Symmetric mixed states of $n$ qubits: local unitary stabilizers and entanglement classes

Details Symmetric mixed states of $n$ qubits: local unitary stabilizers and entanglement classes Symmetric mixed states of $n$ qubits: local unitary stabilizers and entanglement classes

2011-07-07

arxiv.org/abs/1107.1372v2

Phys. Rev. A, 84:042340, 2011

Physics

Quantum Physics

10 pages, 1 table, title change and minor clarifications for published version

Scientific paper

We classify, up to local unitary equivalence, local unitary stabilizer Lie algebras for symmetric mixed states into six classes. These include the stabilizer types of the Werner states, the GHZ state and its generalizations, and Dicke states. For all but the zero algebra, we classify entanglement types (local unitary equivalence classes) of symmetric mixed states that have those stabilizers. We make use of the identification of symmetric density matrices with polynomials in three variables with real coefficients and apply the representation theory of SO(3) on this space of polynomials.

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