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Topology of the three-qubit space of entanglement types

Scott N. Walck·James K. Glasbrenner·Matthew H. Lochman·Shawn A. Hilbert
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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 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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Scott N. Walck, James K. Glasbrenner, Matthew H. Lochman, Shawn A. Hilbert. 2005-08-29. Topology of the three-qubit space of entanglement types. https://doi.org/10.1103/physreva.72.052324

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