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Bell-state diagonal entanglement witnesses for relativistic and nonrelativistic multispinor systems in arbitrary dimensions

机译:任意尺寸中相对论和非椭圆多管子系统的钟声对角线纠缠见证

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摘要

Two kinds of Bell-state diagonal (BSD) entanglement witnesses (EWs) are constructed by using the algebra of Dirac γ matrices in a space-time of arbitrary dimension d, where the first kind can detect some BSD relativistic and nonrelativistic m-partite multispinor bound entangled states in a Hilbert space of dimension 2~(m[d/2]), including the bipartite Bell-type and isoconcurrence-type states in four-dimensional space-time (d=4). By using the connection between the Hilbert-Schmidt measure and the optimal EWs associated with the states, it is shown that, as far as the spin quantum correlations are concerned, the amount of entanglement is not a relativistic scalar and has no invariant meaning. The introduced EWs are manipulated via linear programming (LP) and can be solved exactly by using the simplex method. The decomposability or nondecomposability of these EWs is investigated, the region of nondecomposable EWs of the first kind is partially determined and it is shown that, all of the EWs of the second kind are decomposable. These EWs have the property that in bipartite systems they can determine the region of separable states, i.e., bipartite nondetectable density matrices of the same type as the EWs of the first kind are necessarily separable. Also, multispinor EWs with nonpolygon feasible regions are provided, where the problem is solved by approximate LP, and in contrast to the exactly manipulatable EWs, both the first and second kinds of the optimal approximate EWs can detect some bound entangled states.
机译:两种贝尔状态对角线(BSD)纠缠证人(EWS)的通过使用狄拉克γ中任意尺寸d,的空间 - 时间矩阵的代数,其中第一种可检测一些BSD相对论和非相对论M-三方multispinor构造在尺寸2〜(m [D / 2])的Hilbert空间中的绑定状态,包括四维空间时间(d = 4)中的二分钟铃声和异筒型型状态。通过使用Hilbert-Schmidt测量与与状态相关联的最佳EW之间的连接,表明,就旋转量子相关而言,纠缠的数量不是相对论的标量并且没有不变的含义。引入的EWS通过线性编程(LP)操纵,可以通过使用单纯x方法来完全解决。研究了这些EWS的分解性或非非分解性,部分确定了第一种的非可分解EWS的区域,并且表明,第二种的所有EWS都是可分解的。这些EWS具有在二分体系中的性质,它们可以确定可分离状态的区域,即与第一种的EWS相同类型的二分,其与相同类型的相同类型的密度矩阵。此外,提供了具有非聚合物可行区域的MultiSpinor EWS,其中通过近似LP解决问题,并且与恰好可操纵的EWS相反,第一和第二种最佳近似EWS都可以检测一些绑定的缠结状态。

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