On local invariants of pure three-qubit states

Abstract

We study invariants of three-qubit states under local unitary transformations, i.e. functions on the space of entanglement types, which is known to have dimension 6. We show that there is no set of six independent polynomial invariants of degree less than or equal to 6, and find such a set with maximum degree 8. We describe an intrinsic definition of a canonical state on each orbit, and discuss the (non-polynomial) invariants associated with it.

LateX, 13 pages. Minor typoes corrected. Published version

References in corpus (4)

• Generalized Schmidt decomposition and classification of three-quantum-bit states
• Nonlocal properties of two-qubit gates and mixed states and optimization of quantum computations
• Multipartite generalisation of the Schmidt decomposition
• Local symmetry properties of pure 3-qubit states

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