Controlled teleportation

Abstract

In this article, we review the recent development of controlled teleportation which can be used for sharing quantum information and has important applications in remote quantum computation. We introduce the principles of a couple of controlled teleportation schemes with maximally entangled quantum channels and those with pure entangled quantum channels (non-maximally entangled states). The schemes based on maximally entangled states have the advantage of having maximal efficiency although there are differences in their implementations in experiment. In the controlled teleportation schemes using non-maximally entangled states as the quantum channels, the receiver can reconstruct the originally unknown state by adding an auxiliary particle and performing a unitary evolution. No matter what the unknown state is (a single qubit state or an m-qudit state), the auxiliary particle required is only a two-level quantum system.

References

1. Bennett C H et al.Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-RosenchannelsPhysical Review Letters 1993 7018951899. doi:10.1103/PhysRevLett.70.1895
2. Einstein A Podolsky B Rosen N Can quantum-mechanical description of physical realitybe considered completePhysical Review 1935 47777780. doi:10.1103/PhysRev.47.777
3. Karlsson A Bourennane M Quantum teleportation usingthree-particle entanglementPhysical ReviewA 1998 5843944400. doi:10.1103/PhysRevA.58.4394
4. Lance A M Symul T Bowen W P et al.Tripartite quantum state sharingPhysical Review Letters 2004 92177903. doi: 10.1103/PhysRevLett.92.177903
5. Deng F G Li X H Li C Y et al.Multiparty quantum-state sharing of an arbitrarytwo-particle state with Einstein-Podolsky-Rosen pairsPhysical Review A 2005 72044301. doi: 10.1103/PhysRevA.72.044301
6. Gordon G Rigolin G Generalized quantum-state sharingPhysical Review A 2006 73062316. doi: 10.1103/PhysRevA.73.062316
7. Deng F G Li X H Li C Y et al.Quantum state sharing of an arbitrary two-qubitstate with two-photon entanglements and Bell-state measurementsEuropean Physical Journal D 2006 39459464. doi:10.1140/epjd/e2006‐00124‐1
8. Wang Z Y Yuan H Shi S H et al.Threeparty qutrit-state sharingEuropean Physical Journal D 2007 41371375. doi:10.1140/epjd/e2006‐00215‐y
9. Man Z X Xia Y J An N B Quantum state sharing of an arbitrary multiqubit stateusing nonmaximally entangled GHZ statesEuropean Physical Journal D 2007 42333340. doi:10.1140/epjd/e2007‐00024‐x
10. Yang C P Chu S I Han S Efficient many-party controlled teleportation of multiqubitquantum information via entanglementPhysicalReview A 2004 70022329. doi: 10.1103/PhysRevA.70.022329
11. Deng F G Li C Y Li Y S et al.Symmetric multiparty-controlled teleportation ofan arbitrary two-particle entanglementPhysicalReview A 2004 72022338. doi: 10.1103/PhysRevA.72.022338
12. Li X H Zhou P Li C Y et al.Efficient symmetric multiparty quantum state sharingof an arbitrary m-qubit stateJoural Of Physics B 2006 3919751983. doi:10.1088/0953‐4075/39/8/015
13. Li X H Deng F G Zhou H Y Controlled teleportation of an arbitrary multi-qudit statein a general form with d-dimensional Greenberger–Horne–ZeilingerstatesChinese Physics Letters 2007 2411511153. doi:10.1088/0256‐307X/24/5/007
14. Man Z X Xia Y J et al.Genuine multiqubit entanglementand controlled teleportationPhysical ReviewA 2007 75052306. doi: 10.1103/PhysRevA.75.052306
15. Zhang Z J Controlledteleportation of an arbitrary n-qubit quantum information using quantumsecret sharing of classical messagePhysicsLetters A 2006 3525558. doi:10.1016/j.physleta.2005.11.051
16. Zhang Z J Liu Y Man Z X Many-agent controlled teleportation of multi-qubit quantuminformation via quantum entanglement swappingCommunications In Theoretical Physics 2005 44847850
