Characterizing the Depolarizing Quantum Channel in Terms of Riemannian Geometry

Details Characterizing the Depolarizing Quantum Channel in Terms of Riemannian Geometry Characterizing the Depolarizing Quantum Channel in Terms of Riemannian Geometry

2011-11-17

arxiv.org/abs/1111.4105v1

Physics

Mathematical Physics

7 pages, 0 figures; Accepted contribution to "Folding and Unfolding: Interactions from Geometry", Workshop in honour of Giusep

Scientific paper

We explore the conceptual usefulness of Riemannian geometric tools induced by the statistical concept of distinguishability in quantifying the effect of a depolarizing channel on quantum states. Specifically, we compare the geometries of the interior of undeformed and deformed Bloch spheres related to density operators on a two-dimensional Hilbert space. We show that randomization emerges geometrically through a smaller infinitesimal quantum line element on the deformed Bloch sphere while the uniform contraction manifests itself via a deformed set of geodesics where the spacial components of the deformed four-Bloch vector are simply the contracted versions of the undeformed Bloch vector components.

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