arXiv:quant-ph/0001091 · Journal of Physics A Mathematical and General

Local symmetry properties of pure three-qubit states

Hilary A. Carteret, Anthony Sudbery

Published Jul 7, 2000• 111 citations

Abstract

Entanglement types of pure states of three spin-½ particles are classified by means of their stabilizers in the group of local unitary transformations. It is shown that the stabilizer is generically discrete, and that a larger stabilizer indicates a stationary value for some local invariant. We describe all the exceptional states with enlarged stabilizers.

DOI: 10.1088/0305-4470/33/28/303

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arXiv:quant-ph/0001091 · Journal of Physics A Mathematical and General

Local symmetry properties of pure three-qubit states

Hilary A. Carteret, Anthony Sudbery

Published Jul 7, 2000• 111 citations

arXiv HTML PDF

Abstract

DOI: 10.1088/0305-4470/33/28/303

Related papers

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n

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n

-qubit $(n\ensuremath{\ge}2)$ graph state is associated with three specific configurations in its graph. We further show that the stabilizer dimension of an

n

-qubit $(n\ensuremath{\ge}3)$ graph state is equal to the degree of irreducible two-qubit correlations in the state.

We classify, up to local unitary equivalence, local unitary stabilizer Lie algebras for symmetric mixed states of

n

qubits into six classes. These include the stabilizer types of the Werner states, the Greenberger-Horne-Zeilinger state and its generalizations, and Dicke states. For all but the zero algebra, we classify entanglement types (local unitary equivalence classes) of symmetric mixed states that have those stabilizers. We make use of the identification of symmetric density matrices with polynomials in three variables with real coefficients and apply the representation theory of SO(3) on this space of polynomials.