  We analyze two ways to obtain distinguishability measures between quantum
maps by employing the square root of the quantum Jensen-Shannon divergence,
which forms a true distance in the space of density operators. The arising
measures are the transmission distance between quantum channels and the
entropic channel divergence. We investigate their mathematical properties and
discuss their physical meaning. Additionally, we establish a chain rule for the
entropic channel divergence, which implies the amortization collapse, a
relevant result with potential applications in the field of discrimination of
quantum channels and converse bounds. Finally, we analyze the
distinguishability between two given Pauli channels and study exemplary
Hamiltonian dynamics under decoherence.
