Two and Three Qubits Geometry and Hopf Fibrations

Abstract

This paper reviews recent attempts to describe the two- and three-qubit Hilbert space geometries with the help of Hopf fibrations. In both cases, it is shown that the associated Hopf map is strongly sensitive to states entanglement content. In the two-qubit case, a generalization of the one-qubit celebrated Bloch sphere representation is described.

14 pages, 3 figures. The main content of this paper was presented at the Dresde (Germany) "Topology in Condensed Matter Physics" colloquium in june 2002. To appear in a book

Cited by in corpus (10)

• Qubits and oriented matroids in four time and four space dimensions
• Phirotopes, Super p-branes and Qubit Theory
• Duality, matroids, qubits, twistors and surreal numbers
• Spinor geometry
• Towards an Alternative Gravitational Theory
• Towards establishing a connection between two-level quantum systems and physical spaces
• Qubits and STU Black Holes with Eight Electric and Magnetic Charges
• Quantum Entanglement on Cosmological Scale
• Nanbu-Goto action and qubit theory in any signature and higher dimensions
• Geometric Structure of Higher-Dimensional Spheres