Replica topological order in quantum mixed states and quantum error correction

Topological phases of matter offer a promising platform for quantum computation and quantum error correction. Nevertheless, unlike its counterpart in pure states, descriptions of topological order in mixed states remain relatively under-explored. Our work give two definitions for replica topological order in mixed states, which involve $n$ copies of density matrices of the mixed state. Our framework categorizes topological orders in mixed states as either quantum, classical, or trivial, depending on the type of information that can be encoded. For the case of the toric code model in the presence of decoherence, we associate for each phase a quantum channel and describes the structure of the code space. We show that in the quantum-topological phase, there exists a postselection-based error correction protocol that recovers the quantum information, while in the classical-topological phase, the quantum information has decohere and cannot be fully recovered. We accomplish this by describing the mixed state as a projected entangled pairs state (PEPS) and identifying the symmetry-protected topological order of its boundary state to the bulk topology. We discuss the extent that our findings can be extrapolated to $n \to 1$ limit

Crop Rotation Enhances Agricultural Sustainability: From an Empirical Evaluation of Eco-Economic Benefits in Rice Production

Cropping systems greatly impact the productivity and resilience of agricultural ecosystems. However, we often lack an understanding of the quantitative interactions among social, economic and ecological components in each of the systems, especially with regard to crop rotation. Current production systems cannot guarantee both high profits in the short term and social and ecological benefits in the long term. This study combined statistic and economic models to evaluate the comprehensive effects of cropping systems on rice production using data collected from experimental fields between 2017 and 2018. The results showed that increasing agricultural diversity through rotations, particularly potato-rice rotation (PR), significantly increased the social, economic and ecological benefits of rice production. Yields, profits, profit margins, weighted dimensionless values of soil chemical and physical (SCP) and heavy metal (SHM) traits, benefits and externalities generated by PR and other rotations were generally higher than successive rice cropping. This suggests that agricultural diversity through rotations, particularly PR rotation, is worth implementing due to its overall benefits generated in rice production. However, due to various nutrient residues from preceding crops, fertilizer application should be rationalized to improve the resource and investment efficiency. Furthermore, we internalized the externalities (hidden ecological and social benefits/costs) generated by each of the rotation systems and proposed ways of incenting farmers to adopt crop rotation approaches for sustainable rice production

The Effect Of Humble Leader Behavior, Leader Expertise, And Organizational Identification On Employee Turnover Intention

As a bottom-up leadership style, humble leadership has attracted increasing attention from scholars in recent years. But its effectiveness and mechanism still lack rigorous empirical study. In this study, we investigate the mechanism and boundary condition by which humble leader behavior exerts influence on followers’ turnover intention. Two-wave data collected from 249 scientific and technological personnel in China supported our hypothesized model. We found that humble leader behavior is significantly negatively related to follower turnover intention. The relationship is further partially mediated by organizational identification, and moderated by leader expertise. Implications for theory, practice and future research are discussed.

2-(Dimethyl­amino)­anthraquinone

The mol­ecule of the title compound, C16H13NO2, is almost planar, with a maximum deviation of 0.013 (2) Å from the best plane; the dihedral angle between the two aromatic rings is 1.06 (1)°. In the crystal, mol­ecules are linked through weak intra­molecular C—H⋯O inter­actions, forming chains running parallel to [10]