Quantum discord provides a measure for quantifying quantum correlations beyond entanglement and is very hard to compute even for two-qubit states because of the minimization over all possible measurements. Recently a simple algorithm to evaluate the quantum discord for two-qubit X-states is proposed by Ali, Rau and Alber [Phys. Rev. A 81, 042105 (2010)] with minimization taken over only a few cases. Here we shall at first identify a class of X-states, whose quantum discord can be evaluated analytically without any minimization, for which their algorithm is valid, and also identify a family of X-states for which their algorithm fails. And then we demonstrate that this special family of X-states provides furthermore an explicit example for the inequivalence between the minimization over positive operator-valued measures and that over von Neumann measurements. For an important family of two-qubit states, the so called X-states [25], an algorithm has been proposed to calculate their quantum discord with minimization taken over only a few simple cases [26], which is unfortunately impeded by a counter example [27]. In this paper we shall at first identify a vast class of X-states, whose quantum discord can be evaluated analytically without any minimization at all, for which their algorithm is valid, and also identify a family of X-states X m , the so-called maximally discordant mixed states [24], for which the above mentioned algorithm fails. And then for this family of Xstates X m we construct a POVM showing that the quantum discord obtained by minimization over all POVMs is strictly smaller than that over all possible von Neumann measurements.For a given quantum state ̺ of a composite system AB the total amount of correlations, including classical and quantum correlations, is quantified by the quantum mutual information I(ρ) = S(̺ A ) + S(̺ B ) − S(̺) where S(̺) = −Tr(̺ log 2 ̺) denotes the von Neumann entropy and ̺ A , ̺ B are reduced density matrices for subsystem A, B respectively. An alternative version of the mutual information can be defined aswhere the minimum is taken over all possible POVMs {E defines the quantum discord that quantifies the quantum correlation. Also the minimum in Eq.(1) can be taken over all von Neumann measurements [3] and we

, an outbreak of coronavirus disease 2019 (COVID-19) due to severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) began in China and spread rapidly worldwide. It is unknown whether hemodialysis patients represent a distinct group of patients with certain characteristics that may make them susceptible to infection or severe disease. In this case report, we describe the clinical and epidemiologic features of COVID-19 infection in 201 maintenance hemodialysis patients in Zhongnan Hospital of Wuhan University, including 5 maintenance hemodialysis patients who contracted COVID-19 infection. Of the 5 patients with COVID-19 infection, one had a definite history of contact with an infected person. The age range of the patients was 47 to 67 years. Diarrhea (80%), fever (60%), and fatigue (60%) were the most common symptoms. Lymphopenia occurred in all patients. Computed tomography of the chest showed ground glass opacity in the lungs of all patients. Up to February 13, 2020, none of the patients had developed severe complications (acute respiratory distress syndrome, shock, or multiple organ dysfunction) or died. Complete author and article information provided before references.

It is well known that many operations in quantum information processing depend largely on a special kind of quantum correlation, that is, entanglement. However, there are also quantum tasks that display the quantum advantage without entanglement. Distinguishing classical and quantum correlations in quantum systems is therefore of both fundamental and practical importance. In consideration of the unavoidable interaction between correlated systems and the environment, understanding the dynamics of correlations would stimulate great interest. In this study, we investigate the dynamics of different kinds of bipartite correlations in an alloptical experimental setup. The sudden change in behaviour in the decay rates of correlations and their immunity against certain decoherences are shown. Moreover, quantum correlation is observed to be larger than classical correlation, which disproves the early conjecture that classical correlation is always greater than quantum correlation. Our observations may be important for quantum information processing.

We show that a single Bell's inequality with two dichotomic observables for each observer, which originates from Hardy's nonlocality proof without inequalities, is violated by all entangled pure states of a given number of particles, each of which may have a different number of energy levels. Thus Gisin's theorem is proved in its most general form from which it follows that for pure states Bell's nonlocality and quantum entanglement are equivalent.

We show that the entanglement witnesses based on local orthogonal observables which are introduced in [S. Yu and N.-L. Liu, Phys. Rev. Lett. 95, 150504 (2005) (2006)] in linear and nonlinear forms can be optimized, respectively. As applications, we calculate the optimal nonlinear witnesses of pure bipartite states and show a lower bound on the I-concurrence of bipartite higher dimensional systems with our method.

