Quantum Nonlocality and Quantum Correlations in the Stern–Gerlach Experiment

Abstract

The Stern–Gerlach experiment (SGE) is one of the foundational experiments in quantum physics. It has been used in both the teaching and the development of quantum mechanics. However, for various reasons, some of its quantum features and implications are not fully addressed or comprehended in the current literature. Hence, the main aim of this paper is to demonstrate that the SGE possesses a quantum nonlocal character that has not previously been visualized or presented before. Accordingly, to show the nonlocality into the SGE, we calculate the quantum correlations C ( z , θ ) by redefining the Banaszek–Wódkiewicz correlation in terms of the Wigner operator, that is C ( z , θ ) = ⟨ Ψ | W ^ ( z , p z ) σ ^ ( θ ) | Ψ ⟩ , where W ^ ( z , p z ) is the Wigner operator, σ ^ ( θ ) is the Pauli spin operator in an arbitrary direction θ and | Ψ ⟩ is the quantum state given by an entangled state of the external degree of freedom and the eigenstates of the spin. We show that this correlation function for the SGE violates the Clauser–Horne–Shimony–Holt Bell inequality. Thus, this feature of the SGE might be interesting for both the teaching of quantum mechanics and to investigate the phenomenon of quantum nonlocality.

Keywords

• quantum nonlocality
• quantum mechanics
• Stern–Gerlach experiment