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arXiv quant-ph/0011110quant-ph
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两个量子比特的最大纠缠混合态

Maximally entangled mixed states of two qubits

Frank Verstraete, Koenraad Audenaert, Tijl De Bie, Bart De Moor

摘要:

我们考虑两个量子比特的混合态,并显示下的全球幺正操作的纠缠最大化。这导致了一类状态,这是贝尔状态的推广。我们考虑了三种纠缠度量:形成纠缠、负纠缠和纠缠的相对熵。令人惊讶的是,所有最大化一个度量的状态也最大化其他度量。我们将给出这些广义Bell态的完整刻画,并证明这些态在局域么正变换下对于固定本征值都是等价的。我们将进一步刻画所有最接近最大混合态的近纠缠态,并导出可分混合态体积的新下界。

英文摘要:

We consider mixed states of two qubits and show under which global unitary operations their entanglement is maximized. This leads to a class of states that is a generalization of the Bell states. Three measures of entanglement are considered: entanglement of formation, negativity and relative entropy of entanglement. Surprisingly all states that maximize one measure also maximize the others. We will give a complete characterization of these generalized Bell states and prove that these states for fixed eigenvalues are all equivalent under local unitary transformations. We will furthermore characterize all nearly entangled states closest to the maximally mixed state and derive a new lower bound on the volume of separable mixed states.

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