量子态的随机抽样方法综述
Random Sampling of Quantum States: A Survey of Methods
摘要：
随机量子态（RQS）的数值产生是量子信息科学研究中的一个重要步骤。在这里，我们回顾一些方法，可用于执行该任务。首先，我们提出了一个简单的程序生成随机状态向量，其中的主要工具是无偏离散概率分布（DPD）的随机抽样。然后讨论了随机密度矩阵的建立。在这方面，我们首先提出了标准的方法，它包括在使用的量子态的光谱分解从随机DPD和随机酉矩阵得到RQS。在序列中的布洛赫矢量参数化方法进行了说明。尽管这种方法在一些情况下是有用的，但通常不便于RQS生成。在文章的最后一部分，我们考虑过参数化方法（OPM）和相关的Ginibre和Bures技术。OPM可以用来从随机产生的一般复矩阵中产生具有单位迹的随机半正定矩阵，方法简单，便于数值实现。我们考虑一个物理上相关的问题，可能用于实部和虚部的元素，这样的一般复杂的矩阵的域。随后，注意到在该参数化中出现的量子态空间中的测量的过快集中。
英文摘要：
The numerical generation of random quantum states (RQS) is an important procedure for investigations in quantum information science. Here we review some methods that may be used for performing that task. We start by presenting a simple procedure for generating random state vectors, for which the main tool is the random sampling of unbiased discrete probability distributions (DPD). Afterwards the creation of random density matrices is addressed. In this context we first present the standard method, which consists in using the spectral decomposition of a quantum state for getting RQS from random DPDs and random unitary matrices. In the sequence the Bloch vector parametrization method is described. This approach, despite being useful in several instances, is not in general convenient for RQS generation. In the last part of the article we regard the overparametrized method (OPM) and the related Ginibre and Bures techniques. The OPM can be used to create random positive semidefinite matrices with unit trace from randomly produced general complex matrices in a simple way that is friendly for numerical implementations. We consider a physically relevant issue related to the possible domains that may be used for the real and imaginary parts of the elements of such general complex matrices. Subsequently a too fast concentration of measure in the quantum state space that appears in this parametrization is noticed.
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