Geometry of entanglement in the Bloch sphere

Abstract

Entanglement is an important concept in quantum information, quantum communication, and quantum computing. We provide a geometrical analysis of entanglement and separability for all the rank-2 quantum mixed states: complete analysis for the bipartite states, and partial analysis for the multipartite states. For each rank-2 mixed state, we define its unique Bloch sphere, that is spanned by the eigenstates of its density matrix. We characterize those Bloch spheres into exactly five classes of entanglement and separability, give examples for each class, and prove that those are the only classes.

7 pages; 5 figures

References in corpus (3)

• Entangled three-qubit states without concurrence and three-tangle
• Tangles of superpositions and the convex-roof extension
• Rank three bipartite entangled states are distillable

Cited by in corpus (4)

• Visualizing Entanglement in multi-Qubit Systems
• Geometry of entanglement and separability in Hilbert subspaces of dimension up to three
• Visualizing Quantum States: A Pilot Study on Problem Solving in Quantum Information Science Education
• Useful variants and perturbations of completely entangled subspaces and spans of unextendible product bases