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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., Comment: Published version, and comments are welcome

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.

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., Comment: 13 pages, 11 figures, conference : Principles and Practice of Parallel Programming 2022

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., Comment: Minor corrections, More references, and revision of Fig. 2