Representation Class and Geometrical Invariants of Quantum States under Local Unitary Transformations

We investigate the equivalence of bipartite quantum mixed states under local unitary transformations by introducing representation classes from a geometrical approach. It is shown that two bipartite mixed states are equivalent under local unitary transformations if and only if they have the same representation class. Detailed examples are given on calculating representation classes.Comment: 11 page

Revisiting Computer-Aided Tuberculosis Diagnosis

Tuberculosis (TB) is a major global health threat, causing millions of deaths annually. Although early diagnosis and treatment can greatly improve the chances of survival, it remains a major challenge, especially in developing countries. Recently, computer-aided tuberculosis diagnosis (CTD) using deep learning has shown promise, but progress is hindered by limited training data. To address this, we establish a large-scale dataset, namely the Tuberculosis X-ray (TBX11K) dataset, which contains 11,200 chest X-ray (CXR) images with corresponding bounding box annotations for TB areas. This dataset enables the training of sophisticated detectors for high-quality CTD. Furthermore, we propose a strong baseline, SymFormer, for simultaneous CXR image classification and TB infection area detection. SymFormer incorporates Symmetric Search Attention (SymAttention) to tackle the bilateral symmetry property of CXR images for learning discriminative features. Since CXR images may not strictly adhere to the bilateral symmetry property, we also propose Symmetric Positional Encoding (SPE) to facilitate SymAttention through feature recalibration. To promote future research on CTD, we build a benchmark by introducing evaluation metrics, evaluating baseline models reformed from existing detectors, and running an online challenge. Experiments show that SymFormer achieves state-of-the-art performance on the TBX11K dataset. The data, code, and models will be released.Comment: 14 page

Deep learning the hierarchy of steering measurement settings of qubit-pair states

Quantum steering has attracted increasing research attention because of its fundamental importance, as well as its applications in quantum information science. Regardless of the well-established characterization of the steerability of assemblages, it remains unclear how to detect the degree of steerability even for an arbitrary qubit-pair state due to the cumbersome optimization over all possible incompatible measurements. Here we leverage the power of the deep learning models to infer the hierarchy of steering measurement setting. A computational protocol consisting of iterative tests is constructed to overcome the optimization, meanwhile, generating the necessary training data. According to the responses of the well-trained models to the different physics-driven features encoding the states to be recognized, we can conclude that the most compact characterization of the Alice-to-Bob steerability is Alice's regularly aligned steering ellipsoid; whereas Bob's ellipsoid is irrelevant. Additionally, our approach is versatile in revealing further insights into the hierarchical structure of quantum steering and detecting the hidden steerability.Comment: 11 pages, 3 figure

Numerical modeling of spray combustion with an advanced VOF method

This paper summarizes the technical development and validation of a multiphase computational fluid dynamics (CFD) numerical method using the volume-of-fluid (VOF) model and a Lagrangian tracking model which can be employed to analyze general multiphase flow problems with free surface mechanism. The gas-liquid interface mass, momentum and energy conservation relationships are modeled by continuum surface mechanisms. A new solution method is developed such that the present VOF model can be applied for all-speed flow regimes. The objectives of the present study are to develop and verify the fractional volume-of-fluid cell partitioning approach into a predictor-corrector algorithm and to demonstrate the effectiveness of the present approach by simulating benchmark problems including laminar impinging jets, shear coaxial jet atomization and shear coaxial spray combustion flows

Compartmentalized droplets for continuous flow liquid-liquid interface catalysis

To address the limitations of batch organic-aqueous biphasic catalysis, we develop a conceptually novel method termed Flow Pickering Emulsion or FPE, to process biphasic reactions in a continuous flow fashion. This method involves the compartmentalization of bulk water into micron-sized droplets based on a water-in-oil Pickering emulsion, which are packed into a column reactor. The compartmentalized water droplets can confine water-soluble catalysts, thus “immobilizing” the catalyst in the column reactor, while the interstices between the droplets allow the organic (oil) phase to flow. Key fundamental principles underpinning this method such as the oil phase flow behavior, the stability of compartmentalized droplets and the confinement capability of these droplets towards water-soluble catalysts are experimentally and theoretically investigated. As a proof of this concept, case studies including a sulphuric acid-catalyzed addition reaction, a heteropolyacid-catalyzed ring opening reaction and an enzyme-catalyzed chiral reaction demonstrate the generality and versatility of the FPE method. Impressively, in addition to the excellent durability, the developed FPE reactions exhibit up to 10-fold reaction efficiency enhancement in comparison to the existing batch reactions, indicating a unique flow interface catalysis effect. This study opens up a new avenue to allow conventional biphasic catalysis reactions to access more sustainable and efficient flow chemistry using an innovative liquid-liquid interface protocol

Towards a reliable reconstruction of the power spectrum of primordial curvature perturbation on small scales from GWTC-3

Primordial black holes (PBHs) can be both candidates of dark matter and progenitors of binary black holes (BBHs) detected by the LIGO-Virgo-KAGRA collaboration. Since PBHs could form in the very early Universe through the gravitational collapse of primordial density perturbations, the population of BBHs detected by gravitational waves encodes much information on primordial curvature perturbation. In this work, we take a reliable and systematic approach to reconstruct the power spectrum of the primordial curvature perturbation from GWTC-3, under the hierarchical Bayesian inference framework, by accounting for the measurement uncertainties and selection effects. In addition to just considering the single PBH population model, we also report the results considering the multi-population model, i.e., the mixed PBH and astrophysical black hole binaries model. We find that the maximum amplitude of the reconstructed power spectrum of primordial curvature perturbation can be $\sim2.5\times10^{-2}$ at $\mathcal{O}(10^{5})~\rm Mpc^{-1}$ scales, which is consistent with the PBH formation scenario from inflation at small scales