Method for classifying multiqubit states via the rank of the coefficient matrix and its application to four-qubit states
Method for classifying multiqubit states via the rank of the coefficient matrix and its application to four-qubit states
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DOI：
10.1103/physreva.86.042332
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发表时间：
2012-01
影响因子：
2.9
通讯作者：
Xiangrong Li;Dafa Li
中科院分区：
文献类型：
--
作者：
Xiangrong Li;Dafa Li
我们构造了与纯n比特态相关的2 ^l × 2^{n-l}的系数矩阵，并证明了系数矩阵的秩在随机局域操作和经典通信（SLOCC）下的不变性.秩产生了一种简单的方法，将纯n量子比特状态划分为不等价的家族，并在SLOCC下区分简并家族。此外，通过系数矩阵的秩的分类方案可以与其他方案组合以构建更精细的分类方案。为了证明这一点，我们通过系数矩阵的秩将Verstraete等人[Phys.Rev.A65，052112（2002）]引入的九个四量子比特族进一步分类为不等价的子族，结果，我们发现了28个真正纠缠的族，并且所有的简并类都可以区分为四个量子比特的排列。我们还讨论了四个量子比特分为九个家庭的分类的完整性。
We construct coefficient matrices of size 2^l by 2^{n-l} associated with pure n-qubit states and prove the invariance of the ranks of the coefficient matrices under stochastic local operations and classical communication (SLOCC). The ranks give rise to a simple way of partitioning pure n-qubit states into inequivalent families and distinguishing degenerate families from one another under SLOCC. Moreover, the classification scheme via the ranks of coefficient matrices can be combined with other schemes to build a more refined classification scheme. To exemplify we classify the nine families of four qubits introduced by Verstraete et al. [Phys. Rev. A 65, 052112 (2002)] further into inequivalent subfamilies via the ranks of coefficient matrices, and as a result, we find 28 genuinely entangled families and all the degenerate classes can be distinguished up to permutations of the four qubits. We also discuss the completeness of the classification of four qubits into nine families.