Abstract
No cloning distinguishes the quantum cryptography. Buzek and Hillery have developed a universal quantum cloning machine that allows providing two copies of an arbitrary qubit state with the same accuracy independently of the input-state. The fidelity has been used as a criterion to characterize the cloning. It was found that this parameter can achieve 0.85 for special subsets of quantum states, i.e, equatorial qubits. In the present paper, we investigate the effects of a magnetic field environment as a perturbation of the cloning process. The quantum copying machines studied consist of UQCM-BH and UQCM-PC. Results have been discussed using both the fidelity and the relative entropy. Much attention has been paid to the magnetic field-related decoherence of ancillary qubits before preparation. An attempt to explain the impact of this decoherence on the performance of copying machines will be presented.
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References
Wootters W.K., Zurek W.H.: A single quantum cannot be cloned. Nature 299, 802 (1982)
Parti A.K., Braunstein S.L.: Quantum deleting and signaling. Phys. Lett. A 315, 208 (2003)
Bruβ D., DiVincenzo D.P., Ekert A., Fuchs C.A., Macchiavello C., Smolin J.A.: Optimal universal and state dependent quantum cloning. Phys. Rev. A 57, 2368 (1998)
Werner R.F.: The optimal cloning of quantum coherent states is non-Gaussia. Phys. Rev. A 58, 1827 (1998)
Bužek V., Hillery M.: Quantum copying: beyond the no-cloning theorem. Phys. Rev. A 54, 1844 (1996)
Gisin N., Massar S.: Optimal quantum cloning machines. Phys. Rev. Lett 79, 2153 (1997)
Bužek V., Hillery M.: Universal optimal cloning of arbitrary quantum states: from qubits to quantum registers. Phys. Rev. Lett 81, 5003 (1998)
Zanardi P.: Quantum cloning in d dimensions. Phys. Rev. A 58, 3484 (1998)
Fan H., Mastsumoto K., Wadati M.: Phase-covariant quantum cloning of qudit. Phys. Rev. A 64, 064301 (2001)
Cerf N.J.: Quantum cloning and the capacity of the Pauli channel. Phys. Rev. Lett 84, 4497 (2000)
Bruss D., Cinchetti M., D’Ariano G.M., Macchiavello C.: Phase-covariant quantum cloning. Phys. Rev. A 62, 012302 (2000)
Karimipour V., Rezakhani A.T.: Generation of phase-covariant quantum cloning. Phys. Rev. A 66, 052111 (2002)
Fan H., Matsumoto K., Wang X.-B., Wadati M.: Quantum cloning machines for equatorial qubits. Phys. Rev. A 65, 012304 (2002)
Durt T., Du J.: Economical quantum cloning in any dimension. Phys. Rev. A 69, 062316 (2004)
Zhang W.H., Wu T., Ye L., Dai J.-L.: Erratum: Optimal real state cloning in d dimensions. Phys. Rev. A 75, 044303 (2007)
Zhang W.H., Ye L.: Fidelity of a Bose–Einstein condensates. Phys. Lett. A 353, 130 (2006)
Zhang W.-H., Yu L.-B., Ye L., Dai J.-L.: Optimal symmetric economical phase-covariant quantum cloning. Phys. Lett. A 360, 726–730 (2007)
Zou X., Zhang S.L., Li K., Guo G.: Linear optical implementation of the two-qubit controlled phase gate with conventional photon detectors. Phys. Rev. A 75, 034302 (2007)
Yu L.-B., Zhang W.-H., Ye L.: Implementing an ancilla-free 1 → M economical phase-covariant quantum cloning machine with superconducting quantum- interference devices in cavity QED. Phys.Rev. A 76, 034303 (2007)
Yang J., Yu Y.-F., Zhang Z.-M., Liu S.-H.: Realization of universal quantum cloning with superconducting quantum-interference device qubits in a cavity. Phys. Rev. A 77, 034302 (2008)
Soubusta J., Bartůŝková L., Černoch A., Fiurášek J., Duŝek M.: Several experimental realizations of symmetric phase-covariant quantum cloners of single-photon qubits. Phys. Rev. A 76, 042318 (2007)
Nagali E., De Angelis T., Sciarrino F., De Martini F.: Experimental macroscopic coherence by phase-covariant cloning of a single photon. Phys. Rev. A 76, 042126 (2007)
Sabuncu M., Sabuncu M., Andersen U.L., Leuchs G.: Quantum cloning. Phys. Rev. Lett. 98, 170503 (2007)
Chen H., Zhou X., Suter D., Du J.: Experimental realization of 1 → 2 asymmetric phase-covariant quantum cloning. Phys. Rev. A 75, 012317 (2007)
Long B., Ye L.: Realization of a phase-covariant and real state qubit quantum cloning machine. Phys. Lett. A 374, 1966 (2010)
Baghban Zadeh S., Rezakhani A.T.: Temperature effects on quantum cloning of states and entanglement. Phys. Lett. A 373, 821 (2009)
Dumachev V.N., Orlor S.V.: Cloning of qubits of a quantum computer. JETP Lett. 76, 559 (2002)
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Othmani, B., Machhout, M., Belmabrouk, H. et al. Effects of a magnetic field environment on quantum cloning of qubits. Quantum Inf Process 12, 945–954 (2013). https://doi.org/10.1007/s11128-012-0442-3
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DOI: https://doi.org/10.1007/s11128-012-0442-3