### 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.

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

Article number | 020101 |

Pages | - |

Number of pages | 4 |

Journal | Physical Review A |

Volume | 67 |

Issue number | 2 |

DOIs | |

Publication status | Published - Feb 2003 |

### Fingerprint

### Keywords

- geometry
- positive maps
- parallel transport

### Cite this

*Physical Review A*,

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

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*Physical Review A*, vol. 67, no. 2, 020101, pp. -. https://doi.org/10.1103/PhysRevA.67.020101

**Generalization of the geometric phase to completely positive maps.** / Ericsson, M ; Sjoqvist, E ; Brannlund, J ; Oi, D K L ; Pati, A K .

Research output: Contribution to journal › Article

TY - JOUR

T1 - Generalization of the geometric phase to completely positive maps

AU - Ericsson, M

AU - Sjoqvist, E

AU - Brannlund, J

AU - Oi, D K L

AU - Pati, A K

PY - 2003/2

Y1 - 2003/2

N2 - 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.

AB - 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.

KW - geometry

KW - positive maps

KW - parallel transport

UR - http://arxiv.org/PS_cache/quant-ph/pdf/0205/0205160v2.pdf

U2 - 10.1103/PhysRevA.67.020101

DO - 10.1103/PhysRevA.67.020101

M3 - Article

VL - 67

SP - -

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

IS - 2

M1 - 020101

ER -