Classification of nonproduct states with maximum stabilizer dimension

Abstract

Nonproduct n-qubit pure states with maximum dimensional stabilizer subgroups of the group of local unitary transformations are precisely the generalized n-qubit Greenberger-Horne-Zeilinger states and their local unitary equivalents, for n greater than or equal to 3 but not equal to 4. We characterize the Lie algebra of the stabilizer subgroup for these states. For n=4, there is an additional maximal stabilizer subalgebra, not local unitary equivalent to the former. We give a canonical form for states with this stabilizer as well.

6 pages, version 3 has a typographical correction in the displayed equation just after numbered equation (2), and other minor corrections

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• Local unitary group stabilizers and entanglement for multiqubit symmetric states
• Entanglement verification using local unitary stabilizers
• The Study of Entangled States in Quantum Computation and Quantum Information Science