Abstract
The scheme for a 1–3 economical state-dependent telecloning of a multiparticle GHZ state is proposed. It shows that every one of spatially separated three receivers obtains one copy which is dependent on original state. Fidelity can hit to the optimal fidelity 5/6. Meantime, we also propose a 1–3 asymmetric economical telecloning of a particular multiparticle GHZ state by parameterizing coefficients of state in the channel. The three fidelities can reach the best match that is the same as the symmetric case. Furthermore, the above two schemes can be generalized into the case of \(1-M(M=2k+1,k>0)\) telecloning of a multiparticle GHZ state. Satisfying some certain conditions, optimal fidelities with \(\frac{1}{2}+\frac{(M+1)}{4M}\) can be obtained. As without ancilla in the channel, the number of entangled particles is less than one in current schemes and fidelities can be optimal if the original state is an equatorial state.
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Niestegge, G.: Non-classical conditional probability and the quantum no-cloning theorem. Phys. Scr. 90(9), 095101 (2015)
Daffertshofer, A., Plastino, A.R., Plastino, A.: Classical no-cloning theorem. Phys. Rev. Lett. 88(21), 210601 (2002)
Fan, H., Wang, Y.-N., Jing, L., Yue, J.-D., Shi, H.-D., Zhang, Y.-L., Mu, L.-Z.: Quantum cloning machines and the applications. Phys. Rep. 544(3), 241–322 (2014)
Karmakar, S., Sen, A., Sarkar, D.: Performance of quantum cloning and deleting machines over coherence. Quantum Inf. Process. 16(10), 251 (2017)
Gisin, N., Massar, S.: Optimal quantum cloning machines. Phys. Rev. Lett. 79(11), 2153 (1997)
Bužek, V., Hillery, M.: Quantum copying: beyond the no-cloning theorem. Phys. Rev. A 54(3), 1844 (1996)
Sciarrino, F., De Martini, F.: Realization of the optimal phase-covariant quantum cloning machine. Phys. Rev. A 72(6), 062313 (2005)
Wen-Hai, Z., Long-Bao, Y., Zhuo-Liang, C., Liu, Y.: Optimal 1 M phase-covariant cloning in three dimensions. Chin. Phys. B 23(7), 070304 (2014)
Fan, H., Matsumoto, K., Wang, X.-B., Imai, H.: Phase-covariant quantum cloning. J. Phys. A Math. Gen. 35(34), 7415 (2002)
Karimipour, V., Rezakhani, A.: Generation of phase-covariant quantum cloning. Phys. Rev. A 66(5), 052111 (2002)
Bru\(\beta \), D., Cinchetti, M., D’Ariano, G.M., Macchiavello, C.: Phase-covariant quantum cloning. Phys. Rev. A 62(1), 012302 (2000)
Zhang, W.-H., Yu, L.-B., Ye, L., Dai, J.-L.: Optimal symmetric economical phase-covariant quantum cloning. Phys. Lett. A 360(6), 726–730 (2007)
Zhou, Y.-H., Wang, L.: Scheme for implementing 1 M symmetric economical phase-covariant telecloning based on quantum logic network. J. Mod. Opt. 59(7), 658–662 (2012)
Yan-Hui, Z., Lei, W., Xiao-Lei, L.: Scheme for implementing an economical phase-covariant quantum cloning machine of distant atomic qubits with single-photon interference. Chin. Phys. B 22(5), 050305 (2013)
Zou, X., Dong, Y., Guo, G.: Scheme for realizing ancilla-free 1 M economic phase-covariant quantum cloning of qubits and qutrits. Phys. Lett. A 360(1), 44–48 (2006)
Zhang, W.-H., Ye, L.: Optimal asymmetric economical state-dependent cloners. Opt. Commun. 282(13), 2650–2655 (2009)
Hashagen, A.: Universal Asymmetric Quantum Cloning Revisited (2016). arXiv preprint arXiv:1607.03723
Boudjema, R., Hamici, A.-H., Hachemane, M., Smida, A.: Generalized asymmetric phase-covariant quantum cloning within a nonextensive approach. Quantum Inf. Process. 15(1), 551–563 (2016)
Kay, A., Ramanathan, R., Kaszlikowski, D.: Optimal asymmetric quantum cloning (2012). arXiv preprint arXiv:1208.5574
Iblisdir, S., Acn, A., Cerf, N., Filip, R., Fiuršek, J., Gisin, N.: Multipartite asymmetric quantum cloning. Phys. Rev. A 72(4), 042328 (2005)
Ren, X.-J., Fan, H.: Quantum circuits for asymmetric 1 n quantum cloning. Quantum Inf. Comput. 15(11–12), 914–922 (2015)
Ghiu, I.: Asymmetric quantum telecloning of d-level systems and broadcasting of entanglement to different locations using the “many-to-many” communication protocol. Phys. Rev. A 67(1), 012323 (2003)
Hai-Dan, W., Chuan-Feng, L., Guang-Can, G.: Telebroadcasting of a cat-like state via local operations. Chin. Phys. Lett. 18(9), 1159 (2001)
Yan-Ling, L., Jian, F., Ya-Fei, Y.: Universal telecloning of quantum entangled states. Acta Phys. Sin. 56(12), 6797–6802 (2007)
Shi-Biao, Z.: Simplified scheme for cloning and telecloning quantum states near a given state. Chin. Phys. Lett. 20(3), 325 (2003)
Yong-Jian, G., Yi-Zhuang, Z., Li-Bing, C., Guang-Can, G.: Faithful telecloning with multiparticle entanglement. Chin. Phys. Lett. 19(6), 752 (2002)
Murao, M., Jonathan, D., Plenio, M., Vedral, V.: Quantum telecloning and multiparticle entanglement. Phys. Rev. A 59(1), 156 (1999)
Araneda, G., Cisternas, N., Delgado, A.: Telecloning of qudits via partially entangled states. Quantum Inf. Process. 15(8), 3443–3458 (2016)
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This project was supported by the National Science Foundation (NSF) (61571105, 61601120).
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Meng, FX., Yu, XT. & Zhang, ZC. An economical state-dependent telecloning for a multiparticle GHZ state. Quantum Inf Process 17, 66 (2018). https://doi.org/10.1007/s11128-018-1834-9
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DOI: https://doi.org/10.1007/s11128-018-1834-9