Kochen-Specker set with seven contexts

The Kochen-Specker (KS) theorem is a central result in quantum theory and has applications in quantum information. Its proof requires several yes-no tests that can be grouped in contexts or subsets of jointly measurable tests. Arguably, the best measure of simplicity of a KS set is the number of contexts. The smaller this number is, the smaller the number of experiments needed to reveal the conflict between quantum theory and noncontextual theories and to get a quantum vs classical outperformance. The original KS set had 132 contexts. Here we introduce a KS set with seven contexts and prove that this is the simplest KS set that admits a symmetric parity proof.

Figure 1

Orthogonality relations between the vectors of the seven-context KS set. Vectors are represented by nodes, and contexts (bases) are represented by straight lines. The pair of numbers $ij$, with $i<j$, denotes the vector common to bases $B_i$ and $B_j$ in Eq. (1).