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A completely depolarising quantum channel always outputs a fully mixed stateand 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 quantumstate passes through two such channels in a quantum superposition of differentorders - a setup known as the "quantum switch" - then information cannevertheless be transmitted through the channels. Here, we show that a similareffect can be obtained when one coherently controls between sending a targetsystem through one of two identical depolarising channels. Whereas it istempting to attribute this effect in the quantum switch to the indefinitecausal order between the channels, causal indefiniteness plays no role in thisnew scenario. This raises questions about its role in the corresponding effectin the quantum switch. We study this new scenario in detail and we see that,when quantum channels are controlled coherently, information about theirspecific implementation is accessible in the output state of the jointcontrol-target system. This allows two different implementations of what isusually considered to be the same channel to therefore be differentiated. Moregenerally, we find that to completely describe the action of a coherentlycontrolled quantum channel, one needs to specify not only a description of thechannel (e.g., in terms of Kraus operators), but an additional "transformationmatrix" depending on its implementation.

Communication through coherent control of quantum channels