The norms of Bloch vectors and classification of four qudits quantum states
Ming Li, Zong Wang, Jing Wang, Shu-Qian Shen, and Shao-Ming Fei
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Submission date: 11. Feb. 2019
published in: epl, 125 (2019) 2, art-no. 20006
DOI number (of the published article): 10.1209/0295-5075/125/20006
with the following different title: The norms of Bloch vectors and classification of four-qudits quantum states
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We investigate the norms of the Bloch vectors for any quantum state with subsystems less than or equal to four. Tight upper bounds of the norms are obtained, which can be used to derive tight upper bounds for entanglement measure deﬁned by the norms of Bloch vectors. By using these bounds a trade-oﬀ relation of the norms of Bloch vectors is discussed. Theses upper bounds are then applied on separability. Necessary conditions are presented for diﬀerent kinds of separable states in four-partite quantum systems. We further present a complete classiﬁcation of quantum states for four qudits quantum systems.