Geometry of depolarizing channels
Kuldeep Dixit, E. C. G. Sudarshan · Physical Review A · 2008
Depolarizing maps acting on an $N$-dimensional system are completely positive maps resulting into compression of the Bloch ``ball'' along ${N}^{2}\ensuremath{-}1$ polarization directions. In the qubit case these maps are a convex sum of four extremal maps and form a simplex in the space of compression coefficients along the three polarization directions. We calculate the compression domain for three- and four-level systems. For a three-level system the region has curved surfaces, but it is a simplex for a four-level system. We conjecture that it is a simplex in the case of ${2}^{n}$-level systems.