The norms of Bloch vectors and classification of four qudits quantum states

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.

8 pages, 1 figure

References in corpus (3)

• An Experimentally accessible geometric measure for entanglement in $N$-qubit pure states
• Measure and detection of genuine multipartite entanglement for tripartite systems
• Bell inequalities for multipartite qubit quantum systems and their maximal violation

Cited by in corpus (11)

• Quantum k-uniform states for heterogeneous systems from irredundant mixed orthogonal arrays
• Separability criteria based on Bloch representation of density matrices
• Necessary conditions for classifying m-separability of multipartite entanglements
• Detection of entanglement for multipartite quantum states
• Trade-off relation among genuine three-qubit nonlocalities in four-qubit systems
• Criteria of genuine multipartite entanglement based on correlation tensors
• Detecting multipartite entanglement via complete orthogonal basis
• Detection of multipartite entanglement based on Heisenberg-Weyl representation of density matrices
• On genuine entanglement for tripartite systems
• Quantum channels and some absolute properties of quantum states
• Detection of Genuine Multipartite Entanglement in Arbitrary Multipartite systems