Bell's Inequality and Entanglement in Qubits

We propose an alternative evaluation of quantum entanglement by measuring the maximum violation of the Bell's inequality without performing a partial trace operation. This proposal is demonstrated by bridging the maximum violation of the Bell's inequality and the concurrence of a pure state in an $n$-qubit system, in which one subsystem only contains one qubit and the state is a linear combination of two product states. We apply this relation to the ground states of four qubits in the Wen-Plaquette model and show that they are maximally entangled. A topological entanglement entropy of the Wen-Plaquette model could be obtained by relating the upper bound of the maximum violation of the Bell's inequality to the concurrences of a pure state with respect to different bipartitions.Comment: 10 page

Algebraic Quantum Error-Correction Codes

Based on the group structure of a unitary Lie algebra, a scheme is provided to systematically and exhaustively generate quantum error correction codes, including the additive and nonadditive codes. The syndromes in the process of error-correction distinguished by different orthogonal vector subspaces, the coset subspaces. Moreover, the generated codes can be classified into four types with respect to the spinors in the unitary Lie algebra and a chosen initial quantum state

Revealing nonclassicality beyond Gaussian states via a single marginal distribution

A standard method to obtain information on a quantum state is to measure marginal distributions along many different axes in phase space, which forms a basis of quantum state tomography. We theoretically propose and experimentally demonstrate a general framework to manifest nonclassicality by observing a single marginal distribution only, which provides a novel insight into nonclassicality and a practical applicability to various quantum systems. Our approach maps the 1-dim marginal distribution into a factorized 2-dim distribution by multiplying the measured distribution or the vacuum-state distribution along an orthogonal axis. The resulting fictitious Wigner function becomes unphysical only for a nonclassical state, thus the negativity of the corresponding density operator provides an evidence of nonclassicality. Furthermore, the negativity measured this way yields a lower bound for entanglement potential---a measure of entanglement generated using a nonclassical state with a beam splitter setting that is a prototypical model to produce continuous-variable (CV) entangled states. Our approach detects both Gaussian and non-Gaussian nonclassical states in a reliable and efficient manner. Remarkably, it works regardless of measurement axis for all non-Gaussian states in finite-dimensional Fock space of any size, also extending to infinite-dimensional states of experimental relevance for CV quantum informatics. We experimentally illustrate the power of our criterion for motional states of a trapped ion confirming their nonclassicality in a measurement-axis independent manner. We also address an extension of our approach combined with phase-shift operations, which leads to a stronger test of nonclassicality, i.e. detection of genuine non-Gaussianity under a CV measurement.Comment: 6 pages, 4 figures with Supplemental Informatio

A mammalian Wnt5a-Ror2-Vangl2 axis controls the cytoskeleton and confers cellular properties required for alveologenesis.

Alveolar formation increases the surface area for gas-exchange and is key to the physiological function of the lung. Alveolar epithelial cells, myofibroblasts and endothelial cells undergo coordinated morphogenesis to generate epithelial folds (secondary septa) to form alveoli. A mechanistic understanding of alveologenesis remains incomplete. We found that the planar cell polarity (PCP) pathway is required in alveolar epithelial cells and myofibroblasts for alveologenesis in mammals. Our studies uncovered a Wnt5a-Ror2-Vangl2 cascade that endows cellular properties and novel mechanisms of alveologenesis. This includes PDGF secretion from alveolar type I and type II cells, cell shape changes of type I cells and migration of myofibroblasts. All these cellular properties are conferred by changes in the cytoskeleton and represent a new facet of PCP function. These results extend our current model of PCP signaling from polarizing a field of epithelial cells to conferring new properties at subcellular levels to regulate collective cell behavior

Kinetic Modeling for Microwave-Enhanced Degradation of Methylene Blue Using Manganese Oxide

This study was originally performed to compare the MnO2-based degradation of aqueous methylene blue (MB) under microwave irradiation- (MW-) enhanced and conventional heating- (CH-) enhanced conditions. The degradation process and kinetics were investigated to elucidate the microwave effect on the reaction. The results showed that all three tested conditions, sole MnO2, MnO2/CH, and MnO2/MW, followed the third-order (second upon MB and first upon MnO2) kinetic model. However, a higher degradation rate of MB was available under the MW-enhanced process, which implies that the “athermal effect” of MW might be of more benefit for the generation of electrophilic oxygen ions (, , and ) to degrade MB. The results showed that the degradation percentage of MB could reach 100%, corresponding to 92% total organic carbon (TOC) removal under microwave irradiation at pH 7.20 for 10 min