arXivDaily arXiv每日学术速递 周一至周五更新
arXiv quant-ph/0305120quant-ph
收藏

比较许多量子系统的状态

Comparing the states of many quantum systems

Igor Jex, Erika Andersson, Anthony Chefles

摘要:

我们研究如何确定一组量子系统的状态是否相同。本文对待两个无错误的比较,比较结果中的错误是允许的。无错误比较意味着我们的目标是尽可能多地获得已知正确的明确答案。一般来说,我们也将不得不接受不确定的结果,不提供任何信息。得到系统状态不相同的确定答案总是可能的,然而,在这里考虑的情况下,它们相同的确定答案是不可能的。最优泛无错比较策略是在全对称和不同非对称子空间上的投影,在置换和酉变换下不变。我们还展示了如何构建最优的比较策略时,允许在结果中的一些错误,最大限度地减少错误的概率,或平均成本的错误。我们指出,它是可能实现通用的无误差的比较策略,仅使用线性元件和粒子探测器,虽然与理想的效率。此外,最小误差和最小成本的策略有时可以实现这种方式。这对量子比较的实际应用具有重要意义。

英文摘要:

We investigate how to determine whether the states of a set of quantum systems are identical or not. This paper treats both error-free comparison, and comparison where errors in the result are allowed. Error-free comparison means that we aim to obtain definite answers, which are known to be correct, as often as possible. In general, we will have to accept also inconclusive results, giving no information. To obtain a definite answer that the states of the systems are not identical is always possible, whereas, in the situation considered here, a definite answer that they are identical will not be possible. The optimal universal error-free comparison strategy is a projection onto the totally symmetric and the different non-symmetric subspaces, invariant under permutations and unitary transformations. We also show how to construct optimal comparison strategies when allowing for some errors in the result, minimising either the error probability, or the average cost of making an error. We point out that it is possible to realise universal error-free comparison strategies using only linear elements and particle detectors, albeit with less than ideal efficiency. Also minimum-error and minimum-cost strategies may sometimes be realised in this way. This is of great significance for practical applications of quantum comparison.

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。

↑