Topology of the three-qubit space of entanglement types
Abstract
The three-qubit space of entanglement types is the orbit space of the local unitary action on the space of three-qubit pure states and, hence, describes the types of entanglement that a system of three qubits can achieve. We show that this orbit space is homeomorphic to a certain subspace of R6 , which we describe completely. We give a topologically based classification of three-qubit entanglement types, and we argue that the nontrivial topology of the three-qubit space of entanglement types forbids the existence of standard states with the convenient properties of two-qubit standard states.
- Publication:
-
Physical Review A
- Pub Date:
- November 2005
- DOI:
- 10.1103/PhysRevA.72.052324
- arXiv:
- arXiv:quant-ph/0507208
- Bibcode:
- 2005PhRvA..72e2324W
- Keywords:
-
- 03.67.Mn;
- Entanglement production characterization and manipulation;
- Quantum Physics
- E-Print:
- 9 pages, 3 figures, v2 adds a reference