  Linear optics provides versatile means to simulate and control the dynamics
of open quantum systems. Here, the polarization and frequency of photons often
represent the system and its environment, respectively. Recently, the photon's
path degree of freedom and the effects of interference have been considered as
well, giving rise to the concept of "open system interference". Such models
have been shown to beat traditional parameter estimation schemes in certain
scenarios. In this work, we study the sensitivity of non-Markovian memory
effects arising from an open system Mach-Zehnder interferometer. Our protocol
provides an alternative way to get around the quantum Cram\'er-Rao theorem,
proving itself a noteworthy option for more conventional parameter estimation
protocols.
