Duality of Entanglement Norms
Duality of Entanglement Norms
复制标题
纠缠范数的对偶性
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
D. Kribs
中科院分区：
文献类型：
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作者：
N. Johnston;D. Kribs
我们考虑了量子信息理论中出现的张量积空间上的四个范数，并证明了它们之间的对偶关系。我们证明了乘积的数值半径与纠缠的鲁棒性是对偶的，我们同样证明了S（k）-范数与投射张量范数是对偶的。我们证明了，类似于如何产品的数值半径和S（k）-范数表征k-块的积极运营商，有一个自然版本的投影张量范数的特点施密特数。这样我们得到了交叉范数可分性准则的一个新的初等证明，并将交叉范数和重排准则推广到任意施密特数的情形.
We consider four norms on tensor product spaces that have appeared in quantum information theory and demonstrate duality relationships between them. We show that the product numerical radius is dual to the robustness of entanglement, and we similarly show that the S(k)-norm is dual to the projective tensor norm. We show that, analogous to how the product numerical radius and the S(k)-norm characterize k-block positivity of operators, there is a natural version of the projective tensor norm that characterizes Schmidt number. In this way we obtain an elementary new proof of the cross norm criterion for separability, and we also generalize both the cross norm and realignment criteria to the case of arbitrary Schmidt number.