Highly entangled states with almost no secrecy.
Highly entangled states with almost no secrecy.
复制标题
高度纠缠的国家几乎没有秘密。
DOI：
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发表时间：
2010
影响因子：
8.6
通讯作者：
A. Winter
中科院分区：
文献类型：
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作者：
M. Christandl;N. Schuch;A. Winter
在这封信中，我们通过提供第一个高度纠缠但几乎无法提取秘密的量子态的例子来说明纠缠和保密之间的关系。更准确地说，我们给出了d×d维完全反对称态的二体纠缠的两个界。首先，我们证明了可以从该态中提取的保密量很低；准确地说，它是O(1/d)的界。其次，我们证明了态是高度纠缠的，因为我们需要大量的单态来创建态：纠缠成本大于常数，与d无关。为了得到我们的结果，我们使用表象理论、线性规划和称为压缩纠缠的纠缠度量。我们的发现也阐明了被挤压的纠缠与纠缠的相对熵之间的关系。
In this Letter we illuminate the relation between entanglement and secrecy by providing the first example of a quantum state that is highly entangled, but from which, nevertheless, almost no secrecy can be extracted. More precisely, we provide two bounds on the bipartite entanglement of the totally antisymmetric state in dimension d×d. First, we show that the amount of secrecy that can be extracted from the state is low; to be precise it is bounded by O(1/d). Second, we show that the state is highly entangled in the sense that we need a large amount of singlets to create the state: entanglement cost is larger than a constant, independent of d. In order to obtain our results we use representation theory, linear programming, and the entanglement measure known as squashed entanglement. Our findings also clarify the relation between the squashed entanglement and the relative entropy of entanglement.