Theory of Compression Channels for Post-selected Quantum Metrology

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.