Entanglement distribution using three-mode separable state with imperfect equipments

We show a scheme to distribute the entanglement by using three-mode separable Gaussian state prepared with imperfect equipments. The scheme achieves the aim that the entanglement is distributed between two distant parties with only Gaussian operations and linear optics elements. Moreover, we analyse the logarithmic negativity of the entanglement shared between the two parties when the systems are imperfect and arrive at the conclusion that the logarithmic negativity is asymptotically stable with fluctuations within a certain space range.

Quantum Correlations in a Family of Two-Qubit Separable States

Quantum correlations in a family of two-qubit separable classical-quantum correlated states are intensively studied with four different approaches, namely, quantum discord [Phys. Rev. Lett. 88 （2002） 017901], measurement- induced disturbance （MID） [Phys. Rev. A 77 （2008） 022301], ameliorated MID [J. Phys. A： Math. Theor. 44 （2011） 352002] and quantum dissonance [Phys. Rev. Left. 104 （2010） 080501]. Quantum correlations captured with different approaches are compared and discussed so that their three distinct features are exposed.

A Note on Normal Forms of Quantum States and Separability

We study the normal form of multipartite density matrices.It is shown that the correlation matrix(CM)separability criterion can be improved from the normal form we obtained under filtering transformations.Based on CMcriterion the entanglement witness is further constructed in terms of local orthogonal observables for both bipartite andmultipartite systems.

ENTANGLEMENT WITNESSES CONSTRUCTED BY PERMUTATION PAIRS

For n≥3,we construct a class{Wn,π1,π2}of n^(2)×n^(2) hermitian matrices by the permutation pairs and show that,for a pair{π1,π2}of permutations on(1,2,…,n),Wn,π1,π2 is an entanglement witness of the n⊗n system if{π1,π2}has the property(C).Recall that a pair{π1,π2}of permutations of(1,2,…,n)has the property(C)if,for each i,one can obtain a permutation of(1,…,i−1,i+1,…,n)from(π1(1),…,π1(i−1),π1(i+1),…,π1(n))and(π2(1),…,π2(i−1),π2(i+1),…,π2(n)).We further prove that Wn,π1,π2 is not comparable with Wn,π,which is the entanglement witness constructed from a single permutationπ;Wn,π1,π2 is decomposable ifπ1π2=id orπ21=π22=id.For the low dimensional cases n∈{3,4},we give a sufficient and necessary condition onπ1,π2 for Wn,π1,π2 to be an entanglement witness.We also show that,for n∈{3,4},Wn,π1,π2 is decomposable if and only ifπ1π2=id orπ21=π22=id;W3,π1,π2 is optimal if and only if(π1,π2)=(π,π2),whereπ=(2,3,1).As applications,some entanglement criteria for states and some decomposability criteria for positive maps are established.

Forming solid electrolyte interphase in situ in an ionic conducting Li_(1.5)Al_(0.5)Ge_(1.5)(PO_4)_3-polypropylene(PP) based separator for Li-ion batteries

A new concept of forming solid electrolyte interphases（SEI） in situ in an ionic conducting Li（1.5）Al（0.5）Ge（1.5）（PO4）3-polypropylene（LAGP-PP） based separator during charging and discharging is proposed and demonstrated. This unique structure shows a high ionic conductivity, low interface resistance with electrode, and can suppress the growth of lithium dendrite. The features of forming the SEI in situ are investigated by scanning electron microscopy（SEM） and x-ray photoelectron spectroscopy（XPS）. The results confirm that SEI films mainly consist of lithium fluoride and carbonates with various alkyl contents. The cell assembled by using the LAGP-coated separator demonstrates a good cycling performance even at high charging rates, and the lithium dendrites were not observed on the lithium metal electrode. Therefore, the SEI-LAGP-PP separator can be used as a promising flexible solid electrolyte for solid state lithium batteries.

The entanglement of several graph states

We exactly evaluate the entanglement of a six vertex and a nine vertex graph states which correspond to non ＂two-colorable＂ graphs. The upper bound of entanglement for five vertex ring graph state is improved to 2.9275, less than the upper bound determined by local operations and classical communication. An upper bound of entanglement is proposed based on the definition of graph state.