量子决策树复杂度的熵下界
Entropy lower bounds of quantum decision tree complexity
摘要：
我们证明了量子决策树复杂性的一般下界的熵的概念。我们把计算看作是一个通信过程，其中预言机和计算机交换几轮消息，每轮由O（log（n））位组成。设E（f）是随机变量f（X）的香农熵，其中X在f的域中是一致随机的。我们的主要结果是，它需要Ω（E（f））查询计算任何\emph{total}函数f。有趣的是，将此界与Ω（E（f）/log（n））界进行对比，Ω（E（f）/log（n））界对于\emph{partial}函数是紧的。我们的方法是多项式方法。
英文摘要：
We prove a general lower bound of quantum decision tree complexity in terms of some entropy notion. We regard the computation as a communication process in which the oracle and the computer exchange several rounds of messages, each round consisting of O(log(n)) bits. Let E(f) be the Shannon entropy of the random variable f(X), where X is uniformly random in f's domain. Our main result is that it takes Ω(E(f)) queries to compute any \emph{total} function f. It is interesting to contrast this bound with the Ω(E(f)/log(n)) bound, which is tight for \emph{partial} functions. Our approach is the polynomial method.
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