arXiv 1107.09342011-07quant-ph

量子加速的起源

Origin of the quantum speed-up

Giuseppe Castagnoli

备注：: 21 pages, 1 figure. Corrected a misleading typing error at point III) of Section 3: "Do the same with B" replaced by "Do the same with V"; minor distributed text improvements. arXiv admin note: text overlap with arXiv:1101.4359

摘要：

Bob从一组函数中选择一个函数，并将计算该函数的黑盒交给Alice，Alice通过函数求值来找到该函数的特征。在量子情况下，函数求值的数量可以小于经典可能的最小值。这种违反经典极限的根本原因尚不清楚。我们将其追溯到一个消除歧义的原则，即测量一个可观察确定其特征值之一。将Bob选择的函数标签表示为随机量子测量结果的幺正变换，表明：（i）在Alice的部分上找到函数的特征是重构Bob的选择的副产品，以及（ii）由于选择和重构之间的量子相关性，我们无法判断Bob的选择是由Bob的动作（初始测量和连续的酉变换）还是Alice的动作（进一步的酉变换和最终测量）决定的。假设确定在两个动作之间均匀共享，以所有可能的共享方式的统一叠加，意味着量子算法是历史的叠加，在每个历史中，爱丽丝提前知道鲍勃选择的可能一半之一。在每个历史中，只执行经典地重建鲍勃的选择所需的函数评估，给出了它的一半的高级知识，产生了量子加速。在所有检查的情况下，这伴随着交错函数求值与非计算酉变换，每次最大化Alice通过函数求值获得的关于Bob选择的信息量。

英文摘要：

Bob chooses a function from a set of functions and gives Alice the black box that computes it. Alice is to find a characteristic of the function through function evaluations. In the quantum case, the number of function evaluations can be smaller than the minimum classically possible. The fundamental reason for this violation of a classical limit is not known. We trace it back to a disambiguation of the principle that measuring an observable determines one of its eigenvalues. Representing Bob's choice of the label of the function as the unitary transformation of a random quantum measurement outcome shows that: (i) finding the characteristic of the function on the part of Alice is a by-product of reconstructing Bob's choice and (ii) because of the quantum correlation between choice and reconstruction, one cannot tell whether Bob's choice is determined by the action of Bob (initial measurement and successive unitary transformation) or that of Alice (further unitary transformation and final measurement). Postulating that the determination shares evenly between the two actions, in a uniform superposition of all the possible ways of sharing, implies that quantum algorithms are superpositions of histories in each of which Alice knows in advance one of the possible halves of Bob's choice. Performing, in each history, only the function evaluations required to classically reconstruct Bob's choice given the advanced knowledge of half of it yields the quantum speed-up. In all the cases examined, this goes along with interleaving function evaluations with non-computational unitary transformations that each time maximize the amount of information about Bob's choice acquired by Alice with function evaluation.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

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