For a thermofield double model, Uhlmann parallel transport acts as optimal filtering measurements on one side and as holonomic quantum gates on the other, with an iSWAP gate constructible from geodesic triangles.
Uhlmann, The metric of bures and the geometric phase , in Quantum Groups and Related Topics, R
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A thermofield-double model of Uhlmann anholonomy
For a thermofield double model, Uhlmann parallel transport acts as optimal filtering measurements on one side and as holonomic quantum gates on the other, with an iSWAP gate constructible from geodesic triangles.