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Physics Today

The no-cloning theorem

William K. Wootters, Wojciech Hubert Zurek

Published Feb 1, 2009• 115 citations
Publisher

Abstract

People gather, copy, and distribute information all the time. But in the quantum world, the laws of physics impose a severe restriction on copying: It is impossible to make a perfect copy of an unknown state.
DOI
10.1063/1.3086114

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The celebrated quantum no-cloning theorem establishes the impossibility of making a perfect copy of an unknown quantum state. The discovery of this important theorem for the field of quantum information is currently dated 1982. I show here that an article published in 1970 [J. L. Park, Found. Phys. 1, 23–33 (1970)] contained an explicit mathematical proof of the impossibility of cloning quantum states. I analyze Park's demonstration in the light of published explanations concerning the genesis of the better-known papers on no-cloning.
It is known that the classical information like strings of bits can be copied. In 1982, Wootters and Zurek proposed the quantum no-cloning principle. No-cloning principle says that it is impossible to make an identical copy of an arbitrary unknown quantum pure state by using unitary evolution. In this paper, we call U ∣ψ>|ψ>∣ψ>, where U is any unitary operator, a U-copy of the state ∣ψ>|ψ>∣ψ> and show it is impossible to make a U-copy of an arbitrary unknown quantum pure state by using unitary evolution.
One of the fundamental restrictions that quantum mechanics imposes is the "No deletion Theorem" which tells us that given two identical unknown quantum states, it is impossible to delete one of them. But nevertheless if not perfect, people have tried to delete it approximately. In these approximate deleting processes our basic target is to delete one of the two identical copies as much as possible while preserving the other copy. In this brief report, by using the No communication theorem (NCT) (impossibility of sending signal faster than light using a quantum resource) as a guiding principle, we obtain a bound on the sum of the fidelity of deletion and the fidelity of preservation. Our result not only brings out the complementary relation between these two fidelities but also predicts the optimal value of the fidelity of deletion achievable for a given fidelity of preservation under no signaling constraint. This work eventually saturates the quest for finding out the optimal value of deletion within the NCT framework.