The stabilizer dimension of graph states

Abstract

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 existing for the state. We find that the stabilizer dimension of an $n$-qubit ($n\ge 2$) graph state is associated with three specific configurations in its graph. We further show that the stabilizer dimension of an $n$-qubit ($n\ge 3$) graph state is equal to the degree of irreducible two-qubit correlations in the state.

4.2 pages, 4 figures

References in corpus (5)

• Irreducible multi-particle correlations in states without maximal rank
• Multiparty quantum states stabilized by the diagonal subgroup of the local unitary group
• Classification of nonproduct states with maximum stabilizer dimension
• Maximum stabilizer dimension for nonproduct states
• Minimum orbit dimension for local unitary action on n-qubit pure states

Cited by in corpus (6)

• Local unitary symmetries of hypergraph states
• Maximally Entangled States of Four Nonbinary Particles
• Symmetries and entanglement of stabilizer states
• Transformations of Stabilizer States in Quantum Networks
• Finite-Function-Encoding Quantum States
• Revealing effects of local dimension on variable-range interacting model by connecting Lieb-Robinson bounds and multipartite entanglement