We resolve an old problem about the existence of hidden parameters in a three-dimensional quantum system by constructing an appropriate Bell's type inequality. This reveals the nonclassical nature of most spin-1 states. We shortly discuss some physical implications and an underlying cause of this nonclassical behavior, as well as a perspective of its experimental verification.

The paper contains a brief review of an approach to quantum entanglement based on analysis of dynamic symmetry of systems and quantum uncertainties, accompanying the measurement of mean value of certain basic observables. The latter are defined in terms of the orthogonal basis of Lie algebra, corresponding to the dynamic symmetry group. We discuss the relativity of entanglement with respect to the choice of basic observables and a way of stabilization of robust entanglement in physical systems.

Using the approach to quantum entanglement based on the quantum fluctuations of observables, we show the existence of perfect entangled states of a single "spin-1" particle. We give physical examples related to the photons, condensed matter physics, and particle physics.

Spontaneous generation of the Dicke superradiation (SR) state has been found in the system of inversely polarised proton spins with “frozen” polarisation. SR is observed at the moment when the Larmor frequency crosses the resonance frequency of the passive oscillatory circuit. SR arises from incoherent maser generation of spins. The frequency of a SR generator can be retuned from several hundreds of kilohertz to hundreds of megahertz at very low temperatures. Dependence of incoherent and coherent radiation on the initial polarisation has been investigated. A radio frequency analogue of the optical SR laser is shown to be possible both for weak-amplifying and for strong-amplifying active media, depending on the factor of filling and polarisation of nuclei. SR-reverse of negative polarisation is observed in the latter case.

A definition of entanglement in terms of local measurements is discussed. Viz, the maximum entanglement corresponds to the states that cause the highest level of quantum fluctuations in all local measurements determined by the dynamic symmetry group of the system. A number of examples illustrating this definition is considered.