Quantum nonlocality of density operators and their corresponding density matrices

Abstract Quantum nonlocality represents correlations between subsystems of a composite quantum system, usually including Bell nonlocality, steerability, and entanglement. According to the hypothesis of quantum mechanics, states of a quantum system Q described by a d -dimensional Hilbert space are denoted by density operators acting on . Under a basis e for the Hilbert space , every abstract density operator ρ of the system AB corresponds to a density matrix ρ e , which is a state of the complex Hilbert space . In this work, we discuss the consistency of quantum nonlocality of density operators ρ and their corresponding density matrices ρ e under the chosen basis e . It is proved that only when a basis e is a product one, a density operator ρ is entangled (respectively, Bell nonlocal, steerable) if and only if its density matrix ρ e is entangled (respectively, Bell nonlocal, steerable).