Arvidsson-Shukur David R M, Yunger Halpern Nicole, Lepage Hugo V, Lasek Aleksander A, Barnes Crispin H W, Lloyd Seth
Cavendish Laboratory, Department of Physics, University of Cambridge, Cambridge, CB3 0HE, UK.
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA.
Nat Commun. 2020 Jul 29;11(1):3775. doi: 10.1038/s41467-020-17559-w.
In every parameter-estimation experiment, the final measurement or the postprocessing incurs a cost. Postselection can improve the rate of Fisher information (the average information learned about an unknown parameter from a trial) to cost. We show that this improvement stems from the negativity of a particular quasiprobability distribution, a quantum extension of a probability distribution. In a classical theory, in which all observables commute, our quasiprobability distribution is real and nonnegative. In a quantum-mechanically noncommuting theory, nonclassicality manifests in negative or nonreal quasiprobabilities. Negative quasiprobabilities enable postselected experiments to outperform optimal postselection-free experiments: postselected quantum experiments can yield anomalously large information-cost rates. This advantage, we prove, is unrealizable in any classically commuting theory. Finally, we construct a preparation-and-postselection procedure that yields an arbitrarily large Fisher information. Our results establish the nonclassicality of a metrological advantage, leveraging our quasiprobability distribution as a mathematical tool.
在每一个参数估计实验中，最终测量或后处理都会产生成本。后选择可以提高费舍尔信息率（从一次试验中获得的关于未知参数的平均信息量）与成本的比率。我们表明，这种提高源于一种特定准概率分布的负性，它是概率分布的量子扩展。在所有可观测量都对易的经典理论中，我们的准概率分布是实的且非负的。在量子力学非对易理论中，非经典性表现为负的或非实的准概率。负准概率使后选择实验能够超越最优的无后选择实验：后选择量子实验可以产生异常大的信息成本率。我们证明，在任何经典对易理论中都无法实现这一优势。最后，我们构建了一种制备和后选择程序，它能产生任意大的费舍尔信息。我们的结果利用我们的准概率分布作为数学工具，确立了计量优势的非经典性。
