## No-Cloning Theorem, Kochen-Specker Theorem, and Quantum Measurement Theories

**Authors:** Koji Nagata, Tadao Nakamura, Ahmed Farouk, Do Ngoc Diep

The usual no-cloning theorem implies that two quantum states are
identical or orthogonal if we allow a cloning to be on the two quantum states.
Here, we investigate a
relation between the no-cloning theorem and the projective measurement theory
that the results of measurements are either $+1$ or $-1$.
We introduce
the Kochen-Specker (KS) theorem with the projective measurement theory.
We result in the fact that the two quantum states
under consideration cannot be orthogonal
if we avoid the KS contradiction.
Thus the no-cloning theorem implies that the two quantum states
under consideration are identical in the case.
It turns out that the KS theorem with the projective
measurement theory says a new version
of the no-cloning theorem.
Next, we investigate a
relation between the no-cloning theorem
and the measurement theory based on the truth values
that the results of measurements are either $+1$ or $0$.
We return to the usual no-cloning theorem that the two quantum states are
identical or orthogonal in the case.

**Comments:** 6 Pages. International Journal of Theoretical Physics (2019) https://doi.org/10.1007/s10773-019-04078-8

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### Submission history

[v1] 2019-03-27 02:55:55

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