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

Journal Article · Sat Oct 15 00:00:00 EDT 2011 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.84.042340· OSTI ID:22080379

Lyons, David W; Walck, Scott N ^[1]

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1. Lebanon Valley College, Annville, Pennsylvania 17003 (United States)

We classify, up to local unitary equivalence, local unitary stabilizer Lie algebras for symmetric mixed states of n qubits into six classes. These include the stabilizer types of the Werner states, the Greenberger-Horne-Zeilinger 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.

• OSTI ID: 22080379
• Journal Information: Physical Review. A, Vol. 84, Issue 4; Other Information: (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
DENSITY MATRIX
LIE GROUPS
MIXED STATES
POLYNOMIALS
QUANTUM ENTANGLEMENT
QUBITS
SYMMETRY