We analyze the geometry on the space of non-unital phase-covariant qubit
    maps. Using the corresponding Choi-Jamio{\l}kowski states, we derive the
    Hilbert-Schmidt line and volume elements using the channel eigenvalues together
    with the parameter that characterizes non-unitality. We find the shapes and
    analytically compute the volumes of phase-covariant channels, in particular
    entanglement breaking and obtainable with time-local generators.

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