By Ruark A.E.

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Violations of the Bell theorem by quantum mechanics are therefore generally considered as much more significant quantum manifestations than violations of the BKS theorem. For a general discussion of the status of the various “impossibility theorems” with emphasis on the BKS theorems, see ref. [6] 5 Non-locality and entanglement: where are we now? ”. Both these opinions make sense, depending on what aspect of the debate one wishes to favor. 3; here, we will just add that, whether one personally feels closer to the orthodox camp or to local realism, it remains clear that the line initiated by Einstein and Bell had the decisive role in the last 50 years.

But it turns out that quantum mechanics does allow a simultaneous realization of all three propositions! To see how, let us for instance consider a two-spin state vector of the form: | Ψ >= α | +, − > +β | −, + > +γ | +, + > ′ (8) ′ where the | ±, ± > refer to eigenstates of A and B (NB: axis Oz is chosen as the direction of measurement associated with primed operators). ) remains in a coherent quantum superposition, without decoherence, even if the distance between the peas is large. 35 proposition (iii) is true.

31 operation immediately reduces the number of categories: in a specific example (involving three possible values of each setting), he shows that their number reduces from 49 to (23 )2 = 26 ; with two values only for each setting, the reduction would be from 44 to (22 )2 = 24 . The mathematical origin of the Bell inequalities lies precisely in the possibility of distributing all pairs into this smaller number of categories, with positive probabilities. A general way to express the Bell theorem in logical terms is to state that the following system of three assumptions (which could be called the EPR assumptions) is self-contradictory: 1.