Department of Physics and Astronomy, University of Sheffield, Hounsfield Road, Sheffield, United Kingdom.
Phys Rev Lett. 2010 Oct 29;105(18):180402. doi: 10.1103/PhysRevLett.105.180402. Epub 2010 Oct 27.
Quantum metrology promises improved sensitivity in parameter estimation over classical procedures. However, there is a debate over the question of how the sensitivity scales with the resources and the number of queries that are used in estimation procedures. Here, we reconcile the physical definition of the relevant resources used in parameter estimation with the information-theoretical scaling in terms of the query complexity of a quantum network. This leads to a completely general optimality proof of the Heisenberg limit for quantum metrology. We give an example of how our proof resolves paradoxes that suggest sensitivities beyond the Heisenberg limit, and we show that the Heisenberg limit is an information-theoretic interpretation of the Margolus-Levitin bound, rather than Heisenberg's uncertainty relation.
量子计量学有望在参数估计方面超越经典方法，提高灵敏度。然而，关于灵敏度如何随用于估计过程的资源和查询次数而变化的问题存在争议。在这里，我们将参数估计中使用的相关资源的物理定义与量子网络查询复杂度的信息论尺度联系起来。这导致了对量子计量学的海森堡极限的完全一般性最优证明。我们给出了一个例子，说明了我们的证明如何解决了超出海森堡极限的灵敏度的悖论，并且我们表明，海森堡极限是马古利斯-列维丁界限的信息论解释，而不是海森堡不确定性原理。
