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

David W. Lyons and Scott N. Walck
Phys. Rev. A 84, 042340 – Published 31 October 2011

Abstract

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.

  • Received 13 July 2011

DOI:https://doi.org/10.1103/PhysRevA.84.042340

©2011 American Physical Society

Authors & Affiliations

David W. Lyons* and Scott N. Walck

  • Lebanon Valley College, Annville, Pennsylvania 17003, USA

  • *lyons@lvc.edu
  • walck@lvc.edu

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Issue

Vol. 84, Iss. 4 — October 2011

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