利用相对保真度界定量子精密测量中自适应性的益处
Bounding the benefit of adaptivity in quantum metrology using the relative fidelity
摘要：
用于区分一对信道或用于估计信道参数的协议通常可以通过自适应性或通过探测状态之间的纠缠来辅助。这可能使得难以约束此类协议的最佳可能性能。在本文中，我们引入了一个量，我们称之为相对保真度的一对给定的通道和一对输入状态，这些通道。将允许的输入状态约束为保真度大于某个最小“输入保真度”的所有状态对，并在有效状态对上最小化该数量，我们得到该输入保真度约束的最小相对保真度。然后，我们能够下界之间的保真度的任何协议的可能的输出状态作用于两个可能的通道之一的最小相对保真度。这使得我们能够约束最一般的自适应鉴别和参数估计协议的性能。通过找到相对保真度的连续性界限，我们还提供了一个简单的确认，即$N$使用协议的输出的量子费舍尔信息（QFI）不超过单次QFI的$N^2$倍。
英文摘要：
Protocols for discriminating between a pair of channels or for estimating a channel parameter can often be aided by adaptivity or by entanglement between the probe states. This can make it difficult to bound the best possible performance for such protocols. In this paper, we introduce a quantity that we call the relative fidelity of a given pair of channels and a pair of input states to those channels. Constraining the allowed input states to all pairs of states whose fidelity is greater than some minimum "input fidelity" and minimising this quantity over the valid pairs of states, we get the minimum relative fidelity for that input fidelity constraint. We are then able to lower bound the fidelity between the possible output states of any protocol acting on one of two possible channels in terms of the minimum relative fidelity. This allows us to bound the performance of the most general, adaptive discrimination and parameter estimation protocols. By finding a continuity bound for the relative fidelity, we also provide a simple confirmation that the quantum Fisher information (QFI) of the output of an $N$-use protocol is no more than $N^2$ times the one-shot QFI.
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