  In the domain of quantum metrology, cat states have demonstrated their
utility despite their inherent fragility with respect to losses. Here, we
introduce noise robust optical cat states which exhibit a metrological
robustness for phase estimation in the regime of high photon numbers. These cat
states are obtained from the intense laser driven process of high harmonic
generation (HHG), and show a resilience against photon losses. Focusing on a
realistic scenario including experimental imperfections we opt for the case in
which we can maximize the lower bound of the quantum Fisher information (QFI)
instead of analyzing the best case scenario. We show that the decrease of the
QFI in the lossy case is suppressed for the HHG-cat state compared to the even
and odd counterparts. In the regime of small losses of just a single photon,
the HHG-cat state remains almost pure while the even/odd cat state counterparts
rapidly decohere to the maximally mixed state. More importantly, this
translates to a significantly enhanced robustness for the HHG-cat against
photon loss, demonstrating that high photon number optical cat states can
indeed be used for metrological applications even in the presence of losses.
