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No-Cloning Theorem,Kochen-Specker Theorem,and Quantum Measurement Theories |
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| Authors: | Nagata Koji Nakamura Tadao Farouk Ahmed Diep Do Ngoc |
| Affiliation: | 1.Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon, 34141, Korea ;2.Department of Information and Computer Science, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama, 223-8522, Japan ;3.Department of Physics and Computer Science, Faculty of Science, Wilfrid Laurier University, Waterloo, ON, N2L 3C5, Canada ;4.TIMAS, Thang Long University, Nghiem Xuan Yem road, Hoang Mai district, Hanoi, Vietnam ;5.Institute of Mathematics, VAST, 18 Hoang Quoc Viet road, Cau Giay district, Hanoi, Vietnam ; |
| Abstract: | 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 underconsideration are identical in that 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. |
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