Non-Gaussian quantum steering produced by quasi-phase-matching third-harmonic generation

Abstract With the rapid advancements in fields such as quantum entanglement distillation and quantum metrology, the limitations of Gaussian states in certain applications within quantum computing and information processing have come to the forefront. This has necessitated the development of methods to prepare non-Gaussian states, which exhibit negative Wigner values and are indispensable for enhancing the capabilities of quantum systems in these tasks. Wigner negativity, a renowned indicator of nonclassicality, is integral to quantum computing and the simulation of continuous-variable systems. It is also employed to discern non-Gaussian characteristics in optical fields. We demonstrate Gaussian Einstein–Podolsky–Rosen (EPR) steering between second and third harmonic generations prior to performing non-Gaussian operations. Inducing non-Gaussian attributes in the second harmonic is achieved by coupling the third harmonic with a vacuum state and subtracting photons via a beamsplitter. The Wigner stochastic trajectory approach is utilized to investigate the non-Gaussian properties of both the second and third harmonics. By varying the coupling parameter lambda λ and the ratio of nonlinear coupling constants <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>κ</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:msub> <mml:mi>κ</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:mrow> </mml:math> , symmetric and asymmetric non-Gaussian EPR steering can be observed. This proposed scheme for non-Gaussian EPR steering holds promise for applications in quantum computing and quantum information processing.