关于姚原理的量子版本
On Quantum Versions of the Yao Principle
摘要：
经典的Yao原理指出，对于成功概率为1- 1/2的函数f，最优随机化算法的复杂度R_mu（f）等于对于f的最优确定性算法的复杂度max_mu D_mu ^mu（f），该最优确定性算法在1 - 1/2的输入上是正确的，根据输入上的最难分布mu进行加权。在本文中，我们调查在何种程度上这样的原则适用于量子算法。我们提出了两个自然的候选量子姚原理，一个“弱”和一个“强”。对于这两个原则，我们证明了量子有界错误复杂度是max mu D_n ^mu（f）的量子类似物的下界。然后，我们证明，平等不能获得的“强”的版本，通过展示指数差距。另一方面，作为一个积极的结果，我们证明了“弱”版本举行了一个常数因子的查询复杂性的所有对称布尔函数
英文摘要：
The classical Yao principle states that the complexity R_epsilon(f) of an optimal randomized algorithm for a function f with success probability 1-epsilon equals the complexity max_mu D_epsilon^mu(f) of an optimal deterministic algorithm for f that is correct on a fraction 1-epsilon of the inputs, weighed according to the hardest distribution mu over the inputs. In this paper we investigate to what extent such a principle holds for quantum algorithms. We propose two natural candidate quantum Yao principles, a ``weak'' and a ``strong'' one. For both principles, we prove that the quantum bounded-error complexity is a lower bound on the quantum analogues of max mu D_epsilon^mu(f). We then prove that equality cannot be obtained for the ``strong'' version, by exhibiting an exponential gap. On the other hand, as a positive result we prove that the ``weak'' version holds up to a constant factor for the query complexity of all symmetric Boolean functions
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