Separability problem, to decide whether a given state is entangled or not, is a fundamental problem in quantum information theory. We propose a powerful and computationally simple separability criterion, which allows us to detect the entanglement of many bound entangled states. The criterion is strictly stronger than the criterion based on Bloch representations, the computable cross-norm or realignment criterion and its optimal nonlinear entanglement witnesses. Furthermore, this criterion can be generalized to an analogue of permutation separability criteria in the even-partite systems.Entanglement is one of the most fascinating features of quantum theory that has puzzled generations of physicist. While initially the discussion was mainly driven by conceptual and philosophical consideration [1], in recent years the focus has shifted to mathematical aspects and practical applications. It was realized that entanglement is an essential resource in quantum information and acts an important role in many other physical phenomenon e.g. quantum phase transition [2]. Therefore, the detection and quantification of entanglement became fundamental problems in quantum information theory [3]. However, entanglement is not yet fully understood and it is a challenging task and remains an open question to decide whether a given state is entangled or not despite a great deal of effort in the past years [4,5,6,7,8,9,10,11,12,13,14,15,16].Completely solving the separability problem is far away from us, this is in fact a NP-hard problem as proved in [17]. Nevertheless, there are still many efficient conditions for entanglement such as the partial transposition criterion [5], the computable cross-norm or realignment (CCNR) criterion [6,7], the permutation separability criteria [8,9], the criterion based on Bloch representations [10], local uncertainty relations [11], entanglement witnesses [12] and the covariance matrices (CM) approach [13], etc.. The CCNR criterion is only a necessary condition for arbitrary dimensional systems. However, it can detect many bound entangled states where the partial transposition criterion fails. Recently, Gühne et al. proposed its nonlinear entanglement witness based on local uncertainty relations [14]. The nonlinear entanglement witness is strictly stronger than the original criterion.In this paper, we propose a practical criterion, based on ρ − ρ A ⊗ ρ B which has similar properties as covariance matrices [13]. The criterion is strictly stronger than the dV criterion (i.e. the criterion based on Bloch representations), the CCNR criterion and its optimal nonlinear entanglement witnesses. Then we apply our criterion of separability to a bound entangled state with white noise.

Dynamic contrast material-enhanced magnetic resonance imaging (DCE-MRI) of breasts is an important imaging modality in breast cancer diagnosis with higher sensitivity but relatively lower specificity. The objective of this study is to investigate a new approach to help improve diagnostic performance of DCE-MRI examinations based on the automated detection and analysis of bilateral asymmetry of characteristic kinetic features between the left and right breast. An image dataset involving 130 DCE-MRI examinations was assembled and used in which 80 were biopsyproved malignant and 50 were benign. A computer-aided diagnosis (CAD) scheme was developed to segment breast areas depicted on each MR image, register images acquired from the sequential MR image scan series, compute average contrast enhancement of all pixels in one breast, and a set of kinetic features related to the difference of contrast enhancement between the left and right breast, and then use a multifeature based Bayesian belief network to classify between malignant and benign cases. A leave-one-case-out validation method was applied to test CAD performance. The computed area under a receiver operating characteristic (ROC) curve is 0.78±0.04. The positive and negative predictive values are 0.77 and 0.64, respectively. The study indicates that bilateral asymmetry of kinetic features between the left and right breasts is a potentially useful image biomarker to enhance the detection of angiogenesis associated with malignancy. It also demonstrates the feasibility of applying a simple CAD approach to classify between malignant and benign DCE-MRI examinations based on this new image biomarker.

BackgroundThe conventional degumming process of ramie with alkaline treatment at high temperature causes severe environmental pollution. Pectate lyases can be used to remove pectin from ramie in a degumming process with reduced environmental pollution and energy consumption. Pectate lyase PEL168 from Bacillus subtilis has been previously characterized and the protein structure was resolved. However, Bacillus is not a suitable host for pectate lyases during the degumming process since most Bacillus produce cellulases endogenously with a detrimental effect to the fiber. Pichia pastoris, which does not express endogenous cellulases and has high secretion capability, will be an ideal host for the expression. No previous work was reported concerning the heterologous expression of pectate lyase PEL168 in P. pastoris with an aim for industrial application in ramie bio-degumming.ResultsThe gene pel168 was expressed in P. pastoris in this study. The recombinant protein PEL168 in P. pastoris (PEL168P) showed two bands of 48.6 kDa and 51.4 kDa on SDS-PAGE whereas the enzyme expressed in E. coli (PEL168E) was the same as predicted with a band of 46 kDa. Deglycosylation digestion suggested that PEL168P was glycosylated. The optimum reaction temperature of the two PEL168s was 50°C, and the optimum pH 9.5. After preincubation at 60°C for 20 min, PEL168E completely lost its activity, whereas PEL168P kept 26% of the residual activity. PEL168P had a specific activity of 1320 U/mg with a Km of 0.09 mg/ml and a Vmax of 18.13 μmol/min. K+, Li+, Ni2+ and Sr2+ showed little or no inhibitory effect on PEL168P activity, and Ca2+ enhanced enzyme activity by 38%. PEL168P can remove the pectin from ramie effectively in a degumming process. A 1.5 fold increase of PEL168 enzyme expression in P. pastoris was achieved by further codon optimization.ConclusionsPectate lyase PEL168 with an available protein structure can be heterologously expressed in P. pastoris. The characterized recombinant PEL168P can be used to remove pectin from ramie efficiently and the expression level of PEL168 in P. pastoris was increased markedly by codon optimization. Therefore, PEL168 is an ideal candidate for further optimization and engineering for bio-degumming.