Physics – Quantum Physics
Scientific paper
1998-10-03
Phys.Rev. A60 (1999) 2764-2776
Physics
Quantum Physics
Minor changes. 26 pages RevTex including 7 PS figures
Scientific paper
10.1103/PhysRevA.60.2764
We study the mapping which occurs when a single qubit in an arbitrary state interacts with another qubit in a given, fixed state resulting in some unitary transformation on the two qubit system which, in effect, makes two copies of the first qubit. The general problem of the quality of the resulting copies is discussed using a special representation, a generalization of the usual Schmidt decomposition, of an arbitrary two-dimensional subspace of a tensor product of two 2-dimensional Hilbert spaces. We exhibit quantum circuits which can reproduce the results of any two qubit copying machine of this type. A simple stochastic generalization (using a ``classical'' random signal) of the copying machine is also considered. These copying machines provide simple embodiments of previously proposed optimal eavesdropping schemes for the BB84 and B92 quantum cryptography protocols.
Griffiths Robert B.
Niu Chi-Sheng
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