Entanglement of Observables: Quantum Conditional Probability Approach

Abstract This paper is devoted to clarification of the notion entanglement through decoupling it from tensor product structure and treating as a constraint posed by probabilistic dependence quantum observable A B . In our framework, meaningless speak about without pointing fixed observables , so this AB -entanglement. Dependence formalized non-coincidence conditional probabilities. Starting with definition, we achieve Hilbert space characterization -entangled states amplitude non-factorisable states. case, -entanglement implies standard entanglement, but not vise verse. for dichotomous equivalent their correlation, i.e., $$\langle AB\rangle _{\psi} \not = \langle A\rangle B\rangle .$$ ⟨ A B ⟩ ψ ≠ . We describe class that are $$A_{u} B_{u}$$ u family unitary operators ( u ). Finally, compared random variables in classical probability theory.