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].
