Linearly-Independent Quantum States Can Be Cloned by a Unitary-Reduct ion Operation
Duan Lu-ming, Guo Guang-Can · Communications in Theoretical Physics · 1999
The famous quantum no-cloning theorem [Nature 299(1952)802] forbids replication of an arbitrary unknown quantum state. But it leaves open the following question: If the state is not completely arbitrary, but secretly chosen from a certain set , whether is the cloning possible? It is proved that the states from the set can be faithfully cloned by a general unitary-reduction operation in a probabilistic fashion if and only if and are linearly-independent.