论文标题
量子通道的单位性估计
Unitarity estimation for quantum channels
论文作者
论文摘要
估计未知量子通道的单位性$ \ MATHCAL {E} $提供有关其统一数量的信息，这是量子设备认证和基准测试中的基本和重要问题。可以通过连贯或不连贯的访问来执行单位性估计，而前者总体上会导致更好的查询复杂性，而后者则可以实现更实际的实现。 In this paper, we provide a unified framework for unitarity estimation, which induces ancilla-efficient algorithms that use $O(ε^{-2})$ and $O(\sqrt{d}\cdotε^{-2})$ calls to $\mathcal{E}$ with coherent and incoherent accesses, respectively, where $d$ is the dimension of the system $ \ Mathcal {e} $在上面作用，而$ε$是所需的精度。我们进一步表明，我们算法的$ d $依赖性和$ε$依赖性都是最佳的。作为结果的一部分，我们通过给出匹配的下限$ω（\ sqrt {d}）$来解决与不一致的访问的显着性问题的查询复杂性，从而改善了Aharonov等人的先前最佳下限$ω（\ \ sqrt [3] {D}）$。 （Nat。Commun。2022）和Chen等。 （焦点2021）。
Estimating the unitarity of an unknown quantum channel $\mathcal{E}$ provides information on how much it is unitary, which is a basic and important problem in quantum device certification and benchmarking. Unitarity estimation can be performed with either coherent or incoherent access, where the former in general leads to better query complexity while the latter allows more practical implementations. In this paper, we provide a unified framework for unitarity estimation, which induces ancilla-efficient algorithms that use $O(ε^{-2})$ and $O(\sqrt{d}\cdotε^{-2})$ calls to $\mathcal{E}$ with coherent and incoherent accesses, respectively, where $d$ is the dimension of the system that $\mathcal{E}$ acts on and $ε$ is the required precision. We further show that both the $d$-dependence and $ε$-dependence of our algorithms are optimal. As part of our results, we settle the query complexity of the distinguishing problem for depolarizing and unitary channels with incoherent access by giving a matching lower bound $Ω(\sqrt{d})$, improving the prior best lower bound $Ω(\sqrt[3]{d})$ by Aharonov et al. (Nat. Commun. 2022) and Chen et al. (FOCS 2021).
