Narrow Results

Entangled EPR spin pairs can be treated using the statistical ensemble interpretation of quantum mechanics. As such the singlet state results from an ensemble of spin pairs each with its own specific axis of quantization. This axis acts like a quantum mechanical hidden variable. If the spins lose coherence they disentangle into a mixed state that contains classical correlations. In this paper an infinitesimal phase decoherence is introduced to the singlet state in order to reveal more clearly some of the correlations. It is shown that a singlet state has no classical correlations.

Entangled physical systems are an important resource in quantum information. Many papers were published trying to grasp the meaning of entanglement. It was noticed that a Hilbert space of possible state vectors of compound physical system can be partitioned by introducing various tensor product structures induced by the experimentally accessible observables (interactions and measurements). In this sense, the entanglement is relative to a particular set of experimental capabilities. Inspired by these results some authors claim that in fact all quantum states are entangled. In this paper, we show that this claim is incorrect and we discuss in operational way differences existing between separable and entangled states. A sufficient condition for entanglement is the violation of Bell–CHSH-CH inequalities and/or steering inequalities. Since there exist experiments outside the domain of quantum physics violating these inequalities therefore in the operational approach one cannot say that the entanglement is an exclusive quantum phenomenon. We also explain that an unambiguous experimental certification of the entanglement is a difficult task because classical statistical significance tests may not be trusted if sample homogeneity cannot be tested or is not tested carefully enough.