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Geometry of symmetric and non-invertible Pauli channels (2010.01128v2)
Published 2 Oct 2020 in quant-ph, math-ph, and math.MP
Abstract: We analyze the geometry of positive and completely positive, trace preserving Pauli maps that are fully determined by up to two distinct parameters. This includes five classes of symmetric and non-invertible Pauli channels. Using the Hilbert-Schmidt metric in the space of the Choi-Jamio\lkowski states, we compute the relative volumes of entanglement breaking, time-local generated, and divisible channels. Finally, we find the shapes of the complete positivity regions in relation to the tetrahedron of all Pauli channels.