Remote Quantum-Information Concentration: Reversal of Ancilla-Free Phase-Covariant Telecloning

Xinwen Wang, Shiqing Tang

Department of Physics and Electronic Information Science, Hengyang Normal University, Hengyang, China.
Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Education, Department of Physics, Hunan Normal University, Changsha, China.

DOI: 10.4236/ojm.2013.31004                

Abstract

Telecloning and its reverse process, referred to as remote quantum-information concentration (RQIC), have been attracting considerable interest because of their potential applications in quantum-information processing. The previous RQIC protocols were focused on the reverse process of the optimal universal telecloning. We here study the reverse process of ancilla-free phase-covariant telecloning (AFPCT). It is shown that the quantum information originally distributed into two spatially separated qubits from a single qubit via the optimal AFPCT procedure can be remotely concentrated back to a single qubit with a certain probability by using an asymmetric W state as the quantum channel.

Keywords

Remote Quantum-Information Concentration; Phase-Covariant Telecloning; W State

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	W. K. Wootters and W. H. Zurek, “A Single Quantum Cannot Be Cloned,” Nature, Vol. 299, No. 5886, 1982, pp. 802-803. doi:10.1038/299802a0
[2]	D. Dieks, “Communication by EPR Devices,” Physics Lettters A, Vol. 92, No. 6, 1982, pp. 271-272. doi:10.1016/0375-9601(82)90084-6
[3]	V. Buzek and M. Hillery, “Quantum Copying, beyond the No-Cloning Theorem,” Physical Review A, Vol. 54, No. 3, 1996, pp. 1844-1852. doi:10.1103/PhysRevA.54.1844
[4]	V. Scarani, et al., “Quantum Cloning,” Reviews of Modern Physics, Vol. 77, No. 4, 2005, pp. 1225-1256. doi:10.1103/RevModPhys.77.1225
[5]	E. F. Galvao and L. Hardy, “Cloning and Quantum Computation,” Physical Review A, Vol. 62, No. 2, 2000, Article ID: 022301. doi:10.1103/PhysRevA.62.022301
[6]	M. Ricci, et al., “Separating the Classical and Quantum Information via Quantum Cloning,” Physical Review Letters, Vol. 95, No. 9, 2005, Article ID: 090504. doi:10.1103/PhysRevLett.95.090504
[7]	D. Bruß, J. Calsamiglia and N. Lutkenhaus, “Quantum Cloning and Distributed Measurements,” Physical Review A, Vol. 63, No. 4, 2001, Article ID: 042308. doi:10.1103/PhysRevA.63.042308
[8]	P. Sekatski, et al., “Cloning Entangled Photons to Scales One Can See,” Physical Review A, Vol. 82, No. 5, 2010, Article ID: 053814. doi:10.1103/PhysRevA.82.053814
[9]	N. Spagnolo, F. Sciarrino and F. De Martini, “Resilience to Decoherence of the Macroscopic Quantum Superpositions Generated by Universally Covariant Optimal Quantum Cloning,” Physical Review A, Vol. 82, No. 3, 2010, Article ID: 032325. doi:10.1103/PhysRevA.82.032325
[10]	M. Murao, et al., “Quantum Telecloning and Multiparticle Entanglement,” Physical Review A, Vol. 59, No. 1, 1999, pp. 156-161. doi:10.1103/PhysRevA.59.156
[11]	M. Murao, M. B. Plenio and V. Vedral, “Quantum-Information Distribution via Entanglement,” Physical Review A, Vol. 61, No. 3, 2000, Article ID: 032311. doi:10.1103/PhysRevA.61.032311
[12]	C. H. Bennett, et al., “Teleporting an Unknown Quantum State via Dual Classical and Einstein-Podolsky-Rosen Channels,” Physical Review Letters, Vol. 70, No. 13, 1993, pp. 1895-1899. doi:10.1103/PhysRevLett.70.1895
[13]	I. Ghiu, “Asymmetric Quantum Telecloning of D-Level Systems and Broadcasting of Entanglement to Different Locations Using the ‘Many-To-Many’ Communication Protocol,” Physical Review A, Vol. 67, No. 1, 2003, Article ID: 012323. doi:10.1103/PhysRevA.67.012323
[14]	X. W. Wang and G. J. Yang, “Hybrid Economical Telecloning of Equatorial Qubits and Generation of Multipartite Entanglement,” Physical Review A, Vol. 79, No. 6, 2009, Article ID: 062315. doi:10.1103/PhysRevA.79.062315
[15]	I. Ghiu and A. Karlsson, “Broadcasting of Entanglement at a Distance Using Linear Optics and Telecloning of Entanglement,” Physical Review A, Vol. 72, No. 3, 2005, Article ID: 032331. doi:10.1103/PhysRevA.72.032331
[16]	L. Chen and Y. X. Chen, “Asymmetric Quantum Telecloning of Multiqubit States,” Quantum Information and Computation, Vol. 7, 2007, pp. 716-729.
[17]	X. W. Wang and G. J. Yang, “Probabilistic Ancilla-Free Phase-Covariant Telecloning of Qudits with the Optimal Fidelity,” Physical Review A, Vol. 79, No. 6, 2009, Article ID: 064306. doi:10.1103/PhysRevA.79.064306
