标题： 量子过程的实验表征：任意有限维中的选择性和高效方法 显示英文标题

标题： Experimental characterization of quantum processes: a selective and efficient method in arbitrary finite dimension

摘要： 量子系统的时域演化可以通过量子过程层析成像来表征，这是一个复杂任务，其消耗的物理资源数量随子系统数量呈指数增长。 一种完整的量子信道重构方法允许选择测量其矩阵描述中的哪个系数以及测量的精确度，从而将所需资源减少到多项式级别。 实施这种方法的可能性与构建一组完整的相互 unbiased 基 (MUBs) 的可能性密切相关，而这种基的存在性仅在希尔伯特空间的维度是素数的幂时才被已知。 然而，最近引入了一种扩展方法，该方法使用最大 MUBs 集的张量积。 在这里，我们明确描述了如何实现该算法，以选择性和高效性估计非素数幂维度中任何表征量子过程的参数，并首次在维度为$d=6$的希尔伯特空间中对该方法进行了实验验证。 这是没有已知完整 MUBs 集的小空间，但它可以分解为两个维度分别为$D_1=2$和$D_2=3$的其他希尔伯特空间的张量积，对于这两个空间，已知存在完整的 MUBs 集。 $6$维度的状态被编码在光子波前的离散横向动量中。 状态制备和检测阶段仅使用只相位的空间光调制器进行动态编程，在一个灵活的实验设置中，该设置允许在任何有限维度中实现该算法。 显示英文摘要

摘要： The temporal evolution of a quantum system can be characterized by quantum process tomography, a complex task that consumes a number of physical resources scaling exponentially with the number of subsystems. An alternative approach to the full reconstruction of a quantum channel allows selecting which coefficient from its matrix description to measure, and how accurately, reducing the amount of resources to be polynomial. The possibility of implementing this method is closely related to the possibility of building a complete set of mutually unbiased bases (MUBs) whose existence is known only when the dimension of the Hilbert space is the power of a prime number. However, an extension of the method that uses tensor products of maximal sets of MUBs, has been introduced recently. Here we explicitly describe how to implement this algorithm to selectively and efficiently estimate any parameter characterizing a quantum process in a non-prime power dimension, and we conducted for the first time an experimental verification of the method in a Hilbert space of dimension $d=6$. That is the small space for which there is no known a complete set of MUBs but it can be decomposed as a tensor product of two other Hilbert spaces of dimensions $D_1=2$ and $D_2=3$, for which a complete set of MUBs is known. The $6$-dimensional states were codified in the discretized transverse momentum of the photon wavefront. The state preparation and detection stages are dynamically programmed with the use of only-phase spatial light modulators, in a versatile experimental setup that allows to implement the algorithm in any finite dimension.