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 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.

arXiv comment9 pages, 3 figures, v2 adds a reference

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Cited by in corpus (6)

• How many CNOT gates does it take to generate a three-qubit state ?
• Maximum stabilizer dimension for nonproduct states
• Topological Signals of Singularities in Ricci Flow
• Classification of n-qubit states with minimum orbit dimension
• On the Symplectic Reduced Space of Three-Qubit Pure States
• Schmidt representation of 3-qubits with real amplitudes