[01] Koji Nagata, Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon, Korea. [02] Tadao Nakamura, Department of Information and Computer Science, Keio University, Yokohama, Japan.

We review a property of a new measurement theory based on the truth values. The results of measurements are either 0 or 1. The measurement theory accepts a hidden variable model for a single Pauli observable. Therefore we can introduce a classical probability space for the measurement theory in this case. And we can measure the single Pauli observable by using the measurement theory based on the truth values. Our discussion provides a new insight to formulate quantum measurement theory, by using the measurement theory here based on the truth values. In this paper, we discuss the fact that the projective measurement theory (the results of measurements are either +1 or -1) says the Bell, Kochen, and Specker (BKS) paradox for the single Pauli observable. Therefore, we cannot introduce a classical probability space for the measurement theory in this case. Our discussion says that we cannot measure the single Pauli observable by using the projective measurement theory without the BKS paradox.

Quantum Measurement Theory, Quantum Non Locality, Formalism

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