New Method of Obtaining the Kochen-Specker Theorem
We derive a new type of no-hidden-variable theorem based on the assumptions proposed by Kochen and Specker. We consider N spin-1/2 systems. The hidden results of measurement are either \(+1\) or \(-1\) (in \(\hbar /2\) unit). We derive some proposition concerning a quantum expected value under an assumption about the existence of the Bloch sphere in N spin-1/2 systems. However, the hidden variables theory violates the proposition with a magnitude that grows exponentially with the number of particles. Therefore, we have to give up either the existence of the Bloch sphere or the hidden variables theory. Also we discuss a two-dimensional no-hidden-variables theorem of the KS type. Especially, we systematically describe our assertion based on more mathematical analysis using raw data in a thoughtful experiment.
Keywords03.65.Ud (Quantum non locality) 03.65.Ta (Quantum measurement 03.65.Ca (Formalism)
We would like to thank Professor Niizeki and Dr. Ren for valuable comments.
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