Quantum discord is not extremalized by Gaussian states

Quantum discord is an important measure of quantum correlations that goes beyond the paradigm of quantum entanglement. However, calculating quantum discord involves optimization over measurements, which is computationally challenging and often infeasible. This raises the intriguing question of Gaussian extremality—whether the quantum discord of a reference Gaussian state can provide a meaningful bound to the quantum discord of the original state. In this paper, we investigate this question by comparing the Gaussian discord of a reference Gaussian state with the quantum discord.