Locality and Causality in Hidden Variables Models of Quantum Theory

Motivated by Popescu's example of hidden nonlocality, 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 (and similar) hidden variables models can be extended to an important class of generalized observables. Finally a result of Fine on the equivalence of stochastic and deterministic hidden variables is generalized to causal models. 03.65.Bz Typeset using REVT E X I. INTRODUCTION The nonlocality inherent in the quantum mechanical description of nature is still a much debated subject, 30 years after the pioneering work by John Bell [1]. Bell's starting point was the argument of Einst..