Non-Gaussianity as a resource in quantum information and computational protocols

Abstract: Quantum non-Gaussianity, inherent in continuous variable (CV) Bosonic systems, is a valuable resource that can be leveraged to attain quantum advantage in a plethora of information-theoretic protocols and quantum computation. We will first discuss a new operational monotone for quantum non-Gaussianity – the non-Gaussian rank – which is capable of quantifying the experimental hardness of preparing universal CV quantum circuits. The monotone allows us to characterize the optimal usage of paradigmatic non-Gaussian gates, such as the cubic-phase gate and the SNAP gate, which have been recently implemented in experimental platforms. Next, we move beyond quantum computation and analyze the performance of non-Gaussian states in information-theoretic protocols, viz, telecloning and teleportation, as well as in quantum illumination. While the advantage offered by non-Gaussianity is not ubiquitous, we shall discuss how photon-subtracted states always manage to outperform other non-Gaussian resources.