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We construct a family of parallel channels for controlled quantum communication, and show that the control power of a quantum channel can become larger when it is combined with a zero control power channel. As a consequence, we demonstrate for the first time that control power is non-multiplicative. In contrast to previous results which indicated that increasing control power requires the consumption of channel capacity or the consumption of additional non-local three-qudit entangled resources, in our construction the quantum capacity of the tensor product of two channels remain unchanged and it does not consume non-local three-qudit entangled resources. We show that this lossless channel capacity method is quite generically applicable: every channel can be embedded into our construction, and control power is increased whenever the given channel configuration matches the effect of local operations. Our protocol not only provides a feasible method for achieving higher control power for information transmission with less entangled resources, but also provides new understanding of the resource theory of quantum channels.

Control power of quantum channels is not multiplicative