arXiv 0908.38182009-08quant-ph

不变梳方法及其与多体纠缠态平衡性的关系

The invariant-comb approach and its relation to the balancedness of multipartite entangled states

A. Osterloh, J. Siewert

备注：: 17 pages, revtex4. Substantially extended manuscript (e.g. proofs have been added); title and abstract modified.
发表信息：: New J. Phys. 12, 075025 (2010)
DOI：: 10.1088/1367-2630/12/7/075025

摘要：

不变梳方法是一种构造量子比特多体系统纠缠度量的方法。基本的步骤是构造一个反线性算子，我们称之为{ \em comb}，参考{ \em毛球定理}。这种方法的一个吸引人的特点是，对于量子比特（或自旋1/2）的梳自动不变下$SL(2,\CC)$，这意味着所获得的不变量是纠缠单调的建设。通过询问状态的哪个属性确定它是否被多项式$SL(2,\CC)$不变量检测到，我们发现它是在局部酉变换下持续存在的{ \em平衡部分}的存在。我们对这种多项式不变量检测到的最大纠缠态进行了详细的分析，并由此引出了{ \em不可约平衡}态的概念。后者表明与量子比特纠缠的SLOCC分类有紧密的联系。梳也可以帮助定义高维子系统的多体纠缠的度量。然而，对于更高的自旋，有许多独立的梳，使得它是不平凡的找到一个不变的。通过限制允许的本地操作的坐标系的旋转（即再次到$SL(2,\CC)$），我们设法定义一个独特的扩展的并发一般半整数自旋与解析凸屋顶表达式的混合状态。

英文摘要：

The invariant-comb approach is a method to construct entanglement measures for multipartite systems of qubits. The essential step is the construction of an antilinear operator that we call {\em comb} in reference to the {\em hairy-ball theorem}. An appealing feature of this approach is that for qubits (or spins 1/2) the combs are automatically invariant under $SL(2,\CC)$, which implies that the obtained invariants are entanglement monotones by construction. By asking which property of a state determines whether or not it is detected by a polynomial $SL(2,\CC)$ invariant we find that it is the presence of a {\em balanced part} that persists under local unitary transformations. We present a detailed analysis for the maximally entangled states detected by such polynomial invariants, which leads to the concept of {\em irreducibly balanced} states. The latter indicates a tight connection with SLOCC classifications of qubit entanglement. \\ Combs may also help to define measures for multipartite entanglement of higher-dimensional subsystems. However, for higher spins there are many independent combs such that it is non-trivial to find an invariant one. By restricting the allowed local operations to rotations of the coordinate system (i.e. again to the $SL(2,\CC)$) we manage to define a unique extension of the concurrence to general half-integer spin with an analytic convex-roof expression for mixed states.

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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英文摘要：

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