[18]	X. W. Wang, Y. H. Su and G. J. Yang, “One-to-Many Economical Phase-Covariant Cloning and Telecloning of Qudits,” Chinese Physics Letters, Vol. 27, No. 10, 2010, Article ID: 100303. doi:10.1088/0256-307X/27/10/100303
[19]	M. Murao and V. Vedral, “Remote Information Concen- tration Using a Bound Entangled State,” Physical Review Letters, Vol. 86, No. 2, 2001, pp. 352-355. doi:10.1103/PhysRevLett.86.352
[20]	J. A. Smolin, “Four-party Unlockable Bound Entangled State,” Physical Review A, Vol. 63, No. 3, 2001, Article ID: 032306. doi:10.1103/PhysRevA.63.032306
[21]	D. M. Greenberger, et al., “Bells Theorem without Inequalities,” American Journal of Physics, Vol. 58, 1990, pp. 1131-1143. doi:10.1119/1.16243
[22]	Y. F. Yu, J. Feng and M. S. Zhan, “Remote Information Concentration by a Greenberger-Horne-Zeilinger State and by a Bound Entangled State,” Physical Review A, Vol. 68, No. 2, 2003, Article ID: 024303. doi:10.1103/PhysRevA.68.024303
[23]	R. Augusiak and P. Horodecki, “Generalised Smolin states and Their Properties,” Physical Review A, Vol. 73, No. 1, 2006, Article ID: 012318. doi:10.1103/PhysRevA.73.012318
[24]	L. Y. Hsu, “Remote One-Qubit Information Concentration and Decoding of Operator Quantum Error-Correction Codes,” Physical Review A, Vol. 76, No. 3, 2007, Article ID: 032311. doi:10.1103/PhysRevA.76.032311
[25]	X. W. Wang, et al., “Remote Information Concentration and Multipartite Entanglement in Multilevel Systems,” Physical Review A, Vol. 84, No. 4, 2011, Article ID: 042310. doi:10.1103/PhysRevA.84.042310
[26]	W. D¨ur, et al., “Three Qubits Can Be Entangled in Two Inequivalent Ways,” Physical Review A, Vol. 62, No. 6, 2000, Article ID: 062314. doi:10.1103/PhysRevA.62.062314
[27]	D. Bruß, et al., “Phase-Covariant Quantum Cloning,” Physical Review A, Vol. 62, No. 1, 2000, Article ID: 012302. doi:10.1103/PhysRevA.62.012302
[28]	G. M. D’Ariano and C. Macchiavello, “Optimal Phase-Covariant Cloning for Qubits and Qutrits,” Physical Review A, Vol. 67, No. 4, 2003, Article ID: 042306. doi:10.1103/PhysRevA.67.042306
[29]	X. W. Wang, et al., “Simple Schemes for Quantum Information Processing with W-Type Entanglement,” Quantum Information Processing, Vol. 8, 2009, pp. 431-442. doi:10.1007/s11128-009-0119-8
[30]	X. W. Wang, “Preparation and Manipulation of W-Class Entangled States: Applications to Quantum Information Processing,” International Journal of Quantum Information, Vol. 7, No. 2, 2009, pp. 493-504. doi:10.1142/S0219749909004633
[31]	Z. H. Peng, et al., “Scheme for Implementing Efficient Quantum Information Processing with Multiqubit W-Class States in Cavity QED,” Journal of Physics B, Vol. 41, 2008, Article ID: 065505. doi:10.1088/0953-4075/41/6/065505
[32]	Y. H. Wang and H. S. Song, “Preparation of Partially Entangled W State and Deterministic Multi-controlled Teleportation,” Optics Communications, Vol. 281, 2008, pp. 489-493. doi:10.1016/j.optcom.2007.09.057
[33]	Q. Liu, W. H. Zhang and L. Yie, “Scheme to Implement Scheme 1→M Economical Phase-Covariant Telecloning via Cavity QED,” Chinese Physics Letters, Vol. 25, No. 6, 2008, pp. 1947-1949. doi:10.1088/0256-307X/25/6/007
[34]	W. H. Zhang, J. L. Dai and L. Yie, “Scheme to Implement Optimal Asymmetric Economical Phase-Covariant Quantum Cloning in Cavity QED,” Communications in Theoretical Physics, Vol. 49, No. 6, 2008, pp. 1473-1476. doi:10.1088/0253-6102/49/6/27
[35]	S. Gleyzes, et al., “Quantum Jumps of Light Recording the Birth and Death of a Photon in a Cavity,” Nature, Vol. 446, No. 7133, 2007, pp. 297-300. doi:10.1038/nature05589
[36]	H. Mabuchi and A. C. Doherty, “Cavity Quantum Electrodynamics: Coherence in Context,” Science, Vol. 298, No. 5597, 2002, pp. 1372-1377. doi:10.1126/science.1078446
[37]	R. Reichle, et al., “Experimental Purification of Two-Atom Entanglement,” Nature, Vol. 443, No. 7113, 2006, pp. 838-841. doi:10.1038/nature05146
[38]	S. Olmschenk, et al., “Quantum Teleportation between Distant Matter Qubits,” Science, Vol. 323, No. 5913, 2009, pp. 486-489. doi:10.1126/science.1167209
[39]	X. W. Wang, et al., “Nondestructive Greenberger-Horne- Zeilinger-State Analyzer,” Quantum Information Processing, Vol. 12, No. 2, 2013, pp. 1065-1075. doi:10.1007/s11128-012-0453-0
[40]	X. W. Wang, et al., “Photonic Two-Qubit Parity Gate with Tiny Cross-Kerr Nonlinearity,” Physical Review A, Vol. 85, No. 5, 2012, Article ID: 052326. doi:10.1103/PhysRevA.85.052326