  The progress in building large quantum states and networks requires
sophisticated detection techniques to verify the desired operation. To achieve
this aim, a cost- and resource-efficient detection method is the time
multiplexing of photonic states. This design is assumed to be efficiently
scalable; however, it is restricted by inevitable losses and limited detection
efficiencies. Here, we investigate the scalability of time-multiplexed
detectors under the effects of fiber dispersion and losses. We use the
distinguishability of Fock states up to $n=20$ after passing the
time-multiplexed detector as our figure of merit and find that, for realistic
setup efficiencies of $\eta=0.85$, the optimal size for time-multiplexed
detectors is 256 bins.
