论文标题
使用操作员系统二元性，toeplitz的可分离性，纠缠和完全积极性
Toeplitz separability, entanglement, and complete positivity using operator system duality
论文作者
论文摘要
提出了L. gurvits定理的新证据，该定理指出，带有基质条目的正块toeplitz矩阵锥没有纠缠元素。 Gurvits分离定理的证明是通过利用操作员系统双重$ C（s^1）^{（n）} $的结构来实现的， $ c（s^1）^{（n）} \ omin \ b（\ h）$和$ c（s^1）_ {（n）} \ omin \ b（\ h）$，其中$ \ h $是任意的Hilbert space，$ c（s^1）_ {（n）} $是$ c（n）$ c（n是$ c（n是$ c）。我们的方法还具有提供一些有关正面toeplitz矩阵的新信息，其条目来自$ \ b（\ h）$时，当$ \ h $具有无限的尺寸。特别是，我们证明$ \ b（\ h）$上的正常正线性地图$ψ$在某种意义上是完全积极的，因为$ψ^{（n）}（x）$是$ x $是$ x $的$ x $是$ \ \ b（\ h）$的条目时，$ x $是正面的。我们还建立了某种分解定理（运算符）阳性toeplitz矩阵，显示了分离的方法与T.〜ando与普遍性的早期方法之间的等效性。
A new proof is presented of a theorem of L.~Gurvits, which states that the cone of positive block-Toeplitz matrices with matrix entries has no entangled elements. The proof of the Gurvits separation theorem is achieved by making use of the structure of the operator system dual of the operator system $C(S^1)^{(n)}$ of $n\times n$ Toeplitz matrices over the complex field, and by determining precisely the structure of the generators of the extremal rays of the positive cones of the operator systems $C(S^1)^{(n)}\omin\B(\H)$ and $C(S^1)_{(n)}\omin\B(\H)$, where $\H$ is an arbitrary Hilbert space and $C(S^1)_{(n)}$ is the operator system dual of $C(S^1)^{(n)}$. Our approach also has the advantage of providing some new information concerning positive Toeplitz matrices whose entries are from $\B(\H)$ when $\H$ has infinite dimension. In particular, we prove that normal positive linear maps $ψ$ on $\B(\H)$ are partially completely positive in the sense that $ψ^{(n)}(x)$ is positive whenever $x$ is a positive $n\times n$ Toeplitz matrix with entries from $\B(\H)$. We also establish a certain factorisation theorem for positive Toeplitz matrices (of operators), showing an equivalence between the Gurvits approach to separation and an earlier approach of T.~Ando to universality.
