Mixed State Geometric Phase from Thomas Rotations

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dc.creatorLévay, Péter
dc.date2003-12-02
dc.date.accessioned2026-07-07T06:19:43Z
dc.date.available2026-07-07T06:19:43Z
dc.descriptionIt is shown that Uhlmann's parallel transport of purifications along a path of mixed states represented by $2\times 2$ density matrices is just the path ordered product of Thomas rotations. These rotations are invariant under hyperbolic translations inside the Bloch sphere that can be regarded as the Poincaré ball model of hyperbolic geometry. A general expression for the mixed state geometric phase for an {\it arbitrary} geodesic triangle in terms of the Bures fidelities is derived. The formula gives back the solid angle result well-known from studies of the pure state geometric phase. It is also shown that this mixed state anholonomy can be reinterpreted as the pure state non-Abelian anholonomy of entangled states living in a suitable restriction of the quaternionic Hopf bundle. In this picture Uhlmann's parallel transport is just Pancharatnam transport of quaternionic spinors.
dc.description23 pages
dc.identifierhttps://arxiv.org/abs/quant-ph/0312023
dc.identifierhttp://arxiv.org/abs/quant-ph/0312023
dc.identifierJournal of Physics A37 (2004) 4593-4605
dc.identifierdoi:10.1088/0305-4470/37/16/009
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/95124
dc.subjectQuantum Physics
dc.titleMixed State Geometric Phase from Thomas Rotations
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