The entanglement properties of a multiparty pure state are invariant under local unitary transformations. The stabilizer dimension of a multiparty pure state characterizes how many types of such local unitary transformations exist for the state. We find that the stabilizer dimension of an $n$ -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.The entanglement properties of a multiparty pure state are invariant under local unitary transformations. The stabilizer dimension of a multiparty pure state characterizes how many types of such local unitary transformations exist for the state. We find that the stabilizer dimension of an $n$-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.

arXiv:0901.1435Physical Review AApr 15, 20098 citations

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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.