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.
Berry, Quantal phase factors accompanying adiabatic changes , Proceedings of the Royal Society of London
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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.