-end diffusion model to generate capsid sequences with enhanced viability. Using publicly available AAV2 data, we generated 38,000 diverse AAV2 viral protein (VP) sequences, and evaluated 8,000 for viral selection. The results attested the superiority of our model compared to traditional methods. Additionally, in the absence of AAV9 capsid data, apart from one wild-type sequence, we used the same model to directly generate a number of viable sequences with up to 9 mutations. we transferred the remaining 30,000 samples to the AAV9 domain. Furthermore, we conducted mutagenesis on AAV9 VP hypervariable regions VI and V, contributing to the continuous improvement of the AAV9 VP sequence. This research represents a significant advancement in the design and functional validation of rAAV vectors, offering innovative solutions to enhance specificity and transduction efficiency in gene therapy applications.

cs.AI↗

arXiv2024

Experimental verification of the steering ellipsoid zoo via two-qubit states

Quantum steering ellipsoid visualizes the set of all qubit states that can be steered by measuring on another correlated qubit in the Bloch picture. Together with local reduced states, it provides a faithful geometric characterization of the underlying two-qubit state so that almost all nonclassical state features can be reflected in its geometric properties. Consequently, the various types of quantum ellipsoids with different geometric properties form an ellipsoid zoo, which, in this work, is experimentally verified via measurements on many polarization-path photonic states. By generating two-qubit states with high fidelity, the corresponding ellipsoids are constructed to certify the presence of entanglement, one-way Einstein-Podolsky-Rosen steering, discord, and steering incompleteness. It is also experimentally verified that the steering ellipsoid can be reconstructed from using the twelve vertices of the icosahedron as measurement directions. Our results aid progress in applying the quantum steering ellipsoid to reveal nonclassical features of the multi-qubit system.

quant-ph↗

arXiv2023

Tripartite entanglement measure under local operations and classical communication

Multipartite entanglement is an indispensable resource in quantum communication and computation, however, it is a challenging task to faithfully quantify this global property of multipartite quantum systems. In this work, we study the concurrence fill, which admits a geometric interpretation to measure genuine tripartite entanglement for the three-qubit system in [S. Xie {\it et al.}, Phys. Rev. Lett. \textbf{127}. 040403 (2021)]. First, we use the well-known three-tangle and bipartite concurrence to reformulate this quantifier for all pure states. We then construct an explicit example to conclusively show the concurrence fill can be increased under local operation and classical communications (LOCCs) {\it on average}, implying it is not an entanglement monotone. Moreover, we give a simple proof of the LOCC-monotonicity of three-tangle and find that the bipartite concurrence and the squared can have distinct performances under the same LOCCs. Finally, we propose a reliable monotone to quantify genuine tripartite entanglement, which can also be easily generalised to the multipartite system. Our results shed light on studying genuine entanglement and also reveal the complex structure of multipartite systems.

quant-ph↗

arXiv2023

Hemispheric Dichotomy of Mantle Dynamics Revealed by Machine Learning

Past efforts to interrogate the mantle's contribution to Earth's topography suffer from inadequate in-situ measurements of true bathymetry and the involvement of an empirical plate model whose presumed lithospheric density profile interferes with the interpretation of other mantle forces. Here, we introduce a machine learning algorithm that estimates the oceanic residual topography based solely on surface and crustal attributes, providing a more objective proxy for the topographic contribution from the mantle. Ablation studies show that seafloor age is the most important factor, while other properties help further improve the fit to bathymetry. The resulting residual topography has notably smaller amplitudes than previous estimates, indicating that more surface features can be explained by crustal properties than previously thought. This exercise, designed to allow detection of long-wavelength signals, uncovers a more prominent degree-one topographic component than the degree-two pattern, both with much smaller amplitudes than previously thought. We suggest that this result reflects a hemispheric contrast in mantle dynamics, especially the two large low shear-wave velocity provinces (LLSVPs). This inference is further strengthened by quantifying the respective topographic contributions from lithospheric isostasy and dynamic topography. We conclude that mantle convection beneath the Atlantic is more vigorous than that beneath the Pacific, likely due to their different thermal-chemical states.

physics.geo-ph↗

arXiv2022

Recycling qubits for the generation of Bell nonlocality between independent sequential observers

There is currently much interest in the recycling of entangled systems, for use in quantum information protocols by sequential observers. In this work, we study the sequential generation of Bell nonlocality via recycling one or both components of two-qubit states. We first give a description of two-valued qubit measurements in terms of measurement bias, strength, and reversibility, and derive useful tradeoff relations between them. Then, we derive one-sided monogamy relations for unbiased observables, that strengthen the recent Conjecture in [S. Cheng {\it et al.}, Phys. Rev. A \textbf{104}, L060201 (2021) ] that if the first pair of observers violate Bell nonlocality then a subsequent independent pair cannot, and give semi-analytic results for the best possible monogamy relation. We also extend the construction in [P. J. Brown and R. Colbeck, Phys. Rev. Lett. \textbf{125}, 090401 (2020)] to obtain (i)~a broader class of two-qubit states that allow the recycling of one qubit by a given number of observers on one side, and (ii)~a scheme for generating Bell nonlocality between arbitrarily many independent observers on each side, via the two-sided recycling of multiqubit states. Our results are based on a formalism that is applicable to more general problems in recycling entanglement, and hence is expected to aid progress in this field.

quant-ph↗

arXiv2022

Extending the limit of molecular dynamics with ab initio accuracy to 10 billion atoms

