论文标题
纯量子状态和统一转换的基于于点的自适应估计
Mean-squared-error-based adaptive estimation of pure quantum states and unitary transformations
论文作者
论文摘要
在本文中，我们提出了一种用单个Qudit的高精度纯量子状态进行估算的方法。我们的方法基于未知状态的复杂概率幅度及其估计值之间平方误差的最小化。我们通过数值实验表明，本方法的估计准确性是由状态独立的。此外，我们方法提供的估计准确性接近g玛斯尔下限的两倍，这是所有检查维度的最佳可实现精度。最小化问题是通过复杂同时扰动近似的串联来解决的，一种迭代的随机优化方法在复数范围内起作用，以及最大似然估计，这是一种众所周知的统计推断方法。这可以在多臂干涉阵列的帮助下进行。如果是单个量子，则马赫·齐纳德干涉仪就足够了。我们还表明，我们的估计过程很容易扩展，以估计作用于单个Qudit的未知统一转换。因此，统一转换的估计比基于混合状态的层析成像方法而实现的统一转换的精度更高。
In this article we propose a method to estimate with high accuracy pure quantum states of a single qudit. Our method is based on the minimization of the squared error between the complex probability amplitudes of the unknown state and its estimate. We show by means of numerical experiments that the estimation accuracy of the present method, which is given by the expectation of the squared error on the sample space of estimates, is state independent. Furthermore, the estimation accuracy delivered by our method is close to twice the Gill-Massar lower bound, which represents the best achievable accuracy, for all inspected dimensions. The minimization problem is solved via the concatenation of the Complex simultaneous perturbation approximation, an iterative stochastic optimization method that works within the field of the complex numbers, and Maximum likelihood estimation, a well-known statistical inference method. This can be carried out with the help of a multi-arm interferometric array. In the case of a single qubit, a Mach-Zehnder interferometer suffices. We also show that our estimation procedure can be easily extended to estimate unknown unitary transformations acting on a single qudit. Thereby, the estimation of unitary transformations achieves a higher accuracy than that achieved by processes based on tomographic methods for mixed states.
