Zhao Xiaobin, Yang Yuxiang, Chiribella Giulio
QICI Quantum Information and Computation Initiative, Department of Computer Science, The University of Hong Kong, Pok Fu Lam Road, Hong Kong 999077, China.
The University of Hong Kong Shenzhen Institute of Research and Innovation, Yuexing 2nd Rd Nanshan, Shenzhen 518057, China.
Phys Rev Lett. 2020 May 15;124(19):190503. doi: 10.1103/PhysRevLett.124.190503.
We address the study of quantum metrology enhanced by indefinite causal order, demonstrating a quadratic advantage in the estimation of the product of two average displacements in a continuous variable system. We prove that no setup where the displacements are used in a fixed order can have root-mean-square error vanishing faster than the Heisenberg limit 1/N, where N is the number of displacements contributing to the average. In stark contrast, we show that a setup that probes the displacements in a superposition of two alternative orders yields a root-mean-square error vanishing with super-Heisenberg scaling 1/N^{2}, which we prove to be optimal among all superpositions of setups with definite causal order. Our result opens up the study of new measurement setups where quantum processes are probed in an indefinite order, and suggests enhanced tests of the canonical commutation relations, with potential applications to quantum gravity.
我们研究了由不确定因果序增强的量子计量学，证明了在连续变量系统中估计两个平均位移的乘积时具有二次优势。我们证明，在位移按固定顺序使用的任何设置中，均方根误差都不会比海森堡极限1/N更快地消失，其中N是对平均值有贡献的位移数量。与之形成鲜明对比的是，我们表明，在两个替代顺序的叠加中探测位移的设置会产生以超海森堡标度1/N²消失的均方根误差，我们证明这在具有确定因果序的所有设置叠加中是最优的。我们的结果开启了对以不确定顺序探测量子过程的新测量设置的研究，并建议对正则对易关系进行增强测试，这在量子引力中具有潜在应用。
