Classification of bipartite observables III: simplicity, mixtures and quantum error correction

This is the third of a series of three papers that bring model theory to quantum information. The dividing lines of Shelah's classification theory, which separate the tame first-order theories from the wild ones, become properties of bipartite observables: properties of the expectation values obtained when two independently prepared quantum systems are idealized one after the other. In this paper we focus on simple unstable theories. The Pauli group of quantum error correction, with anticommutation as its relation, has a simple unstable theory, like the random graph. Forking and the Kim–Pillay independence theorem acquire a meaning in stabilizer codes: forking recognizes logical errors, and the independence theorem glues syndromes.