Two-qubit entangled state teleportation via optimal POVM and partially entangled GHZ state
Kan Wang1(), Xu-Tao Yu2, Zai-Chen Zhang1
1. National Mobile Communications Research Laboratory, Southeast University, Nanjing 210096, China 2. State Key Laboratory of Millimeter Waves, Southeast University, Nanjing 210096, China
Quantum teleportation is of significant meaning in quantum information. In this paper, we study the probabilistic teleportation of a two-qubit entangled state via a partially entangled Greenberger- Horne-Zeilinger (GHZ) state when the quantum channel information is only available to the sender. We formulate it as an unambiguous state discrimination problem and derive exact optimal positive-operator valued measure (POVM) operators for maximizing the probability of unambiguous discrimination. Only one three-qubit POVM for the sender, one two-qubit unitary operation for the receiver, and two cbits for outcome notification are required in this scheme. The unitary operation is given in the form of a concise formula, and the fidelity is calculated. The scheme is further extended to more general case for transmitting a two-qubit entangled state prepared in arbitrary form. We show this scheme is flexible and applicable in the hop-by-hop teleportation situation.
S. Pirandola, J. Eisert, C. Weedbrook, A. Furusawa, and S. L. Braunstein, Advances in quantum teleportation, Nat. Photonics 9(10), 641 (2015) https://doi.org/10.1038/nphoton.2015.154
2
C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, Teleporting an unknown quantum state via dual classical and Einstein– Podolsky–Rosen channels, Phys. Rev. Lett. 70(13), 1895 (1993) https://doi.org/10.1103/PhysRevLett.70.1895
K. Wang, X. T. Yu, S. L. Lu, and Y. X. Gong, Quantum wireless multihop communication based on arbitrary Bell pairs and teleportation, Phys. Rev. A 89(2), 022329 (2014) https://doi.org/10.1103/PhysRevA.89.022329
H. L. Huang, Y. W. Zhao, T. Li, F. G. Li, Y. T. Du, X. Q. Fu, S. Zhang, X. Wang, and W. S. Bao, Homomorphic encryption experiments on IBM’s cloud quantum computing platform, Front. Phys. 12(1), 120305 (2017) https://doi.org/10.1007/s11467-016-0643-9
S. Imre and L. Gyongyosi, Advanced Quantum Communications: An En-gineering Approach, Wiley-IEEE Press, 2013
9
D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, Experimental quantum teleportation, Nature 390(6660), 575 (1997) https://doi.org/10.1038/37539
10
X. L. Wang, X. D. Cai, Z. E. Su, M. C. Chen, D. Wu, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, Quantum teleportation of multiple degrees of freedom of a single photon, Nature 518(7540), 516 (2015) https://doi.org/10.1038/nature14246
11
L. Gyongyosi, S. Imre, and H. V. Nguyen, A survey on quantum channel capacities, IEEE Comm. Surv. and Tutor. 20(2), 1149 (2018) https://doi.org/10.1109/COMST.2017.2786748
L. Gyongyosi, Quantum imaging of high-dimensional Hilbert spaces with Radon transform, Int. J. Circuit Theory Appl. 45(7), 1029 (2017) https://doi.org/10.1002/cta.2332
X. F. Cai, X. T. Yu, L. H. Shi, and Z. C. Zhang, Partially entangled states bridge in quantum teleportation, Front. Phys. 9(5), 646 (2014) https://doi.org/10.1007/s11467-014-0432-2
17
D. Liu, Z. Huang, and X. Guo, Probabilistic teleportation via quantum channel with partial information, Entropy (Basel) 17(6), 3621 (2015) https://doi.org/10.3390/e17063621
18
P. Y. Xiong, X. T. Yu, H. T. Zhan, and Z. C. Zhang, Multiple teleportation via partially entangled GHZ state, Front. Phys. 11(4), 110303 (2016) https://doi.org/10.1007/s11467-016-0553-x
S. Bandyopadhyay, Unambiguous discrimination of linearly independent pure quantum states: Optimal average probability of success, Phys. Rev. A 90(3), 030301 (2014) https://doi.org/10.1103/PhysRevA.90.030301
21
H. Sugimoto, T. Hashimoto, M. Horibe, and A. Hayashi, Complete solution for unambiguous discrimination of three pure states with real inner products, Phys. Rev. A 82(3), 032338 (2010) https://doi.org/10.1103/PhysRevA.82.032338
Y. C. Eldar, A semidefinite programming approach to optimal unambiguous discrimination of quantum states, IEEE Trans. Inf. Theory 49(2), 446 (2003) https://doi.org/10.1109/TIT.2002.807291
R. B. M. Clarke, A. Chefles, S. M. Barnett, and E. Riis, Experimental demonstration of optimal unambiguous state discrimination, Phys. Rev. A 63(4), 040305 (2001) https://doi.org/10.1103/PhysRevA.63.040305
26
O. Jiménez, X. Sánchez-Lozano, E. Burgos-Inostroza, A. Delgado, and C. Saavedra, Experimental scheme for unambiguous discrimination of linearly independent symmetric states, Phys. Rev. A 76, 062107 (2007) https://doi.org/10.1103/PhysRevA.76.062107
W. Son, J. Lee, M. S. Kim, and Y. J. Park, Conclusive teleportation of a d-dimensional unknown state, Phys. Rev. A 64(6), 064304 (2001) https://doi.org/10.1103/PhysRevA.64.064304
29
L. Roa, A. Delgado, and I. Fuentes-Guridi, Optimal conclusive teleportation of quantum states, Phys. Rev. A 68(2), 022310 (2003) https://doi.org/10.1103/PhysRevA.68.022310
30
H. Liu, X. Q. Xiao, and J. M. Liu, Conclusive teleportation of an arbitrary three-particle state via positive operator-valued measurement, Commum. Theor. Phys. 50(1), 69 (2008) https://doi.org/10.1088/0253-6102/50/1/14
31
G. Brassard, P. Horodecki, and T. Mor, TelePOVM—A generalized quantum teleportation scheme, IBM J. Res. Develop. 48(1), 87 (2004) https://doi.org/10.1147/rd.481.0087
B. He and J. A. Bergou, A general approach to physical realization of unambiguous quantum-state discrimination, Phys. Lett. A 356(4–5), 306 (2006) https://doi.org/10.1016/j.physleta.2006.03.076