Unitary holonomies by direct degenerate projections

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An incomplete quantum measurement can induce non-trivial dynamics between degenerate subspaces, a closed sequence of such projections produces a non-abelian holonomy. We show how to induce unitary evolution on an initial subspace from such finite discrete sequences and also construct a near deterministic repeat-until-success protocol. We also prove necessary and sufficient criteria on the auxiliary Hilbert space dimension required for inducing isometries between between subspaces.
Original languageEnglish
Article number050102(R)
Number of pages4
JournalPhysical Review A
Publication statusPublished - 15 May 2014


  • unitary holonomies
  • direct degenerate projections
  • non-abelian holonomy
  • isometries
  • Hilbert dimension


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