标题： 最优量子钟的浓缩 显示英文标题

标题： Optimal Distillation of Qubit Clocks

摘要： 我们研究在时间平移不变操作下的相干性纯化：给定许多包含能量本征基中相干性的量子态副本，目标是在尊重时间平移对称性的前提下生成一个更纯的相干态。 这种对称性确保输出与输入保持同步，并且该过程可以通过耦合系统与初始处于能量本征态的热库的能量守恒酉变换来实现，从而建模补充了工作库或电池的热操作。 对于量子比特系统，我们确定了最优渐近保真度，并表明它由相干性的纯度决定，这是一种从右对数导数（RLD）费舍尔信息中导出的不对称性度量。 特别是，我们发现最低可达到的失真度（1减去保真度）按$1/N$乘以每个输入量子比特的相干性纯度的倒数进行缩放，其中$N$是副本数量，使该量具有明确的操作意义。 我们还研究了量子比特相干性纯化问题的其他许多有趣方面，包括计算最低可达到失真度的高阶修正项，直到$O(1/N^3)$，并表达最优通道为一个边界值问题，该问题可以数值求解。 显示英文摘要

摘要： We study coherence distillation under time-translation-invariant operations: given many copies of a quantum state containing coherence in the energy eigenbasis, the aim is to produce a purer coherent state while respecting the time-translation symmetry. This symmetry ensures that the output remains synchronized with the input and that the process can be realized by energy-conserving unitaries coupling the system to a reservoir initially in an energy eigenstate, thereby modeling thermal operations supplemented by a work reservoir or battery. For qubit systems, we determine the optimal asymptotic fidelity and show that it is governed by the purity of coherence, a measure of asymmetry derived from the right logarithmic derivative (RLD) Fisher information. In particular, we find that the lowest achievable infidelity (one minus fidelity) scales as $1/N$ times the reciprocal of the purity of coherence of each input qubit, where $N$ is the number of copies, giving this quantity a clear operational meaning. We additionally study many other interesting aspects of the coherence distillation problem for qubits, including computing higher-order corrections to the lowest achievable infidelity up to $O(1/N^3)$, and expressing the optimal channel as a boundary value problem that can be solved numerically.