Abstract
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.
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