Figure 1

Graph representing the simplest task of the class defined in the main text with quantum but no postquantum advantage. Vertices represent propositions, edges link propositions that cannot be simultaneously true.Reuse & Permissions

Figure 2

Experimental setup for the measurement of the probabilities $p_{i,j}$. In the upper left corner is represented the single photon source, based on spontaneous parametric down-conversion in a nonlinear crystal (BBO) cut for type II SPDC generation of photon pairs and the compensation for the walk-off ($C_w$) followed by two interference filters (IF) with bandwidth $\Delta \lambda =3\mathrm{nm}$. See the Supplemental Material [15] for further details. The four schemes we used for the experiment are presented in the central part of the figure. Each state is prepared by one of the two setups of the “Generation” column: Setup (a) for separable states (quantum transferrer $\pi \to o_2$) and setup (b) for entangled ones [an “entangler” based on a $q$ plate, a quarter-wave plate (QWP), and a half-wave plate (HWP)]. The “Analysis” column shows the setups for the projection on the desired state. Setup (c) for separable states, a deterministic transferrer $o_2\to \pi$ (here $C$ is a compensation stage), and setup (d) for entangled states, where a $q$ plate is needed to have a deterministic detection. (e) Experimental fidelities of generation and analysis for the ten states of the graph in Fig. 1. (f) Experimental results of the exclusiveness test: occurrences of the nonorthogonality component of the experimental projectors adopted for the measurements. All measured values of $p(i,j)$ and $p(j,i)$ are reported in the Supplemental Material [15].Reuse & Permissions