### Abstract

We generalize the notion of relative phase to completely positive (CP) maps with known unitary representation, based on interferometry. Parallel transport conditions that define the geometric phase for such maps are introduced. The interference effect is embodied in a set of interference patterns defined by flipping the environment state in one of the two paths. We show for the qubit that this structure gives rise to interesting additional information about the geometry of the evolution defined by the CP map.

Original language | English |
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Article number | 020101 |

Pages (from-to) | - |

Number of pages | 4 |

Journal | Physical Review A |

Volume | 67 |

Issue number | 2 |

DOIs | |

Publication status | Published - Feb 2003 |

### Keywords

- geometry
- positive maps
- parallel transport

## Cite this

Ericsson, M., Sjoqvist, E., Brannlund, J., Oi, D. K. L., & Pati, A. K. (2003). Generalization of the geometric phase to completely positive maps.

*Physical Review A*,*67*(2), -. [020101]. https://doi.org/10.1103/PhysRevA.67.020101