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.
L´ evay,Thomas rotation and the mixed state geometric phase , Journal of Physics A: Mathematical and General 37 (2004) 4593
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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.