论文标题
层次量子测量下的信息几何形状
Information geometry under hierarchical quantum measurement
论文作者
论文摘要
在大多数量子技术中，需要对参数化量子状态进行测量，以将量子信息转换为经典信息。但是，测量不可避免地会扭曲信息。差异的表征是量子信息科学中的重要主题，在理解量子和经典信息的结构之间的差异中起着关键作用。在这里，我们根据Fisher信息指标分析了差异，并提出了一个框架，该框架可以为分层量子测量下的差异提供分析界限。具体而言，我们在层次p-local量子测量下介绍了一组分析界限，涉及量子和经典渔民信息度量标准，这是可以在量子状态的大多数副本上共同执行的测量。结果可以直接转换为多参数量子计量学的精确限制，从而导致不同参数精确度之间的权衡表征。该框架还通过将特殊情况包括在内，为各种现有结果提供了连贯的图片。
In most quantum technologies, measurements need to be performed on the parametrized quantum states to transform the quantum information to classical information. The measurements, however, inevitably distort the information. The characterization of the discrepancy is an important subject in quantum information science, which plays a key role in understanding the difference between the structures of the quantum and classical information. Here we analyze the discrepancy in terms of the Fisher information metric and present a framework that can provide analytical bounds on the difference under hierarchical quantum measurements. Specifically, we present a set of analytical bounds on the difference between the quantum and classical Fisher information metric under hierarchical p-local quantum measurements, which are measurements that can be performed collectively on at most p copies of quantum states. The results can be directly transformed to the precision limit in multi-parameter quantum metrology, which leads to characterizations of the tradeoff among the precision of different parameters. The framework also provides a coherent picture for various existing results by including them as special cases.
