ar X iv : q ua nt - p h / 04 06 10 4 v 1 1 5 Ju n 20 04 1 Probabilistically Cloning and Quantum Computation ∗

We discuss the usefulness of quantum cloning and present examples of quantum computation tasks for which cloning offers an advantage which cannot be matched by any approach that does not resort to it. In these quantum computations, we need to distribute quantum information contained in states about which we have some partial information. To perform quantum computations, we use state-dependent probabilistic quantum cloning procedure to distribute quantum information in the middle of a quantum computation. Cloning is very useful in classical computing and easy to accomplish with classical information. However, quantum cloning turns out not to be possible in general in quantum mechanics. This no-cloning theorem, independently discovered by Wootters and Zurek [1] and Dieks [2] in the early 1980s, is one of the most fundamental differences between classical and quantum information theories. It tells us that an unknown quantum state can not be copied exactly. Since determinately perfect copying is impossible, much effort has been put into developing optimal cloning processes. [3−14] The universal quantum cloning machines were first invented by Bužek and Hillery [3] and developed by other authors. [4−12] The another kind of cloning procedure first designed by Duan and Guo [13,14] is nondeterministic, consisting in adding an ancilla, performing unitary operations and measurements, with a postselection of the measurement results. The resulting clones are perfect, but the procedure only succeeds with a certain probability p < 1. The imperfect nature of quantum cloning procedure results in lower chances of getting the correct computational outputs at the end. Nonetheless, in some cases cloning improves our chances of correctly computing. Up to now, only a few examples are available to show that quantum cloning is useful in quantum computation. [15−18] In this letter we investigate the possible use of quantum cloning machine and present examples of quantum computation tasks for which cloning offers an advantage which cannot be matched by any approach that does not resort to quantum cloning. In these quantum computations, we need to distribute quantum information contained in states about which we have some partial information. To perform quantum computations, we use state-dependent probabilistic quantum cloning procedure discussed by Duan and Guo [13,14] to distribute quantum information in the middle of a quantum computation. Next we propose a generalization of examples. Let us consider the scenario. There are two different quantum computations with first computational step U 0 in common. We need to find a …