Abstract: Optimal storage and transmission of data is a fundamental task of information processing. For quantum sensing, the outputs of quantum sensors are $N$ ($gg 1$) copies of a quantum state that contains some unknown information to estimate. In this talk, I will show compression protocols that compresses the outputs of quantum sensors into a memory of size $O(log N)$ (qu)bits, with an optimal asymptotic compression rate and a small error vanishing in $N$, and I will prove that this task cannot be achieved by quantum state tomography. The compression covers not only states of fixed dimensions, but also states generated by a large but shallow quantum circuit. Besides the fundamental interest, it also leads to new sensing protocols, such as a quantum stopwatch, that achieves quantum advantage in new regimes of sensing.