We present Boson Sampling schemes in the time-frequency basis that allow for more modes, fewer sources and detectors and are more tolerant to temporal mismatch than Boson Sampling schemes using photons in many spatial modes.
A major challenge for postclassical boson sampling experiments is the need for a large number of coupled optical modes, detectors, and single-photon sources. Here we show that these requirements can be greatly eased by time-bin encoding and dispersive optics-based unitary transformations. Detecting consecutively heralded photons after time-independent dispersion performs boson sampling from unitaries for which an efficient classical algorithm is lacking. We also show that time-dependent dispersion can implement general single-particle unitary operations. More generally, this scheme promises an efficient architecture for a range of other linear optics experiments.
We study the distinguishability of photons in multiphoton interference on a multiport when fast detectors, capable of precise time resolution, are employed. Such a setup was previously suggested for experimental realization of boson sampling with single photons. We investigate if fast photodetection allows us to circumvent distinguishability of realistic single photons in mixed states. To this goal, we compare distinguishability of photons in two setups: (a) with photons in the same average (temporal) profile on a spatial interferometer and photodetection incapable of (or with strongly imprecise) time resolution and (b) with photons in generally different average temporal profiles on the same spatial interferometer and photodetection with precise time resolution. Exact analytical results are obtained for Gaussian-shaped single photons with Gaussian distribution of photon arrival time. Distinguishability of photons in the two setups is found to be strikingly similar. For the same purity of photon states, only the same quality experimental boson sampling can be achieved using either of the two setups. The upshot of our results is that distinguishability due to mixed states is an intrinsic property of photons, whatever the photodetection scheme.
The multimode bunching probability is expected to provide a useful criterion for validating boson sampling experiments. Its applicability, however, is challenged by the existence of anomalous bunching, namely paradoxical situations in which partially distinguishable particles exhibit a higher bunching probability in two or more modes than perfectly indistinguishable ones. Using multimode bunching as a reliable criterion of genuine indistinguishability, therefore, requires a clear identification of the interferometric configurations in which anomalous bunching can or cannot occur. In particular, since uncontrolled small time delays between single-photon pulses constitute a common source of mode mismatch in current photonic platforms, it is essential to determine whether the resulting photon distinguishability might lead to anomalous bunching. Here, we first identify a broad class of interferometric configurations in which anomalous bunching is rigorously excluded, thereby establishing regimes where multimode bunching-based validation remains valid. Then, we find that, quite unexpectedly, temporal mode mismatch does not belong to this class. We exhibit a specific interferometric setup in which temporal distinguishability enhances multimode bunching, demonstrating that time delays can induce an anomalous behavior. These results help clarify the conditions under which multimode bunching remains a reliable validation tool.