不完全知识下的恢复：实时量子存储器的基本界限
Recovery With Incomplete Knowledge: Fundamental Bounds on Real-Time Quantum Memories
AI总结：
本文研究实时量子存储器中噪声参数漂移下的恢复问题，将基于旁观者的不完全知识恢复建模为实时参数估计加最佳猜测恢复映射，给出钻石距离意义下的信息论与计量学基本界限及多周期递推不等式，并揭示不完全噪声知识可能因误差相干而成为优势。
摘要：
从退相干中恢复脆弱的量子态是构建量子存储器的基础，其应用范围涵盖量子通信到量子计算。许多恢复技术，例如量子纠错，依赖于对环境噪声参数的先验知识来实现其最佳性能。然而，在实现长时间量子存储器的背景下，这些参数很可能随时间漂移。这需要使用一个“旁观者”系统，实时估计噪声参数，然后将估计结果作为经典辅助信息前馈给恢复协议。因此，存储器量子比特和旁观者系统构成了实时（即漂移自适应）量子存储器的基本构建模块。在本文中，我将基于旁观者的（不完全知识）恢复协议视为一个实时参数估计问题（通常存在多余参数），随后根据估计结果将“最佳猜测”恢复映射应用于存储器量子比特。我给出了该协议性能的信息论和计量学界限，以“最佳猜测”恢复与最优恢复结果之间的钻石距离来量化，从而确定了实时量子存储器中自适应适应的代价。最后，我以递推不等式的形式给出了多周期恢复的基本界限。后者表明，对噪声的不完全知识可能是一种优势，因为来自不同周期的误差可以相干叠加。这些结果以振幅阻尼信道的近似[4,1]码为例进行了说明，并讨论了与各个领域的联系。
英文摘要：
The recovery of fragile quantum states from decoherence is the basis of building a quantum memory, with applications ranging from quantum communications to quantum computing. Many recovery techniques, such as quantum error correction, rely on the apriori knowledge of the environment noise parameters to achieve their best performance. However, such parameters are likely to drift in time in the context of implementing long-time quantum memories. This necessitates using a "spectator" system, which estimates the noise parameter in real-time, then feed-forwards the outcome to the recovery protocol as a classical side-information. The memory qubits and the spectator system hence comprise the building blocks for a real-time (i.e. drift-adapting) quantum memory. In this article, I consider spectator-based (incomplete knowledge) recovery protocols as a real-time parameter estimation problem (generally with nuisance parameters present), followed by the application of the "best-guess" recovery map to the memory qubits, as informed by the estimation outcome. I present information-theoretic and metrological bounds on the performance of this protocol, quantified by the diamond distance between the "best-guess" recovery and optimal recovery outcomes, thereby identifying the cost of adaptation in real-time quantum memories. Finally, I provide fundamental bounds for multi-cycle recovery in the form of recurrence inequalities. The latter suggests that incomplete knowledge of the noise could be an advantage, as errors from various cycles can cohere. These results are illustrated for the approximate [4,1] code of the amplitude-damping channel and relations to various fields are discussed.
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