Number of superclasses of four-qubit entangled states under the inductive entanglement classification
Number of superclasses of four-qubit entangled states under the inductive entanglement classification
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DOI：
10.1103/physreva.95.022329
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发表时间：
2017-02
影响因子：
2.9
通讯作者：
Miriam Backens
中科院分区：
文献类型：
--
作者：
Miriam Backens
拉马塔等人。使用归纳方法对随机局部操作和经典通信 (SLOCC) 下四个量子位的纠缠纯态进行分类 [PRA 75(2), 022318 (2007)]。归纳方法先验地产生了十个不同的纠缠超类，其中三个被视为空而被丢弃。剩余的超类之一被一分为二，产生八个真正的四量子位纠缠的超类。在这里，我们表明三个被丢弃的超类中的两个实际上是非空的，应该被保留。我们给出了这些超类的规范状态的显式表达式，直至 SLOCC 和量子位排列。此外，我们确认第三个被丢弃的超类确实是空的，在归纳分类方案下总共产生了十个真正的四量子位纠缠的超类。
Lamata et al. use an inductive approach to classify the entangled pure states of four qubits under stochastic local operations and classical communication (SLOCC) [PRA 75(2), 022318 (2007)]. The inductive method yields a priori ten different entanglement superclasses, of which they discard three as empty. One of the remaining superclasses is split in two, resulting in eight superclasses of genuine four-qubit entanglement. Here, we show that two of the three discarded superclasses are in fact non-empty and should have been retained. We give explicit expressions for the canonical states for those superclasses, up to SLOCC and qubit permutations. Furthermore, we confirm that the third discarded superclass is indeed empty, yielding a total of ten superclasses of genuine four-qubit entanglement under the inductive classification scheme.