### Abstract

Language | English |
---|---|

Article number | 050102(R) |

Number of pages | 4 |

Journal | Physical Review A |

Volume | 89 |

DOIs | |

Publication status | Published - 15 May 2014 |

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### Keywords

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

### Cite this

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*Physical Review A*, vol. 89, 050102(R). https://doi.org/10.1103/PhysRevA.89.050102

**Unitary holonomies by direct degenerate projections.** / Oi, Daniel K.L.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Unitary holonomies by direct degenerate projections

AU - Oi, Daniel K.L.

PY - 2014/5/15

Y1 - 2014/5/15

N2 - 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.

AB - 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.

KW - unitary holonomies

KW - direct degenerate projections

KW - non-abelian holonomy

KW - isometries

KW - Hilbert dimension

UR - http://journals.aps.org/pra/

U2 - 10.1103/PhysRevA.89.050102

DO - 10.1103/PhysRevA.89.050102

M3 - Article

VL - 89

JO - Physical Review A - Atomic, Molecular, and Optical Physics

T2 - Physical Review A - Atomic, Molecular, and Optical Physics

JF - Physical Review A - Atomic, Molecular, and Optical Physics

SN - 1050-2947

M1 - 050102(R)

ER -