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.

Using a single spin-1 object as an example, we discuss a recent approach to quantum entanglement. [A.A. Klyachko and A.S. Shumovsky, J. Phys: Conf. Series 36, 87 (2006), E-print quant-ph/0512213]. The key idea of the approach consists in presetting of basic observables in the very definition of quantum system. Specification of basic observables defines the dynamic symmetry of the system. Entangled states of the system are then interpreted as states with maximal amount of uncertainty of all basic observables. The approach gives purely physical picture of entanglement. In particular, it separates principle physical properties of entanglement from inessential. Within the model example under consideration, we show relativity of entanglement with respect to dynamic symmetry and argue existence of single-particle entanglement. A number of physical examples are considered.

We discuss an algebraic way to construct generic entangled states of qunits based on the polar decomposition of the su (2) algebra. In particular, we show that these states can be defined as eigenstates of certain Hermitian operators.

We discussed a recent approach to quantum entanglement. The approach is based on presetting of basic observables of quantum system. Entangled states are interpreted as states with maximal amount of uncertainty of all basic observables.

It is shown how to construct generic entangled states for an arbitrary system of n-state quantum objects (qunits) by means of the (n × n) cyclic permutation operator.