Figure 1

Possible input-output configurations with four time-bin case. Inputs: Sets I, II, and III show input configurations where one, two, and three weak coherent states are positioned in time-bins, respectively. Subsets I and II are subsections of set II where the overlap is mixed. Outputs: 16 possible outcome configurations for four time-bin case, where some are theoretically impossible, e.g., obtaining four detection events, while real-world errors such as the detector’s dark counts make it probable