High-performance computing, together with a neural network model trained from data generated with first-principles methods, has greatly boosted applications of \textit{ab initio} molecular dynamics in terms of spatial and temporal scales on modern supercomputers. Previous state-of-the-art can achieve $1-2$ nanoseconds molecular dynamics simulation per day for 100-million atoms on the entire Summit supercomputer. In this paper, we have significantly reduced the memory footprint and computational time by a comprehensive approach with both algorithmic and system innovations. The neural network model is compressed by model tabulation, kernel fusion, and redundancy removal. Then optimizations such as acceleration of customized kernel, tabulation of activation function, MPI+OpenMP parallelization are implemented on GPU and ARM architectures. Testing results of the copper system show that the optimized code can scale up to the entire machine of both Fugaku and Summit, and the corresponding system size can be extended by a factor of $134$ to an unprecedented $17$ billion atoms. The strong scaling of a $13.5$-million atom copper system shows that the time-to-solution can be 7 times faster, reaching $11.2$ nanoseconds per day. This work opens the door for unprecedentedly large-scale molecular dynamics simulations based on {\it ab initio} accuracy and can be potentially utilized in studying more realistic applications such as mechanical properties of metals, semiconductor devices, batteries, etc. The optimization techniques detailed in this paper also provide insight for relevant high-performance computing applications.

cs.DC↗

arXiv2021

Limitations on sharing Bell nonlocality between sequential pairs of observers

We give strong analytic and numerical evidence that, under mild measurement assumptions, two qubits cannot both be recycled to generate Bell nonlocality between multiple independent observers on each side. This is surprising, as under the same assumptions it is possible to recycle just one of the qubits an arbitrarily large number of times [P. J. Brown and R. Colbeck, Phys. Rev. Lett. 125, 090401 (2020)]. We derive corresponding 'one-sided monogamy relations' that rule out two-sided recycling for a wide range of parameters, based on a general tradeoff relation between the strengths and maximum reversibilities of qubit measurements. We also show if the assumptions are relaxed to allow sufficiently biased measurement selections, then there is a narrow range of measurement strengths that allows two-sided recycling for two observers on each side, and propose an experimental test. Our methods may be readily applied to other types of quantum correlations, such as steering and entanglement, and hence to general information protocols involving sequential measurements.

quant-ph↗

arXiv2018

Global stability of a network-based SIRS epidemic model with nonmonotone incidence rate

This paper studies the dynamics of a network-based SIRS epidemic model with vaccination and a nonmonotone incidence rate. This type of nonlinear incidence can be used to describe the psychological or inhibitory effect from the behavioral change of the susceptible individuals when the number of infective individuals on heterogeneous networks is getting larger. Using the analytical method, epidemic threshold $R_0$ is obtained. When $R_0$ is less than one, we prove the disease-free equilibrium is globally asymptotically stable and the disease dies out, while $R_0$ is greater than one, there exists a unique endemic equilibrium. By constructing a suitable Lyapunov function, we also prove the endemic equilibrium is globally asymptotically stable if the inhibitory factor $α$ is sufficiently large. Numerical experiments are also given to support the theoretical results. It is shown both theoretically and numerically a larger $α$ can accelerate the extinction of the disease and reduce the level of disease.

q-bio.PE↗

arXiv2018

Monogamy relations for nonclassical correlations of multi-qubit states

Nonclassical correlations have been found useful in many quantum information processing tasks, and various measures have been proposed to quantify these correlations. In this work, we mainly study one of nonclassical correlations, called measurement-induced nonlocality (MIN). First, we establish a close connection between this nonlocal effect and the Bell nonlocality for two-qubit states. Then, we derive a tight monogamy relation of MIN for any pure three-qubit state and provide an alternative way to obtain similar monogamy relations for other nonclassical correlation measures, including squared negativity, quantum discord, and geometric quantum discord. Finally, we find that the tight monogamy relation of MIN is violated by some mixed three-qubit states, however, a weaker monogamy relation of MIN for mixed states and even multi-qubit states is still obtained.

quant-ph↗

arXiv2014

Real-time Information, Uncertainty and Quantum Feedback Control

Feedback is the core concept in cybernetics and its effective use has made great success in but not limited to the fields of engineering, biology, and computer science. When feedback is used to quantum systems, two major types of feedback control protocols including coherent feedback control (CFC) and measurement-based feedback control (MFC) have been developed. In this paper, we compare the two types of quantum feedback control protocols by focusing on the real-time information used in the feedback loop and the capability in dealing with parameter uncertainty. An equivalent relationship is established between quantum CFC and non-selective quantum MFC in the form of operator-sum representation. Using several examples of quantum feedback control, we show that quantum MFC can theoretically achieve better performance than quantum CFC in stabilizing a quantum state and dealing with Hamiltonian parameter uncertainty. The results enrich understanding of the relative advantages between quantum MFC and quantum CFC, and can provide useful information in choosing suitable feedback protocols for quantum systems.

quant-ph↗

arXiv2014

High Precision Inertial Rotation Rate and Magnetic Field Estimate via Extended Kalman Filter

Recent developments of technology have enabled atomic spins as the most sensitive inertial and magnetic sensors. Atomic spin gyroscope (magnetometer) essentially outputs the estimate of the inertial rotation rate (magnetic filed) to be measured. Conventional methods for estimating a static or quasi-static inertial rotation rate (magnetic field) employ the dependency relationship between the steady state signal and the input rotation rate (magnetic field). In this paper we present an extended Kalman filter (EKF) method for the atomic spin gyroscope and magnetometer. It is demonstrated that the EKF method is much more accurate and faster than the conventional steady state estimation method.

quant-ph↗