Volume 125, Number 2, January 2019
|Number of page(s)||4|
|Published online||18 February 2019|
The norms of Bloch vectors and classification of four-qudits quantum states
1 College of the Science, China University of Petroleum - 266580 Qingdao, China
2 Max-Planck-Institute for Mathematics in the Sciences - 04103 Leipzig, Germany
3 School of Mathematical Sciences, Capital Normal University - 100048 Beijing, China
Received: 29 August 2018
Accepted: 15 January 2019
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 measures defined by the norms of Bloch vectors. By using these bounds a trade-off relation of the norms of Bloch vectors is discussed. These 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.
PACS: 03.67.-a – Quantum information / 02.20.Hj – Classical groups / 03.65.-w – Quantum mechanics
© EPLA, 2019
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