17. Zhang Z J Man Z X Many-agent controlled teleportationof multi-qubit quantum informationPhysicsLetters A 2005 3415559. doi:10.1016/j.physleta.2005.04.062
18. Yan F L Wang D Probabilistic and controlledteleportation of unknown quantum statesPhysics Letters A 2003 316297303. doi:10.1016/j.physleta.2003.08.007
19. Zhou P Li X H Deng F G et al.Multiparty-controlled teleportation of an arbitrarym-qudit state with a pure entangled quantum channelJoural Of Physics A 2007 401312113130. doi:10.1088/1751‐8113/40/43/019
20. Wang Y H Song H S Preparation of partially entangledstate and deterministic multi-controlled teleportationOptics Communications 2008 281489493
21. Cao Z L Zhou J Yang M Probabilistic and controlled teleportation of unknown ionicstates via linear optical elementsInternationalJournal of Quantum Information 2007 5431435. doi:10.1142/S0219749907002931
22. Gao T Quantumlogic networks for probabilistic and controlled teleportation of unknownquantum statesCommunications in TheoreticalPhysics 2004 42223228
23. Pati A K Agrawal P Probabilistic teleportationof a quditPhysics Letters A 2007 371185189. doi:10.1016/j.physleta.2007.07.016
24. Li C Y Li X H Deng F G et al.Efficient quantum cryptography network without entanglementand quantum memoryChinese Physics Letters 2006 2328962899. doi:10.1088/0256‐307X/23/11/004
25. Li X H Deng F G Li C Y et al.Deterministic secure quantum communication withoutmaximally entangled statesJournal of theKorean Physical Society 2006 4913541359
26. Wang C Deng F G Li Y S et al.Quantum secure direct communication with high-dimensionquantum superdense codingPhysical ReviewA 2005 71044305. doi: 10.1103/PhysRevA.71.044305
27. Liu X S Long G L Tong D M et al.General scheme for superdense coding between multipartiesPhysical Review A 2002 65022304. doi: 10.1103/PhysRevA.65.022304
28. Shi B S Jiang Y K Guo G C Probabilistic teleportation of two-particle entangled statePhysics Letters A 2000 268161164. doi:10.1016/S0375‐9601(00)00174‐2
29. Gao T Yan F L Li Y C Optimal controlled teleportatione-print: arXiv:0710.1055
30. Gao T Yan F L Li Y C Optimal controlled teleportation via several kinds of three-qubitstatese-print: arXiv:0802.2469
31. Acín A Andrianov A Costa L et al.Generalized Schmidt decomposition and classificationof three-quantum-bit statesPhysical ReviewLetters 2000 851560. doi: 10.1103/PhysRevLett.85.1560
32. Verstraete F Popp M Cirac J I Entanglement versus correlations in spin systemsPhysical Review Letters 2004 92027901. doi: 10.1103/PhysRevLett.92.027901
33. Deng F G Long G L Liu X S Two-step quantum direct communication protocol using theEinstein-Podolsky-Rosen pair blockPhysicalReview A 2003 68042317. doi: 10.1103/PhysRevA.68.042317
34. Deng F G Long G L Secure direct communicationwith a quantum one-time padPhysical ReviewA 2004 69052319. doi: 10.1103/PhysRevA.69.052319
35. Wang C Deng F G Long G L Multi-step quantum secure direct communication using multi-particleGreen-Horne-Zeilinger stateOptics Communications 2005 25215. doi: 10.1016/j.optcom.2005.04.048
36. Deng F G Li X H Zhou H Y Opaque attack on threeparty quantum secret sharing basedon entanglemente-print: arXiv:0705.0279
37. Li C Y Zhou H Y Wang Y et al.Secure quantum key distribution network with Bellstates and local unitary operationsChinesePhysics Letters 2005 2210491052. doi:10.1088/0256‐307X/22/5/006
38. Chen P Deng F G Long G L High-dimension multiparty quantum secret sharing schemewith Einstein-Podolsky-Rosen pairsChinesePhysics 2006 1522282235. doi:10.1088/1009‐1963/15/7/017
39. Deng F G Li X H Li C Y et al.Quantum secure direct communication network withsuperdense coding and decoy photonsPhysicaScripta 2007 762530. doi:10.1088/0031‐8949/76/1/005