噪声前后的量子控制抑制噪声
Noise suppression by quantum control before and after the noise
摘要：
我们讨论了通过噪声过程之前和之后的测量/操作来保护经历噪声的量子系统的状态的可能性。其目的是寻求最佳的协议，使输入和输出状态尽可能接近，并澄清其中的测量的作用。我们考虑两种情况，一种可以执行量子测量/操作（i）仅在噪声过程之后，以及（ii）在噪声过程之前和之后。我们证明在二维希尔伯特空间中，在情况（i）中，噪声抑制基本上是不可能的所有类型的噪声，在情况（ii）中，最佳的协议去极化噪声是“什么都不做”协议或“歧视和重新准备”协议。这些协议不是“真正的量子”，可以被认为是经典的。它们不涉及测量或仅使用测量结果。这些结果从控制论的观点描述了量子力学的基本局限性。最后，我们猜想，一个类似的情况下（ii）的声明持有高维希尔伯特空间，并提出了一些数值证据。
英文摘要：
We discuss the possibility of protecting the state of a quantum system that goes through noise, by measurements/operations before and after the noise process. The aim is to seek for the optimal protocol that makes the input and output states as close as possible and clarify the role of the measurements therein. We consider two cases, one can perform quantum measurements/operations (i) only after the noise process and (ii) both before and after that. We prove in the two-dimensional Hilbert space that, in the case (i), the noise suppression is essentially impossible for all types of noise and, in the case (ii), the optimal protocol for the depolarizing noise is either the "do nothing" protocol or the "discriminate & reprepare" protocol. These protocols are not "truly quantum" and can be considered as classical. They involve no measurement or only use the measurement outcomes. These results describe the fundamental limitations in quantum mechanics from the viewpoint of control theory. Finally, we conjecture that a statement similar to the case (ii) holds for higher-dimensional Hilbert spaces and present some numerical evidence.
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