Locality and causality in hidden-variables models of quantum theory

Motivated by Popescu’s example of hidden nonlocality [Phys. Rev. Lett. 74, 2619 (1995)], we elaborate on the conjecture that quantum states that are intuitively nonlocal, i.e., entangled, do not admit a local causal hidden-variables model. We exhibit quantum states which either (i) are nontrivial counterexamples to this conjecture or (ii) possess a new kind of more deeply hidden irreducible nonlocality. Moreover, we propose a nonlocality complexity classification scheme suggested by the latter possibility. Furthermore, we show that Werner’s [Phys. Rev. A 40, 4277 (1989)] (and similar) hidden-variables models can be extended to an important class of generalized observables. Finally, a result of Fine [Phys. Rev. Lett. 48, 291 (1982)] on the equivalence of stochastic and deterministic hidden variables is generalized to causal models.