Programming quantum measurements of time inside a multimode fibre

The temporal degree-of-freedom of light is incredibly exciting for many quantum technologies, ranging from photonic quantum computing to quantum key distribution. The generalized measurement of large and complex superpositions of the time-of-arrival of a photon presents a unique experimental challenge. Here we show how the coupling of spatial and temporal information inside a multi-mode fiber (MMF) can be harnessed to program generalized measurements for large photonic time-bin qudits. By exciting superpositions of special sets of spatial modes that are temporally unscattered through the fiber, we engineer arbitrary measurements of photon time-bins in dimensions up to 11. The single fiber serves as a scalable, common-path interferometer for time-bin qudits that significantly eases the experimental overheads of standard approaches based on unbalanced Franson-type interferometers.