Gaussian systems for quantum-enhanced multiple phase estimation
Gaussian systems for quantum-enhanced multiple phase estimation
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DOI：
10.1103/physreva.94.042342
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发表时间：
2016-10-28
影响因子：
2.9
通讯作者：
Datta, Animesh
中科院分区：
文献类型：
--
作者：
Gagatsos, Christos N.;Branford, Dominic;Datta, Animesh
对于固定的平均能量，多个相位的同时估计可以提供比单独估计它们更好的总体精度。我们通过计算协方差矩阵，对使用高斯输入和无源元件的多模干涉仪显示了这一点。量子Cramer-Rao界通过量子Fisher信息矩阵提供了协方差矩阵的下界，我们推导出其元素是跨模的光子数的协方差。我们证明了这个界是饱和的。尽管问题的性质是高斯的，但需要计算非高斯积分，这是我们解析完成的。我们发现我们的同步策略在总精度上的提高不超过2倍，这可能是因为高斯态的基本性能限制。我们的工作表明，对于多个相位的同时量子增强估计，不需要模式纠缠。
For a fixed average energy, the simultaneous estimation of multiple phases can provide a better total precision than estimating them individually. We show this for a multimode interferometer with a phase in each mode, using Gaussian inputs and passive elements, by calculating the covariance matrix. The quantum Cramer-Rao bound provides a lower bound to the covariance matrix via the quantum Fisher information matrix, whose elements we derive to be the covariances of the photon numbers across the modes. We prove that this bound can be saturated. In spite of the Gaussian nature of the problem, the calculation of non-Gaussian integrals is required, which we accomplish analytically. We find our simultaneous strategy to yield no more than a factor-of-2 improvement in total precision, possibly because of a fundamental performance limitation of Gaussian states. Our work shows that no modal entanglement is necessary for simultaneous quantum-enhanced estimation of multiple phases.