Topology of the three-qubit space of entanglement types

Details Topology of the three-qubit space of entanglement types Topology of the three-qubit space of entanglement types

2005-07-21

arxiv.org/abs/quant-ph/0507208v2

Phys. Rev. A 72, 052324 (2005)

Physics

Quantum Physics

9 pages, 3 figures, v2 adds a reference

Scientific paper

10.1103/PhysRevA.72.052324

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.

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