  Accurate phase estimation in the presence of unknown phase diffusive noise is
a crucial yet challenging task in noisy quantum metrology. This problem is
particularly interesting due to the detrimental impact of the associated noise.
Here, we investigate the joint estimation of phase and phase diffusion using
generalized Holland-Burnett states, known for their experimental accessibility.
These states provide performance close to the optimal state in single-parameter
phase estimation, even in the presence of photon losses. We adopt a twofold
approach by analyzing the joint information extraction through the double
homodyne measurement and the joint information availability across all probe
states. Through our analysis, we find that the highest sensitivities are
obtained by using states created by directing all input photons into one port
of a balanced beam splitter. Furthermore, we infer that good levels of
sensitivity persist even in the presence of moderate photon losses,
illustrating the remarkable resilience of our probe states under lossy
conditions.
