Operational approach to the entanglement

Abstract

In early days of quantum theory it was believed that the results of measurements performed on two distant physical systems should be uncorrelated thus their quantum state should be separable it means described by a simple tensor product of the individual local state vectors or a tensor product of individual local density operators. It was shown many years ago by EPR that two systems which interacted in the past and separated afterwards had to be described in most cases by particular non-separable states which are called entangled. It was noticed by Zanardi et al. that a Hilbert space of possible state vectors of compound physical system could be partitioned in different way by introducing various tensor product structures induced by the experimentally accessible observables (interactions and measurements). Therefore a separable state in one partition could become entangled in different partition. In this sense the entanglement was relative to a particular set of experimental capabilities. Continuing this line of thought Torre et al. claimed to prove that for any separable state there existed strongly correlated physical observables therefore all quantum states were entangled. The same claims one may find in several recent papers. In this paper we will discuss in operational way the differences existing between separable, non-separable and entangled states and we will show that the conclusions of Torre et al. were unjustified. A sufficient condition for entanglement is the violation of BI-CHSH and/or steering inequalities. Since there exist experiments outside the quantum physics violating these inequalities therefore in the operational approach one cannot say that the entanglement is an exclusive quantum phenomenon.