Testing Computational Complementarity for Mermin Automata

Abstract

Mermin [15] described a simple device to explain Einstein-Podolsky-Rosen (EPR) [12] correlations. This device was studied by means of a class of probabilistic (Mermin) automata in [4]. In [5] one shows that every deterministic automaton simulating with confidence 1/2 a probabilistic Mermin automaton features a classical behaviour. Is the above result true when the simulation is done at higher levels of confidence? To answer this question we study the distribution of two computational complementarity principles for two classes of deterministic automata which mimic the behaviour of Mermin's device with confidence in the intervals (1/2, 11/16] and (11/16, 7/8]. Since the class of automata to be studied is large, it contains 918≈ 150 ∙10 ¹⁵ elements, we use simulation techniques. We show that, statistically, at any level of confidence α Є (1/2, 11/16], the class of deterministic automata simulating Mermin probabilistic automata display less correlations than typical deterministic automata with 9 states and 7 outputs, but at higher levels of confidence α Є (11/16, 7/8], when the simulation is more accurate, deterministic automata simulating Mermin probabilistic automata display more correlations than typical deterministic automata with 9 states and 2 outputs. In the last case, EPR correlations established in [4] for Mermin probabilistic automata correspond to computational complementarity of the deterministic automata simulating Mermin probabilistic automata, [10, 13, 18, 3, 6].