Chiribella G, Yang Y, Huang C
Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China.
Phys Rev Lett. 2015 Mar 27;114(12):120504. doi: 10.1103/PhysRevLett.114.120504. Epub 2015 Mar 25.
Quantum states obey an asymptotic no-cloning theorem, stating that no deterministic machine can reliably replicate generic sequences of identically prepared pure states. In stark contrast, we show that generic sequences of unitary gates can be replicated deterministically at nearly quadratic rates, with an error vanishing on most inputs except for an exponentially small fraction. The result is not in contradiction with the no-cloning theorem, since the impossibility of deterministically transforming pure states into unitary gates prevents the application of the gate replication protocol to states. In addition to gate replication, we show that N parallel uses of a completely unknown unitary gate can be compressed into a single gate acting on O(log_{2}N) qubits, leading to an exponential reduction of the amount of quantum communication needed to implement the gate remotely.
量子态服从渐近不可克隆定理，该定理表明，没有任何确定性机器能够可靠地复制相同制备的纯态的一般序列。与之形成鲜明对比的是，我们证明酉门的一般序列可以以接近二次的速率被确定性地复制，除了指数级小的一部分输入外，大多数输入上的误差都趋于零。该结果与不可克隆定理并不矛盾，因为将纯态确定性地转换为酉门是不可能的，这阻止了门复制协议应用于态。除了门复制，我们还证明，一个完全未知的酉门的N次并行使用可以被压缩为作用于O(log₂N)个量子比特的单个门，从而使远程实现该门所需的量子通信量呈指数级减少。
