Abstract
We present a scheme for probabilistic teleportation via a non-maximally entangled GHZ state. Quantum teleportation will succeed with a calculable probability. The teleportation process requires the sender to make a generalized Bell state measurement, the cooperator to perform a generalized X basis measurement, and the receiver to perform a collective unitary transformation and to make a measurement on an auxiliary particle. The success probability of the teleportation is given. We also obtain the maximum of the success probability of the teleportation.
Similar content being viewed by others
References
Nielsen M A, Chuang I L. Quantum Computation and Quantum Information. Cambridge: Cambridge University Press, 2000
Bennett C H, Brassard G, Crépeau C, et al. Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys Rev Lett, 1993, 70: 1895–1899
Gisin N, Ribordy G, Tittel W, et al. Quantum cryptography. Rev Mod Phys, 2002, 74: 145–195
Bennett C H, Wiesner S J. Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states. Phys Rev Lett, 1992, 69: 2881–2884
Raussendorf R, Briegel H J. A one-way quantum computer. Phys Rev Lett, 2001, 86: 5188–5191
Wang X B, Hiroshima T, Tomita A, et al. Quantum information with Gaussian states. Phys Rep, 2007, 448: 1–111
Long G L, Deng F G, Wang C, et al. Quantum secure direct communication and deterministic secure quantum communication. Front Phys China, 2007, 2: 251–272
Bruβ D, DiVincenzo D P, Ekert A, et al. Optimal universal and state-dependent quantum cloning. Phys Rev A, 1998, 57: 2368–2378
Ding S C, ** Z. Review on the study of entanglement in quantum computation speedup. Chinese Sci Bull, 2007, 52: 2161–2166
Braunstein S L, van Loock P. Quantum information with continuous variables. Rev Mod Phys, 2005, 77: 513–577
Vaidman L. Teleportation of quantum states. Phys Rev A, 1994, 49: 1473–1476
Braunstein S L, Kimble H J. Teleportation of continuous quantum variables. Phys Rev Lett, 1998, 80: 869–872
Gordon G, Rigolin G. Generalized teleportation protocol. Phys Rev A, 2006, 73: 042309
Karlsson A, Bourennane M. Quantum teleportation using three-particle entanglement. Phys Rev A, 1998, 58: 4394–4400
Deng F G, Li C Y, Li Y S, et al. Symmetric multiparty-controlled teleportation of an arbitrary two-particle entanglement. Phys Rev A, 2005, 72: 022338
Zhang Z J. Controlled teleportation of an arbitrary n-qubit quantum information using quantum secret sharing of classical message. Phys Lett A, 2006, 352: 55–58
Li X H, Deng F G. Controlled teleportation. Front Comput Sci China, 2008, 2: 147–160
Gao T, Yan F L, Li Y C. Optimal controlled teleportation. Europhys Lett, 2008, 84: 50001
Gao T, Yan F L, Li Y C. Optimal controlled teleportation via several kinds of three-qubit states. Sci China Ser G-Phys Mech Astron, 2008, 51: 1529–1556
Agrawal P, Pati A K. Probabilistic quantum teleportation. Phys Lett A, 2002, 305: 12–17
Pati A K, Agrawal P. Probabilistic teleportation and quantum operation. J Opt B Quant Semiclass Opt, 2004, 6: S844–S848
Tian D P, Tao Y J, Qin M. Teleportation of an arbitrary two-qubit state based on the non-maximally four-qubit cluster state. Sci China Ser G-Phys Mech Astron, 2008, 51: 1523–1528
Zhang X H, Yang Z Y, Xu P P. Teleporting N-qubit unknown atomic state by utilizing the V-type three-level atom. Sci China Ser G-Phys Mech Astron, 2009, 52: 1034–1038
Bouwmeester D, Pan J W, Mattle K, et al. Experimental quantum teleportation. Nature, 1997, 390: 575–579
Furusawa A, Sørensen J L, Braunstein S L, et al. Unconditional quantum teleportation. Science, 1998, 282: 706–709
Nielsen M A, Knill E, Laflamme R. Complete quantum teleportation using nuclear magnetic resonance. Nature, 1998, 396: 52–55
Boschi D, Branca S, De Martini F, et al. Experimental realization of teleporting an unknown pure quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys Rev Lett, 1998, 80: 1121–1125
Gottesman D. Stabilizer codes and quantum error correction. ar**v: quant-ph/9705052
Bennett C H, Brassard G, Popescu S, et al. Purification of noisy entanglement and faithful teleportation via noisy channels. Phys Rev Lett, 1996, 76: 722–725
Author information
Authors and Affiliations
Corresponding author
Additional information
This work was supported by the National Natural Science Foundation of China (Grant No. 10971247), Hebei Natural Science Foundation of China (Grant Nos. 07M006, F2009000311) and Key Project of Science and Technology Research of Education Ministry of China (Grant No. 207011).
About this article
Cite this article
Yan, F., Yan, T. Probabilistic teleportation via a non-maximally entangled GHZ state. Chin. Sci. Bull. 55, 902–906 (2010). https://doi.org/10.1007/s11434-009-0725-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11434-009-0725-y