发表机构
Beijing Institute of Technology; Tsinghua University（北京理工大学; 清华大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究子系统丢失后量子信息恢复问题，通过引入标量测度等方法，确定不可恢复性根源，证明通用误差下限，发现采样成本光谱相变，将多部分量子态分类，揭示条件互信息与虚拟可恢复性无关，为容错量子计量设检测阈值。
AI 中文摘要
子系统丢失后量子信息的恢复是量子信息处理中的核心挑战。然而，有些状态无法通过任何恢复策略恢复。我们确定了不可恢复性的代数根源，即幽灵信息——全局状态中编码的相关性，在任何可访问子系统上都不留痕迹。我们引入了一个标量来量化其大小，并证明了一个通用误差下限，低于此下限，任何虚拟恢复映射都无法运行，无论资源投入如何。我们还发现了采样成本中的光谱相变：当底层线性映射呈现光谱间隙时是有界的，在无间隙状态下以通用指数发散。这种二分法与通用误差下限一起将所有多部分量子态分为四类。此外，还表明条件互信息——标准熵诊断——与虚拟可恢复性根本无关。这意味着误差下限为容错量子计量设定了检测阈值。
英文摘要
The recovery of quantum information after subsystem loss is a central challenge in quantum information processing. However, some states remain beyond the reach of any recovery strategies. Here we identify the algebraic origin of virtual irrecoverability, the \emph{ghost information}---correlations encoded in the global state that leave no trace on any accessible subsystem. We introduce a scalar measure quantifying its magnitude and prove a universal error floor below which no virtual recovery map can operate, irrespective of resource investment. In such cases only \emph{approximate} virtual recovery is available. We study the sampling cost when approaching the minimal attainable recovery error, and find it bounded when the underlying linear map exhibits a spectrum gap, and divergent in the gapless regime, respectively. Together with the universal error floor, this dichotomy partitions all multipartite quantum states into four classes. Moreover, we show that conditional mutual information, the standard entropic diagnostic, does not constrain virtual recoverability. As an implication, we show that the error floor imposes a detection threshold for loss-tolerant quantum metrology.
