Entanglement or separability: the choice of how to factorize the algebra of a density matrix
Entanglement or separability: the choice of how to factorize the algebra of a density matrix
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DOI：
10.1140/epjd/e2011-20452-1
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发表时间：
2011-10-01
影响因子：
1.8
通讯作者：
Narnhofer, H.
中科院分区：
文献类型：
--
作者：
Thirring, W.;Bertlmann, R. A.;Narnhofer, H.
近几十年来，量子纠缠已成为量子信息和量子通信领域发展的重要资源。它量化了表示复合系统量子态的密度矩阵的某种非经典相关性质。我们讨论了关于描述整个量子系统的代数的不同分解，纠缠如何变化的概念。根据所考虑的因数分解，量子态要么是纠缠的，要么是可分离的。对于纯态，我们总是可以在可分性和纠缠性之间进行统一切换，然而对于混合态，我们只需要最小的混合性。我们详细讨论了量子比特的一般情况，即GHZ态、Werner态和Gisin态，并强调了它们的几何特征。作为理论家，我们使用和玩弄这种自由选择的分解，这对于一个实验主义者通常是自然固定的。对于理论学家来说，它提供了解释的延伸，并且足以概括，正如我们在量子隐形传态和纠缠交换的例子中指出的那样。
Quantum entanglement has become a resource for the fascinating developments in quantum information and quantum communication during the last decades. It quantifies a certain nonclassical correlation property of a density matrix representing the quantum state of a composite system. We discuss the concept of how entanglement changes with respect to different factorizations of the algebra which describes the total quantum system. Depending on the considered factorization a quantum state appears either entangled or separable. For pure states we always can switch unitarily between separability and entanglement, however, for mixed states a minimal amount of mixedness is needed. We discuss our general statements in detail for the familiar case of qubits, the GHZ states, Werner states and Gisin states, emphasizing their geometric features. As theorists we use and play with this free choice of factorization, which for an experimentalist is often naturally fixed. For theorists it offers an extension of the interpretations and is adequate to generalizations, as we point out in the examples of quantum teleportation and entanglement swapping.