Criterion of Quantum Entanglement and the Covariance Correlation Tensor in the Theory of Quantum Network

This article discusses the covariance correlation tensor (CCT) in quantum network theory for four Bell bases in detail. Furthermore, it gives the expression of the density operator in terms of CCT for a quantum network of three nodes, thus gives the criterion of entanglement for this case, i.e. the conditions of complete separability and partial separability for a given quantum state of three bodies. Finally it discusses the general case for the quantum network of nodes.

Separability of Pure States and Mixed States of the Quantum Network of Two Nodes

This article discusses the separability of the pure states and mixed states of the quantum network of two nodes by means of the criterion of no entanglement in terms of the covariance correlation tensor in quantum network theory, i.e. for a composite system consisting of two nodes. The covariance correlation tensor is equal to zero for all possible and .

Structural covariance network of the hippocampus–amygdala complex in medication-nale patients with first-episode major depressive disorder

Background The hippocampus and amygdala are densely interconnected structures that work together in multiple affective and cognitive processes that are important to the etiology of major depressive disorder(MDD).Each of these structures consists of several heterogeneous subfields.We aim to explore the topologic properties of the volume-based intrinsic network within the hippocampus–amygdala complex in medication-nale patients with first-episode MDD.Methods High-resolution T1-weighted magnetic resonance imaging scans were acquired from 123 first-episode,medication-nale,and noncomorbid MDD patients and 81 age-,sex-,and education level-matched healthy control participants(HCs).The structural covariance network(SCN)was constructed for each group using the volumes of the hippocampal subfields and amygdala subregions;the weights of the edges were defined by the partial correlation coefficients between each pair of subfields/subregions,controlled for age,sex,education level,and intracranial volume.The global and nodal graphmetrics were calculated and compared between groups.Results Compared with HCs,the SCN within the hippocampus–amygdala complex in patients with MDD showed a shortened mean characteristic path length,reduced modularity,and reduced small-worldness index.At the nodal level,the left hippocampal tail showed increased measures of centrality,segregation,and integration,while nodes in the left amygdala showed decreased measures of centrality,segregation,and integration in patients with MDD compared with HCs.Conclusion Our results provide the first evidence of atypical topologic characteristics within the hippocampus–amygdala complex in patients with MDD using structure network analysis.It provides more delineate mechanism of those two structures that underlying neuropathologic process in MDD.

Probing bundle-wise abnormalities in patients infected with human immunodeficiency virus using fixel-based analysis:new insights into neurocognitive impairments

Background:Changes in white matter(WM)underlie the neurocognitive damages induced by a human immunodeficiency virus(HIV)infection.This study aimed to examine using a bundle-associated fixel-based analysis(FBA)pipeline for investigating the microstructural and macrostructural alterations in the WM of the brain of HIV patients.Methods:This study collected 93 HIV infected patients and 45 age/education/handedness matched healthy controls(HCs)at the Beijing Youan Hospital between January 1,2016 and December 30,2016.All HIV patients underwent neurocognitive evaluation and laboratory testing followed by magnetic resonance imaging(MRI)scanning.In order to detect the bundle-wise WM abnormalities accurately,a specific WM bundle template with 56 tracts of interest was firstly generated by an automated fiber clustering method using a subset of subjects.Fixel-based analysis was used to investigate bundle-wise differences between HIV patients and HCs in three perspectives:fiber density(FD),fiber cross-section(FC),and fiber density and cross-section(FDC).The between-group differences were detected by a two-sample t-test with the false discovery rate(FDR)correction(P<0.05).Furthermore,the covarying relationship in FD,FC and FDC between any pair of bundles was also accessed by the constructed covariance networks,which was subsequently compared between HIV and HCs via permutation t-tests.The correlations between abnormal WM metrics and the cognitive functions of HIV patients were explored via partial correlation analysis after controlling age and gender.Results:Among FD,FC and FDC,FD was the only metric that showed significant bundle-wise alterations in HIV patients compared to HCs.Increased FD values were observed in the bilateral fronto pontine tract,corona radiata frontal,left arcuate fasciculus,left corona radiata parietal,left superior longitudinal fasciculus III,and right superficial frontal parietal(SFP)(all FDR P<0.05).In bundle-wise covariance network,HIV patients displayed decreased FD and increased FC covarying patterns in comparison to HC(P<0.05),especially between associated pathways.Finally,the FCs of several tracts exhibited a significant correlation with language and attention-related functions.Conclusions:Our study demonstrated the utility of FBA on detecting the WM alterations related to HIV infection.The bundle-wise FBA method provides a new perspective for investigating HIV-induced microstructural and macrostructural WM-related changes,which may help to understand cognitive dysfunction in HIV patients thoroughly.