Abstract: Detection of weak forces and precise measurement of time are two of the many applications of quantum metrology to science and technology. I will introduce and study a fundamental trade-off which relates the amount by which noise reduces the accuracy of a quantum clock to the amount of information about the energy of the clock that leaks to the environment. The trade-off is quantified in terms of the quantum Fisher information, which is a standard measure of sensitivity in quantum estimation theory. I will then connect our results to the notion of quantum error correction. Indeed, a weaker variant of the standard conditions for quantum error correction turn out to be necessary and sufficient conditions for a state's sensitivity to be unaffected by the noise. I will discuss how such states, which we call "metrological codes," enrich the broader picture of developing schemes in metrology based on quantum error correction. Joint work with: Mischa P. Woods, Victor V. Albert, Joseph M. Renes, Jens Eisert, and John Preskill. Reference: https://arxiv.org/abs/2207.13707