Limits of the time-multiplexed photon-counting method

The progress in building large quantum states and networks requires sophisticated detection techniques to verify the desired operation. To achieve this aim, a costand 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 η = 0.85, the optimal size for time-multiplexed detectors is 256 bins.