Maximum stabilizer dimension for nonproduct states

Details Maximum stabilizer dimension for nonproduct states Maximum stabilizer dimension for nonproduct states

2007-06-12

arxiv.org/abs/0706.1785v2

Phys. Rev. A 76, 022303 (2007)

Physics

Quantum Physics

6 pages

Scientific paper

10.1103/PhysRevA.76.022303

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.

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