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.

我们构造了一系列用于受控量子通信的并行通道，并显示了与零控制功率通道结合使用时，量子通道的控制功率会变得更大。结果，我们首次证明了控制能力是不可乘的。与先前的结果表明，增加控制功率需要消耗通道容量或消耗其他非本地三量子纠缠资源相反，在我们的构造中，两个通道张量积的量子容量保持不变，并且没有变化消耗非本地的三级纠缠资源。我们证明了这种无损信道容量方法非常通用：每个信道都可以嵌入到我们的结构中，只要给定的通道配置与本地操作的效果相匹配，控制功率就会增加。我们的协议不仅为在较少纠缠资源的情况下实现更高的信息传输控制能力提供了一种可行的方法，而且为量子信道的资源理论提供了新的认识。