论文标题
通过量子rényi信息，更好的海森伯格限制，连贯的界限和能源时间折衷
Better Heisenberg limits, coherence bounds, and energy-time tradeoffs via quantum Rényi information
论文作者
论文摘要
An uncertainty relation for the Rényi entropies of conjugate quantum observables is used to obtain a strong Heisenberg limit of the form ${\rm RMSE} \geq f(α)/(\langle N\rangle+\frac12)$, bounding the root mean square error of any estimate of a random optical phase shift in terms of average photon number, where $f(α)$对于非香农熵，最大化。还获得了相关的简单而强的不确定性关系，将相位不确定性与光子数分布联系起来，例如$Δφ\ geq \ geq \ max_n p_n $。这些结果通过与不对称和卷积有关的量子通信通道的Rényi互通道的上限和下限显着增强，并应用于单位移位参数（例如旋转角度和时间）的估计（先前信息），例如旋转角度和时间，并获得了相干度量的强大界限。还获得了SharperRényi熵不确定性关系，包括带有离散光谱的汉密尔顿人的时间能量不确定性关系。在后一种情况下，对于非周期系统，引入了几乎周期性的rényi熵。
An uncertainty relation for the Rényi entropies of conjugate quantum observables is used to obtain a strong Heisenberg limit of the form ${\rm RMSE} \geq f(α)/(\langle N\rangle+\frac12)$, bounding the root mean square error of any estimate of a random optical phase shift in terms of average photon number, where $f(α)$ is maximised for non-Shannon entropies. Related simple yet strong uncertainty relations linking phase uncertainty to the photon number distribution, such as $ΔΦ\geq \max_n p_n$, are also obtained. These results are significantly strengthened via upper and lower bounds on the Rényi mutual information of quantum communication channels, related to asymmetry and convolution, and applied to the estimation (with prior information) of unitary shift parameters such as rotation angle and time, and to obtain strong bounds on measures of coherence. Sharper Rényi entropic uncertainty relations are also obtained, including time-energy uncertainty relations for Hamiltonians with discrete spectra. In the latter case almost-periodic Rényi entropies are introduced for nonperiodic systems.
