Quantum state tomography (QST) aims at estimating a quantum state from averaged quantum measurements made on copies of the state. Most quantum algorithms rely on QST at some point and it is a well explored topic in the literature, mostly for mixed states. In this paper we focus on the QST of a pure quantum state using parallel unentangled measurements. Pure states are a small but useful subset of all quantum states, their tomography requires fewer measurements and is essentially a phase recovery problem. Parallel unentangled measurements are easy to implement in practice because they allow the user to measure each qubit individually. We propose two sets of quantum measurements that one can make on a pure state as well as the algorithms that use the measurements outcomes in order to identify the state. We also discuss how those estimates can be fined tuned by finding the state that maximizes the likelihood of the measurements with different variants of the likelihood. The performances of the proposed three types of QST methods are validated by means of detailed numerical tests.

量子状态层析成像(QST)的目的是从 对状态副本进行的平均量子测量。最多的量子 算法在某种程度上依赖于QST，这是一个在 文学，主要是针对混合州的。在这篇文章中，我们集中讨论了一个QST 使用平行无纠缠测量的纯量子态。纯态是一种 所有量子态的小但有用的子集，它们的层析成像需要更少 测量结果，本质上是一个相位恢复问题。平行无纠缠 测量在实践中很容易实现，因为它们允许用户 分别测量每个量子比特。我们提出了两组量子测量 可以对纯状态以及使用 测量结果，以确定状态。我们还讨论了这些 可以通过找到最大化可能性的状态来调整估计 不同可能性变量的测量结果。演出 对所提出的三种QST方法进行了详细的验证 数字测试。