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

In this paper, based on the nonbinary graph state, we present a systematic way of constructing good non-binary quantum codes, both additive and nonadditive, for systems with integer dimensions. With the help of computer search, which results in many interesting codes including some nonadditive codes meeting the Singleton bounds, we are able to construct explicitly four families of optimal codes, namely, [[6, 2, 3]]p, [[7, 3, 3]]p, [[8, 2, 4]]p and [[8, 4, 3]]p for any odd dimension p and a family of nonadditive code ( (5, p, 3))p for arbitrary p > 3. In the case of composite numbers as dimensions, we also construct a family of stabilizer codes ((6, 2 · p 2 , 3))2p for odd p, whose coding subspace is not of a dimension that is a power of the dimension of the physical subsystem.

A new technology for 6-hydroxy-3-succinoyl-pyridine (HSP) production from (S)-nicotine in tobacco waste by whole cells of a Pseudomonas sp. has been developed. When deionized water was used in the transformation reaction as a medium and the initial pH value of reaction mixture was adjusted to 7.0, 1.45 g/L HSP was produced from 3 g/L of nicotine in 5 h with 3.4 g/L of cells in a 5-L flask at 30 degrees C. HSP could be easily purified from the reaction without perplexing separation steps. A quantity of 1.3 g of HSP was recovered without impurity, and the overall yield of HSP was 43.8% (w/w), based on an initial concentration of 3.0 g/L of nicotine in reaction. This biotransformation made it possible to convert nicotine in tobacco wastes with high nicotine content into valuable compounds.

We report the first nonadditive quantum error-correcting code, namely, a ((9, 12, 3)) code which is a 12-dimensional subspace within a 9-qubit Hilbert space, that outperforms the optimal stabilizer code of the same length by encoding more levels while correcting arbitrary single-qubit errors.The quantum error-correcting code (QECC) [1,2,3,4] provides an active way of protecting our quantum data from decohering. Almost all the QECCs constructed so far are stabilizer codes [5,6,7], codes that have the structure of an eigenspace of an Abelian group generated by mulitilocal Pauli operators. Codes without such a structure are called nonadditive codes. The first nonadditive code [8,9] that outperforms the stabilizer codes is the ((5, 6, 2)) code, a 5-qubit code encoding 6 levels capable of correcting single-qubit erasure, i.e., a code of distance 2. Recently a family of distance 2 nonadditive codes with a higher encoding rate has been constructed [10]. Though some nonadditive error-correcting codes had been constructed [11,12], the question of whether the nonadditive error-correcting codes with a distance larger than 2 can encode more levels than the corresponding stabilizer codes remains open.In this Letter we report the first nonadditive code of distance 3 that beats the corresponding stabilizer code: a nonadditive ((9, 12, 3)) code that is a 12-dimensional subspace in a 9-qubit Hilbert space against arbitrary single-qubit errors. In comparison, the best stabilizer code [[9, 3, 3]] of the same length can encode only 3 logical qubits, i.e., an 8-dimensional subspace [7].Our new code is most conveniently formulated in terms of graph states [13,14]. Let G = (V, Γ) be an undirected simple graph with |V | = n vertices and Γ, called as the adjacency matrix of the graph, is an n× n symmetric matrix with vanishing diagonal entries and Γ ab = 1 if vertices a, b are connected and Γ ab = 0 otherwise. Consider a system of n qubits labeled by V and denote by X a , Y a , and Z a three Pauli operators acting on qubit a ∈ V . The graph state associated with graph G readswhere | µ z is the common eigenstates of {Z a } a∈V with (−1) µa as eigenvalues, |+ V x denotes the simultaneous +1 eigenstate of {X a } a∈V , and U ab = (1 + Z a + Z b − Z a Z b )/2 is the controlled-phase operation between qubit a and b. The graph state is also the unique simultaneous +1 eigenstate of n vertex stabilizers G a = X a Z Na with a ∈ V where N a is the neighborhood of a and we denote by Z U = a∈U Z a for a subset of vertices U ⊆ V . We consider in what follows the loop graph L 9 on 9 vertices which are labeled by integers from 1 to 9. Its adjacency matrix has nonvanishing entries Γ aa± = 1 (1 ≤ a ≤ 9) only where a ± = a ± 1 with identifications 9 + = 1 and 1 − = 9. The corresponding graph state is denoted as |L 9 . We claim that the 12-dimensional subspace D spanned by the states {Z Vi |L 9 } 12 i=1 where 3,4,5,6,7,8, 9} V 7 = {1, 4, 7}, V 8 = {1, 2, 4, 6}, V 9 = {1, 5, 7, 9} V 10 = {1, 2, 3, 4, 6, 7, 8}, V 11 = {1, 3, 4, 5, 7, 8, 9}as shown in Fig.1, ...

