Kochen-Specker Theorem and the Two Quantum Measurement Theories

Koji Nagata, Tadao Nakamura, Han Geurdes, Josep Batle, Soliman Abdalla, Ahmed Farouk

Abstract


We consider the two quantum measurement theories for measuring a single Pauli observable. We assume also the existence of a classical probability space for the two measurement theories. We cannot avoid the Kochen-Specker (KS) contradiction when we measure the Pauli observable by using the projective measurement theory if we introduce a classical probability space. The results of measurement are either $+1$ or $-1$ (in $\hbar/2$ unit) when we consider a spin-1/2 system. The projective measurement theory does not accept a classical probability space when we measure the Pauli observable. We propose a new measurement theory based on the truth values, i.e., the truth T (1) for true and the falsity F (0) for false. The results of measurement are either $+1$ or 0 (in $\hbar/2$ unit). We avoid the KS contradiction when we measure the Pauli observable by using the new measurement theory if we introduce a classical probability space. The new measurement theory accepts a classical probability space when we measure the Pauli observable.

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