Squashed entanglement in infinite dimensions
Squashed entanglement in infinite dimensions
复制标题
无限维度中的压扁纠缠
DOI：
10.1063/1.4943598
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
M. Shirokov
中科院分区：
文献类型：
--
作者：
M. Shirokov
我们分析了无限维二部系统中压缩纠缠的两种可能的定义：有限维定义的直接平移及其普遍推广。证明了这两种定义在具有至少一个有限边际熵的态集上产生具有压扁纠缠的所有基本性质的相同的下半连续纠缠测度。并证明了第二个定义将该测度适当地推广到无限维二部系统的所有状态集合。
We analyse two possible definitions of the squashed entanglement in an infinite-dimensional bipartite system: direct translation of the finite-dimensional definition and its universal extension. It is shown that the both definitions produce the same lower semicontinuous entanglement measure possessing all basis properties of the squashed entanglement on the set of states having at least one finite marginal entropy. Is also shown that the second definition gives an adequate extension of this measure to the set of all states of infinite-dimensional bipartite system.
A general condition relating continuity of the squashed entanglement to continuity of the quantum mutual information is proved and its corollaries are considered.
Continuity bound for the squashed entanglement under the energy constraint on one subsystem is obtained by using the tight continuity bound for conditional mutual information (proved in the Appendix by using Winter's technique). It is shown that the same continuity bound is valid for the entanglement of formation. As a result the asymptotic continuity of the both entanglement measures under the energy constraint on one subsystem is proved.