In quantum mechanics, states are subdivided into entangled and separable. In particular, for a system of two particles with density matrices ρ (1) k and ρ (2) k, the separable state of these two particles is described by the density matrix ρ, which can be represented as a convex sum of tensor products of the matrices ρ (1) k and ρ (2) k: with coefficients pk 0 satisfying the normalization condition

On the contrary, states that cannot be represented in the form (1) are called entangled states. Examples of entangled states are the EPR state of a pair:

| ψ EPR = (| ↑ 1 ⊗ | ↓ 2 - | ↓ 1 ⊗ | ↑ 2) / √2, - and even and odd coherent states (the so-called Schrödinger cat): | ψ Sc = N (| αeiϕ ± | −αe − iϕ) / √2. Entanglement is one of the most interesting properties that fundamentally distinguish the quantum mechanical state from the classical one.

In contrast to quantum physics, these studies did not invoke arguments such as nonlocality and “death of reality”. In particular, from the non-existence of a single

probability space does not follow that it is impossible to construct a realistic description (mapping λ → a (λ)). Bell-type inequalities were considered as signs (sufficient conditions) for the impossibility of simultaneous measurements of all random variables from the family under consideration. This interpretation can be used for statistical data obtained in the EPR – Bohm experiment for entangled photons