论文标题
RLD Fisher信息限制用于量子通道的多参数估计
RLD Fisher Information Bound for Multiparameter Estimation of Quantum Channels
论文作者
论文摘要
量子计量学的基本任务之一是估计嵌入在嘈杂过程中的多个参数，即量子通道。在本文中，我们通过摊销概念和正确的对数衍生物（RLD）Fisher信息价值研究了量子通道估计的基本限制。我们的主要技术结果是证明了RLD Fisher信息价值的链条规则不平等，这意味着摊销，即访问催化剂状态家族，不会增加量子通道的RLD Fisher信息价值。这一技术结果会根据RLD Fisher信息价值在顺序设置中的多组分通道估计带来基本且有效的计算限制。结果，我们得出的结论是，如果RLD Fisher信息价值是有限的，那么在多参数计的设置中，Heisenberg缩放是无法实现的。
One of the fundamental tasks in quantum metrology is to estimate multiple parameters embedded in a noisy process, i.e., a quantum channel. In this paper, we study fundamental limits to quantum channel estimation via the concept of amortization and the right logarithmic derivative (RLD) Fisher information value. Our key technical result is the proof of a chain-rule inequality for the RLD Fisher information value, which implies that amortization, i.e., access to a catalyst state family, does not increase the RLD Fisher information value of quantum channels. This technical result leads to a fundamental and efficiently computable limitation for multiparameter channel estimation in the sequential setting, in terms of the RLD Fisher information value. As a consequence, we conclude that if the RLD Fisher information value is finite, then Heisenberg scaling is unattainable in the multiparameter setting.
