Zambrano Leonardo, Pereira Luciano, Niklitschek Sebastián, Delgado Aldo
Instituto Milenio de Investigación en Óptica, Universidad de Concepción, Concepción, Chile.
Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Concepción, Concepción, Chile.
Sci Rep. 2020 Jul 29;10(1):12781. doi: 10.1038/s41598-020-69646-z.
Quantum tomography has become a key tool for the assessment of quantum states, processes, and devices. This drives the search for tomographic methods that achieve greater accuracy. In the case of mixed states of a single 2-dimensional quantum system adaptive methods have been recently introduced that achieve the theoretical accuracy limit deduced by Hayashi and Gill and Massar. However, accurate estimation of higher-dimensional quantum states remains poorly understood. This is mainly due to the existence of incompatible observables, which makes multiparameter estimation difficult. Here we present an adaptive tomographic method and show through numerical simulations that, after a few iterations, it is asymptotically approaching the fundamental Gill-Massar lower bound for the estimation accuracy of pure quantum states in high dimension. The method is based on a combination of stochastic optimization on the field of the complex numbers and statistical inference, exceeds the accuracy of any mixed-state tomographic method, and can be demonstrated with current experimental capabilities. The proposed method may lead to new developments in quantum metrology.
量子层析成像已成为评估量子态、过程和器件的关键工具。这推动了对实现更高精度的层析成像方法的探索。对于单个二维量子系统的混合态，最近引入了自适应方法，这些方法达到了由林和吉尔以及马萨尔推导的理论精度极限。然而，对于高维量子态的精确估计仍然知之甚少。这主要是由于存在不相容的可观测量，这使得多参数估计变得困难。在这里，我们提出了一种自适应层析成像方法，并通过数值模拟表明，经过几次迭代后，它渐近地接近高维纯量子态估计精度的基本吉尔 - 马萨尔下界。该方法基于复数域上的随机优化和统计推断的结合，超过了任何混合态层析成像方法的精度，并且可以用当前的实验能力来证明。所提出的方法可能会导致量子计量学的新发展。
