Symmetric states: local unitary equivalence via stabilizers

  • Authors:

  • Curt D. Cenci;David W. Lyons;Laura M. Snyder;Scott N. Walck

  • Affiliations:

  • Mathematics, Lebanon Valley College, Annville, Pennsylvania;Mathematics, Lebanon Valley College, Annville, Pennsylvania;Physics, Lebanon Valley College, Annville, Pennsylvania;Physics, Lebanon Valley College, Annville, Pennsylvania

  • Venue:
  • Quantum Information & Computation
  • Year:
  • 2010

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Abstract

We classify local unitary equivalence classes of symmetric states via a classification oftheir local unitary stabilizer subgroups. For states whose local unitary stabilizer groupshave a positive number of continuous degrees of freedom, the classification is exhaustive.We show that local unitary stabilizer groups with no continuous degrees of freedom areisomorphic to finite subgroups of the rotation group SO(3), and give examples of stateswith discrete stabilizers.