Incompatibility Between Quantum Mechanics and Leggett-Type Nonlocal Hidden Variable Theory for a Singlet State

Abstract

Local hidden variable theory has been abandoned because it violates the Bell inequality. However, the Bell inequality does not tell us which assumption, either locality or reality or even both, should be discarded in local hidden variable theory. A recently proposed incompatibility theorem for Leggett-type nonlocal hidden variable theory provides some progress in addressing this question. We propose a very simple incompatibility theorem by inspecting the properties of the singlet state within Leggett-type nonlocal hidden variable theory and discuss the characteristics of the incompatibility.