Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom.
Computer Science and York Centre for Quantum Technologies, University of York, York YO10 5GH, United Kingdom.
Phys Rev Lett. 2015 Dec 31;115(26):260501. doi: 10.1103/PhysRevLett.115.260501. Epub 2015 Dec 22.
We derive a computable analytical formula for the quantum fidelity between two arbitrary multimode Gaussian states which is simply expressed in terms of their first- and second-order statistical moments. We also show how such a formula can be written in terms of symplectic invariants and used to derive closed forms for a variety of basic quantities and tools, such as the Bures metric, the quantum Fisher information, and various fidelity-based bounds. Our result can be used to extend the study of continuous-variable protocols, such as quantum teleportation and cloning, beyond the current one-mode or two-mode analyses, and paves the way to solve general problems in quantum metrology and quantum hypothesis testing with arbitrary multimode Gaussian resources.
我们推导出了一种可计算的解析公式，用于计算任意多模高斯态之间的量子保真度，该公式可以简单地用它们的一阶和二阶统计矩来表示。我们还展示了如何用辛不变量来表示这样的公式，并将其用于推导出各种基本量和工具的封闭形式，例如 Bures 度量、量子 Fisher 信息和各种基于保真度的界。我们的结果可用于将连续变量协议（如量子隐形传态和克隆）的研究扩展到当前的单模或双模分析之外，并为使用任意多模高斯资源解决量子计量学和量子假设检验中的一般问题铺平了道路。
