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arXiv:0704.0323 · Journal of Physics A Mathematical and Theoretical

General sequential quantum cloning

Gui-Fang Dang, Heng Fan

Published Apr 2, 2008• 5 citations
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Abstract

Some multipartite quantum states can be generated in a sequential manner which may be implemented by various physical setups like microwave and optical cavity QED, trapped ions, and quantum dots etc. We analyze the general N to M qubits Universal Quantum Cloning Machine (UQCM) within a sequential generation scheme. We show that the N to M sequential UQCM is available. The case of d-level quantum states sequential cloning is also presented.

DOI
10.1088/1751-8113/41/15/155303

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Some multipartite quantum states can be generated in a sequential manner which may be implemented by various physical setups like microwave and optical cavity QED, trapped ions, and quantum dots etc. We analyze the general N to M qubits Universal Quantum Cloning Machine (UQCM) within a sequential generation scheme. We show that the N to M sequential UQCM is available. The case of d-level quantum states sequential cloning is also presented.
We propose an implementation of an universal quantum cloning machine [UQCM, V. Buzek and M. Hillery, Phys. Rev. A 54, 1844 (1996)] in a cavity quantum electrodynamics experiment. This UQCM acts on the electronic states of atoms that interact with the electromagnetic field of a high-QQQ cavity. We discuss here the specific case of the $\stackrel{\ensuremath{\rightarrow}}{1}2$ cloning process using either a one- or a two-cavity configuration.
Not all unitary operations upon a set of qubits can be implemented by sequential interactions between each qubit and an ancillary system. We analyze the specific case of sequential quantum cloning, 1-->M, and prove that the minimal dimension D of the ancilla grows linearly with the number of clones M. In particular, we obtain D=2M for symmetric universal quantum cloning and D=M+1 for symmetric phase-covariant cloning. Furthermore, we provide a recipe for the required ancilla-qubit interactions in each step of the sequential procedure for both cases.
Schemes for implementing a 1 ? 2 optimal universal quantum cloning machine (UQCM) and a 1 ? 3 ancilla-free optimal phase-covariant quantum cloning machine (PCCM) are proposed by manipulating the transverse spin?spin interactions of quantum dots mediated by a vacuum single-mode cavity. The interactions among different quantum dots are selectively controlled by the classical laser fields. These quantum cloning machines are more robust due to the very long spin decoherence time of quantum dots. Furthermore, the experimental implementation is simplified in comparison with those using atoms as qubits. The quantum dots are embedded in the cavity simultaneously; hence the troubles caused by the qubits passing through multiple cavities are effectively avoided.