Minimizing the loss of entanglement under dimensional reduction
Minimizing the loss of entanglement under dimensional reduction
复制标题
最大限度地减少降维下的纠缠损失
DOI：
10.1140/epjd/e2004-00029-y
复制
发表时间：
2004
期刊：
影响因子：
--
通讯作者：
K. Mølmer
中科院分区：
文献类型：
--
作者：
V. Petersen;V. Petersen;L. Madsen;K. Mølmer;K. Mølmer
摘要。我们研究了在局部操作和经典通信下，将dA x dB张量积空间上的一般二部量子态转换为2 x 2维的最终态的可能性，同时保持尽可能多的纠缠。对于纯态，我们证明了尼尔森定理提供了最优协议，并给出了降维前后纠缠度的定量结果。对于混合状态，我们确定了一个我们认为对各向同性和维尔纳状态最优的协议。在文献中，有人推测一些维尔纳态是束缚纠缠的，为了支持这一推测，我们的协议给出了这类态的无纠缠的最终态。对于所有其他纠缠的维尔纳态和所有纠缠的各向同性态，都保持一定程度的自由纠缠。在这个意义上，我们的协议可以用来区分束缚和自由纠缠。
Abstract.We investigate the possibility of transforming, under local operations and classical communication, a general bipartite quantum state on a dA x dB tensor-product space into a final state in 2 x 2 dimensions, while maintaining as much entanglement as possible. For pure states, we prove that Nielsen’s theorem provides the optimal protocol, and we present quantitative results on the degree of entanglement before and after the dimensional reduction. For mixed states, we identify a protocol that we argue is optimal for isotropic and Werner states. In the literature, it has been conjectured that some Werner states are bound entangled and in support of this conjecture our protocol gives final states without entanglement for this class of states. For all other entangled Werner states and for all entangled isotropic states some degree of free entanglement is maintained. In this sense, our protocol may be used to discriminate between bound and free entanglement.