We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
MiS Preprint
20/2019
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
Abstract
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.
