Unitary holonomies by direct degenerate projections

Abstract

An incomplete quantum measurement can induce nontrivial dynamics between degenerate subspaces, a closed sequence of such projections produces a nonabelian 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 subspaces.