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arXiv quant-ph/0702040quant-ph
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接近最大混合态的纠缠态

Entangled states close to the maximally mixed state

Roland Hildebrand

摘要:

给出了m量子比特系统在最大混合态附近的最大可分态球半径的改进上界。因此,上限和最佳已知下限(Hildebrand,quant.ph/0601201)之间的比率缩小到常数c = \sqrt{34/27} ~ 1.122,与先前已知的最佳上限(Aubrun和Szarek,quant.ph/0503221)的\sqrt{m\log m}阶项相反。我们给出了具体的例子,可分离状态的边界纠缠实现这些上界。作为一个副产品,我们计算了适合R^3中四个单位球的射影张量积和适合R^n中任意数量单位球的射影张量积(n = 2,4,8)的最大球的半径。

英文摘要:

We give improved upper bounds on the radius of the largest ball of separable states of an m-qubit system around the maximally mixed state. The ratio between the upper bound and the best known lower bound (Hildebrand, quant.ph/0601201) thus shrinks to a constant c = \sqrt{34/27} ~ 1.122, as opposed to a term of order \sqrt{m\log m} for the best upper bound known previously (Aubrun and Szarek, quant.ph/0503221). We give concrete examples of separable states on the boundary to entanglement which realize these upper bounds. As a by-product, we compute the radii of the largest balls that fit into the projective tensor product of four unit balls in R^3 and in the projective tensor product of an arbitrary number of unit balls in R^n for n = 2,4,8.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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