Fig. 3: Quantum vs classical sets.
The sets of quantum states that admit a classical model with complexity r ∈ {1, …, d} are convex and form a nested structure, leading up to the full collection of classical sets \({{{\mathcal{S}}}}\). Commuting sets \({{{{\mathcal{C}}}}}_{r}\) in dimension r are represented as the red boundaries in the figure. The white region represents quantum sets that cannot be classically simulated, while the black boundary denotes the space of non-commuting pure states sets.
