Generalization of the geometric phase to completely positive maps

M  Ericsson; E  Sjoqvist; J  Brannlund; D K L  Oi; A K  Pati

doi:10.1103/PhysRevA.67.020101

Generalization of the geometric phase to completely positive maps

M Ericsson, E Sjoqvist, J Brannlund, D K L Oi, A K Pati

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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
Article number	020101
Pages (from-to)	-
Number of pages	4
Journal	Physical Review A
Volume	67
Issue number	2
DOIs	https://doi.org/10.1103/PhysRevA.67.020101
Publication status	Published - Feb 2003

Keywords

geometry
positive maps
parallel transport

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10.1103/PhysRevA.67.020101

0205160v2Submitted manuscript, 126 KB

Cite this

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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.",

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KW - parallel transport

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Generalization of the geometric phase to completely positive maps

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