Heralded generation of displaced qudits from quantum optical catalysis

Creating non-Gaussian photonic states in the continuous variable regime, with high fidelity is essential for implementing universal quantum computation. However, this is a challenging task to achieve the essential nonlinearity. Alternatively, various non-Gaussian states of light can be created by the use of a simple linear setup called quantum optical catalysis (QOC). In this work, we attempt to bring out the salient features of the multi-photon QOC process in terms of state preparation and characterization. The notion of state preparation from the QOC is achieved by expressing the output state as displaced qudits (DQ). The obtained superposition coefficients facilitate the characterization of states and carve a path to get desired non-Gaussian states. Moreover, the figures of merit of the prepared states are employed through Hilbert Schmidt distance, Wigner negativity, and quadrature squeezing. From the results, it is inferred that the creation of individual displaced number states plays a predominant role in non-Gaussianity among the states derived. Meanwhile, the superposition of number states remains effective in achieving a significant degree of squeezing. In addition, the non-ideal preparation of DQ under realistic experimental conditions is investigated by incorporating imperfect photon detectors and mixed photon sources. The calculated success probability also attests to the potential for state generation.