Control power of quantum channels is not multiplicative

Abstract

Abstract 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.