ENTANGLEMENT, LOCALITY, AND SEPARABILITY: A TREATISE ON DIFFERENT VIEWPOINTS

Abstract

Within the framework of a statistical interpretation of quantum mechanics, entanglement (in a mathematical sense) manifests itself in the non-separability of the statistical operator ρ representing the ensemble in question. In experiments, on the other hand, entanglement can be detected, in the form of non-locality, by the violation of Bell's inequality Δ ≤ 2. How can these different viewpoints be reconciled? We first show that (non-)separability follows different laws to (non-)locality, and, moreover, it is much more difficult to characterize as long as the mostly employed operational rather than an ontic definition of separability is used. In consequence, (i) "entanglement" has two different meanings which may or may not be realized simultaneously on one and the same ensemble, and (ii) we have to disadvise the use of the common separability definition which is still employed by the majority of the physical community.