论文标题
量子波动反应不平等及其在量子假设测试中的应用
Quantum Fluctuation-Response Inequality and Its Application in Quantum Hypothesis Testing
论文作者
论文摘要
我们揭示了量子波动反应不平等，在最通用的环境中，该响应不平等在两个不同量子状态下可观察到的平均差异建立了一个绑定，就量子相对熵而言。当可观察到的频谱被界定时，下高斯的特性将通过将绑定与可观察到的可观察到的统一的界定联系起来来进一步取得我们的结果，我们基于我们在量子假设测试中的统计误差之和的新颖结合。与基于量子Pinsker的不平等相比，这种错误的限制是非偶然的，并且比基于量子的不平等更强大，更有信息。我们还通过在热力学推断和速度限制等问题中应用了结果的多功能性。
We uncover the quantum fluctuation-response inequality, which, in the most general setting, establishes a bound for the mean difference of an observable at two different quantum states, in terms of the quantum relative entropy. When the spectrum of the observable is bounded, the sub-Gaussian property is used to further our result by explicitly linking the bound with the sub-Gaussian norm of the observable, based on which we derive a novel bound for the sum of statistical errors in quantum hypothesis testing. This error bound holds nonasymptotically and is stronger and more informative than that based on quantum Pinsker's inequality. We also show the versatility of our results by their applications in problems like thermodynamic inference and speed limit.
