Maximum stabilizer dimension for nonproduct states

Abstract

Composite quantum states can be classified by how they behave under local unitary transformations. Each quantum state has a stabilizer subgroup and a corresponding Lie algebra, the structure of which is a local unitary invariant. In this paper, we study the structure of the stabilizer subalgebra for n-qubit pure states, and find its maximum dimension to be n-1 for nonproduct states of three qubits and higher. The n-qubit Greenberger-Horne-Zeilinger state has a stabilizer subalgebra that achieves the maximum possible dimension for pure nonproduct states. The converse, however, is not true: we show examples of pure 4-qubit states that achieve the maximum nonproduct stabilizer dimension, but have stabilizer subalgebra structures different from that of the n-qubit GHZ state.

6 pages

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Cited by in corpus (8)

• Subsystem stabilizer codes cannot have a universal set of transversal gates for even one encoded qudit
• Only n-Qubit Greenberger-Horne-Zeilinger States are Undetermined by their Reduced Density Matrices
• Multiparty quantum states stabilized by the diagonal subgroup of the local unitary group
• Symmetric mixed states of $n$ qubits: local unitary stabilizers and entanglement classes
• Classification of nonproduct states with maximum stabilizer dimension
• The stabilizer dimension of graph states
• Local unitary group stabilizers and entanglement for multiqubit symmetric states
• Entanglement groups