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 |
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Keywords
- geometry
- positive maps
- parallel transport
Cite this
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Generalization of the geometric phase to completely positive maps. / Ericsson, M ; Sjoqvist, E ; Brannlund, J ; Oi, D K L ; Pati, A K .
In: Physical Review A, Vol. 67, No. 2, 020101, 02.2003, p. -.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 -