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Fortschritte der Physik

Flocks of Quantum Clones: Multiple Copying of Qubits

Vladimír Bužek, Vladimír Bužek, Mark S. Hillery, P. L. Knight

Published Jun 1, 1998• 15 citations
Publisher

Abstract

We present a quantum netwoprk for an optimal quantum copying “machine” (transformation) which poduces N + 1 identical copies from the original qubit. The quality (fidelity) of the copies does not depend on the state of the original and is only a function of the number of copies, N.
DOI
10.1002/(sici)1521-3978(199806)46:4/5<521::aid-prop521>3.0.co;2-k

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We present quantum cloning machines that transform NNN identical qubits into M>NM>NM>N identical copies and we prove that the fidelity (quality) of these copies is optimal. The connection between cloning and measurement is discussed in detail. When the number of clones MMM tends towards infinity, the fidelity of each clone tends towards the optimal fidelity that can be obtained by a measurement on the input qubits. More generally, quantum cloning machines are universal devices to translate quantum information into classical information.
We review our recent work on the universal (i.e. input state independent) optimal quantum copying (cloning) of qubits. We present unitary transformations which describe the optimal cloning of a qubit and we present the corresponding quantum logical network. We also present network for an optimal quantum copying ``machine'' (transformation) which produces N+1 identical copies from the original qubit. Here again the quality (fidelity) of the copies does not depend on the state of the original and is only a function of the number of copies, N. In addition, we present the machine which universaly and optimally clones states of quantum objects in arbitrary-dimensional Hilbert spaces. In particular, we discuss universal cloning of quantum registers.
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Quantum cloning of two identical mixed qubits ρ⊗ρ\rho \otimes \rhoρ⊗ρ is studied. We propose the quantum cloning transformations not only for the triplet (symmetric) states but also for the singlet (antisymmetric) state. We can copy these two identical mixed qubits to MMM (M≥2M\ge 2M≥2) copies. This quantum cloning machine is optimal in the sense that the shrinking factor between the input and the output single qubit achieves the upper bound. The result shows that we can copy two identical mixed qubits with the same quality as that of two identical pure states.