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nomadreid
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In an explanation to distinguish the Heisenberg Uncertainty Principle from the Observer Effect, on p. 89 of "Quantum Computation and Quantum Information", Nielsen and Chuang start by writing:
"The correct interpretation of the uncertainty principle is that if we prepare a large number of quantum systems in identical states..."
However, according to the no-cloning theorem, we cannot perfectly copy an arbitrarily chosen unknown quantum state. So, do the authors mean "...if we were able to prepare (although in reality we cannot) a large number..." or "...if it happened that there were a large number of quantum systems in identical states and we knew that without measurement (which would collapse the states)..." Seems almost metaphysical to me, but maybe I am misinterpreting what Nielsen and Chuang meant, or maybe I am misinterpreting the no-cloning theorem, or maybe I am misapplying.
Any help would be appreciated.
"The correct interpretation of the uncertainty principle is that if we prepare a large number of quantum systems in identical states..."
However, according to the no-cloning theorem, we cannot perfectly copy an arbitrarily chosen unknown quantum state. So, do the authors mean "...if we were able to prepare (although in reality we cannot) a large number..." or "...if it happened that there were a large number of quantum systems in identical states and we knew that without measurement (which would collapse the states)..." Seems almost metaphysical to me, but maybe I am misinterpreting what Nielsen and Chuang meant, or maybe I am misinterpreting the no-cloning theorem, or maybe I am misapplying.
Any help would be appreciated.