Mutually unbiased maximally entangled bases from difference matrices

Based on maximally entangled states, we explore the constructions of mutually unbiased bases in bipartite quantum systems. We present a new way to construct mutually unbiased bases by difference matrices in the theory of combinatorial designs. In particular, we establish $q$ mutually unbiased bases with $q-1$ maximally entangled bases and one product basis in $\mathbb{C}^q\otimes \mathbb{C}^q$ for arbitrary prime power $q$. In addition, we construct maximally entangled bases for dimension of composite numbers of non-prime power, such as five maximally entangled bases in $\mathbb{C}^{12}\otimes \mathbb{C}^{12}$ and $\mathbb{C}^{21}\otimes\mathbb{C}^{21}$, which improve the known lower bounds for $d=3m$, with $(3,m)=1$ in $\mathbb{C}^{d}\otimes \mathbb{C}^{d}$. Furthermore, we construct $p+1$ mutually unbiased bases with $p$ maximally entangled bases and one product basis in $\mathbb{C}^p\otimes \mathbb{C}^{p^2}$ for arbitrary prime number $p$.Comment: 24 page

Novel Constructions of Mutually Unbiased Tripartite Absolutely Maximally Entangled Bases

We develop a new technique to construct mutually unbiased tripartite absolutely maximally entangled bases. We first explore the tripartite absolutely maximally entangled bases and mutually unbiased bases in $\mathbb{C}^{d} \otimes \mathbb{C}^{d} \otimes \mathbb{C}^{d}$ based on mutually orthogonal Latin squares. Then we generalize the approach to the case of $\mathbb{C}^{d_{1}} \otimes \mathbb{C}^{d_{2}} \otimes \mathbb{C}^{d_{1}d_{2}}$ by mutually weak orthogonal Latin squares. The concise direct constructions of mutually unbiased tripartite absolutely maximally entangled bases are remarkably presented with generality. Detailed examples in $\mathbb{C}^{3} \otimes \mathbb{C}^{3} \otimes \mathbb{C}^{3},$ $\mathbb{C}^{2} \otimes \mathbb{C}^{2} \otimes \mathbb{C}^{4}$ and $\mathbb{C}^{2} \otimes \mathbb{C}^{5} \otimes \mathbb{C}^{10}$ are provided to illustrate the advantages of our approach

Quantum kk-uniform states from quantum orthogonal arrays

The quantum orthogonal arrays define remarkable classes of multipartite entangled states called $k$-uniform states whose every reductions to $k$ parties are maximally mixed. We present constructions of quantum orthogonal arrays of strength 2 with levels of prime power, as well as some constructions of strength 3. As a consequence, we give infinite classes of 2-uniform states of $N$ systems with dimension of prime power $d\geq 2$ for arbitrary $N\geq 5$; 3-uniform states of $N$-qubit systems for arbitrary $N\geq 6$ and $N\neq 7,8,9,11$; 3-uniform states of $N$ systems with dimension of prime power $d\geq 7$ for arbitrary $N\geq 7$.Comment: 26 pages, 1 figure

Hypertensive nephropathy treatment by heart-protecting musk pill: a study of anti-inflammatory therapy for target organ damage of hypertension

This study was designed to investigate the protective effect of the heart-protecting musk pill (HMP) on inflammatory injury of kidney from spontaneously hypertensive rat (SHR). Male SHRs aged 4 weeks were divided into SHR model group, HMP low-dosage group (13.5 mg/kg), and HMP high-dosage group (40 mg/kg). Age-matched Wistar–Kyoto rats were used as normal control. All rats were killed at 12 weeks of age. Tail-cuff method and enzyme-linked immunosorbent assay were used to determine rat systolic blood pressure and angiotensin II (Ang II) contents, respectively. Renal inflammatory damage was evaluated by the following parameters: protein expressions of inflammatory cytokines, carbonyl protein contents, nitrite concentration, infiltration of monocytes/macrophages in interstitium and glomeruli, kidney pathological changes, and excretion rate of urinary protein. HMP did not prevent the development of hypertension in SHR. However, this Chinese medicinal compound decreased renal Ang II content. Consistent with the change of renal Ang II, all the parameters of renal inflammatory injury were significantly decreased by HMP. This study indicates that HMP is a potent suppressor of renal inflammatory damage in SHR, which may serve as a basis for the advanced preventive and therapeutic investigation of HMP in hypertensive nephropathy

The Cerebellum Is Related to Cognitive Dysfunction in White Matter Hyperintensities

ObjectiveWhite matter hyperintensities (WMHs) on magnetic resonance imaging (MRI) is frequently presumed to be secondary to cerebral small vessel disease (CSVD) and associated with cognitive decline. The cerebellum plays a key role in cognition and has dense connections with other brain regions. Thus, the aim of this study was to investigate if cerebellar abnormalities could occur in CSVD patients with WMHs and the possible association with cognitive performances.MethodsA total of 104 right-handed patients with WMHs were divided into the mild WMHs group (n = 39), moderate WMHs group (n = 37), and severe WMHs group (n = 28) according to the Fazekas scale, and 36 healthy controls were matched for sex ratio, age, education years, and acquired resting-state functional MRI. Analysis of voxel-based morphometry of gray matter volume (GMV) and seed-to-whole-brain functional connectivity (FC) was performed from the perspective of the cerebellum, and their correlations with neuropsychological variables were explored.ResultsThe analysis revealed a lower GMV in the bilateral cerebellum lobule VI and decreased FC between the left- and right-sided cerebellar lobule VI with the left anterior cingulate gyri in CSVD patients with WMHs. Both changes in structure and function were correlated with cognitive impairment in patients with WMHs.ConclusionOur study revealed damaged GMV and FC in the cerebellum associated with cognitive impairment. This indicates that the cerebellum may play a key role in the modulation of cognitive function in CSVD patients with WMHs