Optimizing real state cloning based on the rotation of coordinate system

Abstract

Abstract: Real state cloning is an important part of quantum cloning. However，for obtaining the optimal asymmetric real state cloning by using the method of optimizing the fidelity directly, the mathematical operation process is very cumbersome, and the results are not very simple and clear. For this reason, the method of coordinate system rotation transformation is introduced. Based on the transformation of coordinate system rotation, a real state cloning in the original coordinate system will become a well-known phase-covariant cloning in the new coordinate system. According to representation transformation, the optimization of asymmetric real state cloning can be realized easily in the original coordinate system by comparison with optimized asymmetric phase covariant cloning, that is, a set of coefficients for the optimized asymmetric real state clone transformation can be obtained. It is shown that using the method to optimize asymmetric real state cloning, the idea of processing operation is clear, and the optimization result is symmetrical, neat, and concise. In addition, the specific relationships between different coefficients of the optimized asymmetric real state clone can be obtained explicitly.

Key words: quantum information, quantum cloning, representation transformation, real state cloning, phase-covariant cloning

CLC Number:

O431.2

ZHU Mengzheng, ZHAO Chunran, GONG Pifeng, YE Liu. Optimizing real state cloning based on the rotation of coordinate system[J]. Chinese Journal of Quantum Electronics, 2020, 37(3): 337-341.

References 15

[1]	Scarani V, Bechmann-Pasquinucci H, Cerf N J, et al. The security of practical quantum key distribution[J]. Reviews of Modern Physics 2009, 81(3): 1301-1350.
[2]	Wootters W K, Zurek W H. A single quantum cannot be cloned[J]. Nature，1982, 299(5886): 802-803.
[3]	Bužek V, Hillery M. Quantum copying: Beyond the no-cloning theorem[J]. Physical Review A， 1996, 54(3): 1844-1852.
[4]	Fiurášek J, Cerf N J. Quantum cloning of a pair of orthogonally polarized photons with linear optics[J]. Physical Review A， 2008, 77: 052308.
[5]	Bartkiewicz K, Lemr K, Černoch A, et al. Experimental eavesdropping based on optimal quantum cloning[J]. Physical Review Letters 2013, 110: 173601.
[6]	Fan H, Wang Y N, Jing L, et al. Quantum cloning machines and the applications[J]. Physics Reports, 2014, 544(3): 241-322.
[7]	Scarani V, Iblisdir S, Gisin N, et al. Quantum cloning[J]. Reviews of Modern Physics, 2005, 77(4): 1225-1256.
[8]	Bennett C, Brassard G. Quantum cryptography: Public key distribution and coin tossing[C]. Proceedings of IEEE International Conference on Computers, Systems, and Signal Processing，1984：175-179.
[9]	Gisin N, Ribordy G E, Tittel W, et al. Quantum cryptography[J]. Reviews of Modern Physics， 2002, 74(1): 145-195.
[10]	Bruß D, Cinchetti M, Mauro D'Ariano G, et al. Phase-covariant quantum cloning[J]. Physical Review A， 2000, 62: 012302.
[11]	Zhang W H, Wu T, Ye L, et al. Optimal real state cloning in d dimensions[J]. Physical Review A， 2007, 75: 044303.
[12]	Cerf N J. Asymmetric quantum cloning in any dimension[J]. Journal of Modern Optics，2000, 47(2-3): 187-209.
[13]	Bartkiewicz K, Miranowicz A. Optimal cloning of qubits given by an arbitrary axisymmetric distribution on the Bloch sphere[J]. Physical Review A， 2010, 82: 042330.
[14]	Zhang Z P, Liu G J, Lu X, et al. Security performance analysis of quantum key distribution protocol based on depolarization channel[J]. Chinese Journal of Quantum Electronics(量子电子学报) 2019, 36(4): 464-470(in Chinese).
[15]	Zhang S J, Zhang W H. Probabilistic quantum cloning of two states with arbitrary a prior probabilities[J]. Chinese Journal of Quantum Electronics(量子电子学报) 2019, 36(4): 471-475(in Chinese).