Sensing in the presence of environmental noise is a problem of increasing practical interest. In a master equation description, where the state of the environment is unobserved, the effect of signal and noise is described by system operators only. In this context it is well-known that noise that is orthogonal on an external signal can be corrected for without perturbing the signal, while similarly efficient strategies for non-orthogonal signal and noise operators are not known. Here we make use of the fact that system-environment interaction typically arises via local two-body interactions describing the exchange of quanta between system and environment, which are observable in principle. That two-body-interactions are usually orthogonal on system operators, allows us to develop error corrected sensing supported by the observation of the quanta that are emitted into the environment. We describe such schemes and outline a realistic proof-of-principle experiment in an ion trap set-up.
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