Infinitesimal local operations and differential conditions for entanglement monotones
Infinitesimal local operations and differential conditions for entanglement monotones
复制标题
纠缠单调的无穷小局部运算和微分条件
DOI：
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
T. Brun
中科院分区：
文献类型：
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作者：
O. Oreshkov;T. Brun
大部分的纠缠理论都涉及到在经典通信的局部操作（LOCC）下可能发生的状态转换;然而，这组操作是复杂的，难以用数学描述。一个已经证明非常有用的想法是纠缠单调性：在局部酉变换下不变的状态的函数，并且在任何局部操作之后总是平均减少（或增加）。在本文中，我们把LOCC看作是由无穷小的局部操作产生的一组操作，这些操作可以在局部执行，并且使状态几乎没有变化。我们表明，一个函数的状态是一个纠缠单调的本地操作，不涉及信息损失的一个充分必要条件是，该函数是一个单调的无穷小本地操作。然后，我们推导出一个函数的状态是纠缠单调的必要和充分的微分条件。我们首先推导出两个条件的本地操作没有信息损失，然后表明，它们可以扩展到更一般的操作，通过添加凸性的要求。然后，我们证明了一些已知的纠缠单调满足这些微分更多»标准。最后，作为应用，我们利用微分条件构造了一个新的三比特纯态的多项式纠缠单调。我们希望这种方法可以避免多体和混合态纠缠理论中的一些困难。«少
Much of the theory of entanglement concerns the transformations that are possible to a state under local operations with classical communication (LOCC); however, this set of operations is complicated and difficult to describe mathematically. An idea which has proven very useful is that of the entanglement monotone: a function of the state which is invariant under local unitary transformations and always decreases (or increases) on average after any local operation. In this paper we look on LOCC as the set of operations generated by infinitesimal local operations, operations which can be performed locally and which leave the state little changed. We show that a necessary and sufficient condition for a function of the state to be an entanglement monotone under local operations that do not involve information loss is that the function be a monotone under infinitesimal local operations. We then derive necessary and sufficient differential conditions for a function of the state to be an entanglement monotone. We first derive two conditions for local operations without information loss, and then show that they can be extended to more general operations by adding the requirement of convexity. We then demonstrate that a number of known entanglement monotones satisfy these differentialmore » criteria. Finally, as an application, we use the differential conditions to construct a new polynomial entanglement monotone for three-qubit pure states. It is our hope that this approach will avoid some of the difficulties in the theory of multipartite and mixed-state entanglement.« less