Topology of the three-qubit space of entanglement types

Walck, Scott N.; Glasbrenner, James K.; Lochman, Matthew H.; Hilbert, Shawn A.

Topology of the three-qubit space of entanglement types

Authors

Walck, Scott N.

Glasbrenner, James K.

Lochman, Matthew H.

Hilbert, Shawn A.

Description

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 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.
9 pages, 3 figures, v2 adds a reference