Extracting classical information from quantum systems is an essential step of many quantum algorithms. However, this information could be corrupted as the systems are prone to quantum noises, and its distortion under quantum dynamics has not been adequately investigated. In this work, we introduce a systematic framework to study how well we can retrieve information from noisy quantum states. Given a noisy quantum channel, we fully characterize the range of recoverable classical information. This condition allows a natural measure quantifying the information recoverability of a channel. Moreover, we resolve the minimum information retrieving cost, which, along with the corresponding optimal protocol, is efficiently computable by semidefinite programming. As applications, we establish the limits on the information retrieving cost for practical quantum noises and employ the corresponding protocols to mitigate errors in ground state energy estimation. Our work gives the first full characterization of information recoverability of noisy quantum states from the recoverable range to the recovering cost, revealing the ultimate limit of probabilistic error cancellation.
翻译:从量子系统中提取经典信息是许多量子算法的重要步骤。然而,由于量子噪声的存在,这些信息可能会被损坏。对于经过量子动力学失真的信息,其恢复情况尚未得到充分的研究。在本文中,我们引入了一个系统框架来研究噪声量子状态的信息恢复能力。给定噪声量子通道,我们完全刻画了可恢复经典信息的范围。这个条件可以自然地量化通道的信息恢复能力。此外,我们还解决了最小信息检索成本,在相应的最优协议的帮助下,这一成本是可以通过半正定规划来有效计算的。作为应用,我们为实际量子噪声的信息检索成本确立了极限,并采用相应的协议来缓解基态能量估计中的误差。我们的工作给出了噪声量子状态的信息可恢复性的第一个完整特性描述:从可恢复范围到信息恢复成本,揭示了概率误差消除的最终极限。