量子过程的实验表征:在任意有限维度上的一种选择性和有效的方法

Q. P. Stefano, I. Perito, Juan Jos'e Miguel Varga, Lorena Reb'on, Claudio Iemmi
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引用次数: 0

摘要

量子系统的时间演化可以通过量子过程层析来表征,这是一项复杂的任务,它消耗的物理资源与子系统的数量呈指数级增长。量子通道完全重建的另一种方法允许从矩阵描述中选择要测量的系数,以及测量的准确度,从而减少了多项式资源的数量。实现这种方法的可能性与建立一组完备的互无偏基(mub)的可能性密切相关,这些互无偏基只有在希尔伯特空间的维数为素数的幂时才存在。然而,最近引入了一种使用mub极大集的张量积的方法的扩展。在这里,我们明确地描述了如何实现该算法来有选择性地和有效地估计表征非素数幂维量子过程的任何参数,并首次在维度$d=6$的Hilbert空间中对该方法进行了实验验证。这是一个小空间它没有已知的mub的完整集合但是它可以被分解成两个维度分别为D_1=2和D_2=3的希尔伯特空间的张量积,在这个空间中,mub的完整集合是已知的。在光子波前的离散横动量中编码了6维状态。状态准备和检测阶段使用单相位空间光调制器进行动态编程,在一个通用的实验设置中,允许在任何有限维度中实现算法。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Experimental characterization of quantum processes: A selective and efficient method in arbitrary finite dimensions
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.
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