A conformal metric g with constant curvature one and finitely many conical singularities on a compact Riemann surface can be thought of as the pullback of the standard metric on the 2-sphere by a multivalued locally univalent meromorphic function f on \{singularities}, called the developing map of the metric g. When the developing map f of such a metric g on the compact Riemann surface has reducible monodromy, we show that, up to some Möbius transformation on f , the logarithmic differential d(log f) of f turns out to be an abelian differential of the third kind on , which satisfies some properties and is called a character 1-form of g. Conversely given such an abelian differential ω of the third kind satisfying the above properties, we prove that there exists a unique 1-parameter family of conformal metrics on such that all these metrics have constant curvature one, the same conical singularities, and have ω as one of their character 1-forms. This provides new examples of conformal metrics on compact Riemann surfaces of constant curvature one and with singularities. Moreover we prove that the developing map is a rational function for a conformal metric g with constant curvature one and finitely many conical singularities with angles in 2π‫ޚ‬ >1 on the two-sphere.

Developing high‐performance donor polymers is important for nonfullerene organic solar cells (NF‐OSCs), as state‐of‐the‐art nonfullerene acceptors can only perform well if they are coupled with a matching donor with suitable energy levels. However, there are very limited choices of donor polymers for NF‐OSCs, and the most commonly used ones are polymers named PM6 and PM7, which suffer from several problems. First, the performance of these polymers (particularly PM7) relies on precise control of their molecular weights. Also, their optimal morphology is extremely sensitive to any structural modification. In this work, a family of donor polymers is developed based on a random polymerization strategy. These polymers can achieve well‐controlled morphology and high‐performance with a variety of chemical structures and molecular weights. The polymer donors are D–A1–D–A2‐type random copolymers in which the D and A1 units are monomers originating from PM6 or PM7, while the A2 unit comprises an electron‐deficient core flanked by two thiophene rings with branched alkyl chains. Consequently, multiple cases of highly efficient NF‐OSCs are achieved with efficiencies between 16.0% and 17.1%. As the electron‐deficient cores can be changed to many other structural units, the strategy can easily expand the choices of high‐performance donor polymers for NF‐OSCs.

SO2 capture through physisorption is a promising environmental benign technology to eliminate the emission of SO2. However, designing an efficient adsorption material with high capacity and selectivity of SO2 as well as excellent reversibility remains challenging. Here, a class of highly crosslinked nonporous poly(ionic liquid)s (PILs) xerogels is prepared with high ionic density by photopolymerization of Gemini IL monomers and a microfluidic technology is further explored to prepare the corresponding monodisperse PIL microgels with uniform and controllable sizes at the diameter range from 43 to 250 µm. This kind of novel dense nonporous ionic xerogels/microgels completely exclude the adsorption of common gases (CO2, CH4, etc.), but exhibit very high SO2 adsorption capacity (498 mg g−1) via selective swelling mechanism. Unprecedented SO2/CO2 and SO2/CH4 uptake selectivities with the value up to 614 and 1992, respectively, are achieved. The selective swelling mechanism is validated by optical microscope and differential scanning calorimetry measurements. More importantly, these kinds of xerogels show excellent reversibility in adsorption–desorption cycles. Column breakthrough experiments confirm the excellent performance of these PIL xerogels in SO2 capture. This work demonstrates that designing a nonporous material that has specific swelling interactions with certain molecules can be an effective strategy for realizing extremely high selectivity.

BackgroundSheeppox virus (SPPV) and goatpox virus (GTPV), members of the Capripoxvirus genus of the Poxviridae family are causative agents of sheep pox and goat pox respectively, which are important contagious diseases and endemic in central and northern Africa, the Middle and Far East, and the Indian sub-continent. Both sheep pox and goat pox can cause wool and hide damage, and reduce the production of mutton and milk, which may result in significant economic losses and threaten the stockbreeding. In this study, three SPPVs and two GTPVs were collected from China in 2009 and 2011. We described the sequence features and phylogenetic analysis of the P32 gene, GPCR gene and RPO30 gene of the SPPVs and GTPVs to reveal their genetic relatedness.ResultsSequence and phylogenetic analysis showed that there was a close relationship among SPPV/GanS/2/2011/China, SPPV/GanS/1/2011/China and SPPV/NingX/2009/China. They were clustered on the same SPPV clade. GTPV/HuB/2009/China and GS-V1 belonged to the GTPV lineage. GS-V1 was closely related to other GTPV vaccine strains. GTPV/HuB/2009/China and GS-V1 were clustered with GTPVs from China and some southern Asian countries.ConclusionThis study may expand the datum for spread trend research of Chinese SPPVs and GTPVs, meanwhile provide theoretical references to improve the preventive and control strategy.