Post-selected quantum metrological scheme is especially advantageous when the final measurements are either very noisy or expensive in practical experiments. In this work, we put forward a general theory on the compression channels in post-selected metrology. We define the basic notions characterizing the compression quality and illuminate the underlying structure of lossless compression channels. Previous experiments on post-selected optical phase estimation and weak-value amplification are shown to be particular cases of this general theory. Furthermore, for two categories of bipartite systems, we show that the compression loss can be made arbitrarily small even when the compression channel acts only on one subsystem. These findings can be employed to distribute quantum measurements so that the measurement noise and cost are dramatically reduced.

翻译：后选择量子度量方案在实际实验中，当最终测量非常嘈杂或昂贵时尤为有利。本文提出了后选择度量学中压缩通道的通用理论。我们定义了表征压缩质量的基本概念，并阐明了无损压缩通道的底层结构。先前关于后选择光学相位估计和弱值放大的实验被证明是该通用理论的特定案例。此外，对于两类二分体系统，我们证明即使压缩通道仅作用于其中一个子系统，压缩损失也可以任意减小。这些发现可用于分布量子测量，从而显著降低测量噪声和成本。