  A completely depolarising quantum channel always outputs a fully mixed state
and thus cannot transmit any information. In a recent Letter [D. Ebler et al.,
Phys. Rev. Lett. 120, 120502 (2018)], it was however shown that if a quantum
state passes through two such channels in a quantum superposition of different
orders - a setup known as the "quantum switch" - then information can
nevertheless be transmitted through the channels. Here, we show that a similar
effect can be obtained when one coherently controls between sending a target
system through one of two identical depolarising channels. Whereas it is
tempting to attribute this effect in the quantum switch to the indefinite
causal order between the channels, causal indefiniteness plays no role in this
new scenario. This raises questions about its role in the corresponding effect
in the quantum switch. We study this new scenario in detail and we see that,
when quantum channels are controlled coherently, information about their
specific implementation is accessible in the output state of the joint
control-target system. This allows two different implementations of what is
usually considered to be the same channel to therefore be differentiated. More
generally, we find that to completely describe the action of a coherently
controlled quantum channel, one needs to specify not only a description of the
channel (e.g., in terms of Kraus operators), but an additional "transformation
matrix" depending on its implementation.
