Topology of the three-qubit space of entanglement types
Scott N. Walck, James K. Glasbrenner, Matthew H. Lochman, Shawn A. Hilbert · Physical Review A · 2005
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 ${\mathbb{R}}^{6}$, 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.