The ``quantum'' Turán problem for operator systems (Q2305335)

The classical theorem of Turán gives the maximum number of edges a graph with $n$ vertices can have without having any \((k+1)\)-cliques. Motivated by this, the author considers an analogous version for operator systems, namely, the ``quantum Turán problem''. For a finite dimensional operator system \(V\) in \(M_n(\mathbb{C})\), the author provides upper and lower bounds for both the largest dimension of \(V\) which would ensure the existence of a quantum $k$-anticlique, and for the smallest dimension of \(V\) which would ensure the existence of a quantum $k$-clique.