近日，丹麦哥本哈根大学的Ranyiliu Chen及其研究小组取得一项新进展。经过不懈努力，他们证实所有真实投影测量都可以自测试。相关研究成果已于2024年8月1日在国际知名学术期刊《自然—物理学》上发表。

该研究团队证明，每一个真实的投影测量都具备自测试的能力。为了实现这一目标，他们采用了扩展现有自测试的想法，以验证那些额外的、可能不可信的测量，这种方法被称为事后推理自测试。研究人员对事后推理自测试的方法进行了形式化描述，并明确了其可应用的条件。

基于这一条件，他们成功构建了针对所有实数投影测量的自测试。在此基础上，研究人员还开发了一种迭代的自测试技术，为从已有的自测试中构建新的自测试提供了明确的方法。

据悉，纠缠量子系统的特征是非局部关联，比经典理论更强。这种特性使得自测试成为可能，这是量子功能验证的最强形式，它允许经典用户推断用于产生给定测量统计集的量子态和测量。虽然量子态的自测试被很好地理解，但测量的自测试，特别是在高维中，仍然相对未被探索。

附：英文原文

Title: All real projective measurements can be self-tested

Author: Chen, Ranyiliu, Maninska, Laura, Voli, Jurij

Issue&Volume: 2024-08-01

Abstract: Entangled quantum systems feature non-local correlations that are stronger than could be realized classically. This property makes it possible to perform self-testing, the strongest form of quantum functionality verification, which allows a classical user to deduce the quantum state and measurements used to produce a given set of measurement statistics. While self-testing of quantum states is well understood, self-testing of measurements, especially in high dimensions, remains relatively unexplored. Here we prove that every real projective measurement can be self-tested. Our approach employs the idea that existing self-tests can be extended to verify additional untrusted measurements, known as post-hoc self-testing. We formalize the method of post-hoc self-testing and establish the condition under which it can be applied. Using this condition, we construct self-tests for all real projective measurements. We build on this result to develop an iterative self-testing technique that provides a clear methodology for constructing new self-tests from pre-existing ones.

DOI: 10.1038/s41567-024-02584-z

Source: https://www.nature.com/articles/s41567-024-02584-z