Scientists have successfully established an upper bound for the negativity of the Kirkwood-Dirac (KD) quasiprobability in quantum states subjected to Gaussian processes. The KD negativity is a fundamental measure of a quantum state's nonclassicality, and its extremal value in the general case has remained unknown until now. This breakthrough provides a deeper understanding of the nonclassical properties of quantum systems under transformations that are ubiquitous in experimental physics.

The Kirkwood-Dirac quasiprobability offers an operational representation of a quantum state. Its negativity is a key indicator that a system cannot be described by classical physics, analogous to the negativity of the Wigner function. The study focused on arbitrary quantum states interacting with Gaussian processes, which are transformations that preserve the Gaussian character of input states, such as displacement or squeezing operations in quantum optics.

The team derived an upper bound for this negativity applicable to any number of modes and measurements. For the specific case of a single mode and two measurements, they showed that the eigenstates of the quadrature operators (such as Fock states or squeezed states) saturate this upper bound. Conversely, pure Gaussian states, which are the most classical among quantum states, achieve a nontrivial minimum of negativity. These results suggest that Gaussian states are sufficient to achieve extreme values of nonclassicality, which is relevant for quantum computing and metrology.