Genuine Continuous Quantumness

Randomness is a key feature of quantum physics. Heisenberg's uncertainty principle reveals the existence of an intrinsic noise, usually explored through Gaussian squeezed states. Due to their insufficiency for quantum advantage, the focus is currently shifting towards genuinely quantum non-Gaussian states. However, while genuine quantum behavior comes naturally to discrete variable systems, its preparation and verification are difficult in continuous ones. Simultaneously, a unifying theoretical framework based on the continuous nature is missing. Here, we introduce nonlinear squeezing as a general framework to describe and verify genuine quantumness in the noise of continuous quantum states. Using this approach, we certify the non-Gaussianity of experimentally prepared multi-photon-added coherent states of light for the first time. Chiefly, we demonstrated the nonlinear squeezing corresponding to third- and fifth-order quantum nonlinearities, going significantly beyond the current state-of-the-art in quantum technology. This framework enables uncovering intricate quantum properties in cutting-edge experiments and provides an efficient tool for further development of quantum technologies.