Abstract
During the realization of one-qubit quantum teleportation, an EPR pair shared between two parties is required, followed by a joint Bell state measurement on the teleported qubit and the sender’s qubit. In this paper, we analyze the joint measurements in the case of teleporting multiple qubits. By carefully dividing the sender’s qubit space into several subspaces, we show that the receiver can restore the qubits if the measurement is taken in the mutually unbiased basis. We generalize our protocol to teleporting special entangled states and high-dimensional state. Our protocol may have potential application in multi-qubit quantum teleportation.
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Ekert, A.K.: Quantum cryptography based on Bells theorem. Phys. Rev. Lett. 67(6), 661 (1991). https://doi.org/10.1103/PhysRevLett.67.661
Gisin, N., Ribordy, G., Tittel, W., Zbinden, H.: Quantum cryptography. Rev. Mod. Phys. 74(1), 145 (2002). https://doi.org/10.1103/RevModPhys.74.145
Bouwmeester, D., Pan, J.W., Mattle, K., Eibl, M., Weinfurter, H., Zeilinger, A.: Experimental quantum teleportation. Nature 390(6660), 575 (1997). https://doi.org/10.1038/37539
Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2010)
Bennett, C.H., Brassard, G., Crépeau, C., Jozsa, R., Peres, A., Wootters, W.K.: 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
Braunstein, S.L., Kimble, H.J.: Teleportation of continuous quantum variables. Phys. Rev. Lett. 80(4), 869 (1998). https://doi.org/10.1103/PhysRevLett.80.869
Yonezawa, H., Aoki, T., Furusawa, A.: Demonstration of a quantum teleportation network for continuous variables. Nature 431(7007), 430 (2004). https://doi.org/10.1038/nature02858
Dell’ Anno, F., De Siena, S., Albano, L., Illuminati, F.: Continuous-variable quantum teleportation with non-Gaussian resources. Phys. Rev. A 76(2), 022301 (2007). https://doi.org/10.1103/PhysRevA.76.022301
Riebe, M., Häffner, H., Roos, C., Hänsel, W., Benhelm, J., Lancaster, G., Körber, T., Becher, C., Schmidt-Kaler, F., James, D., et al.: Deterministic quantum teleportation with atoms. Nature 429(6993), 734 (2004). https://doi.org/10.1038/nature02570
Barrett, M., Chiaverini, J., Schaetz, T., Britton, J., Itano, W., Jost, J., Knill, E., Langer, C., Leibfried, D., Ozeri, R., et al.: Deterministic quantum teleportation of atomic qubits. Nature 429(6993), 737 (2004). https://doi.org/10.1038/nature02608
Krauter, H., Salart, D., Muschik, C., Petersen, J.M., Shen, H., Fernholz, T., Polzik, E.S.: Deterministic quantum teleportation between distant atomic objects. Nat. Phys. 9(7), 400 (2013). https://doi.org/10.1038/nphys2631
Joo, J., Park, Y.J., Oh, S., Kim, J.: Quantum teleportation via a W state. N. J. Phys. 5(1), 136 (2003). https://doi.org/10.1088/1367-2630/5/1/136
Ikram, M., Zhu, S.Y., Zubairy, M.S.: Quantum teleportation of an entangled state. Phys. Rev. A 62(2), 022307 (2000). https://doi.org/10.1103/PhysRevA.62.022307
Yang, K., Huang, L., Yang, W., Song, F.: Quantum teleportation via GHZ-like state. Int. J. Theor. Phys. 48(2), 516 (2009). https://doi.org/10.1007/s10773-008-9827-6
Jin-Ming, L., Guang-Can, G.: Quantum teleportation of a three-particle entangled state. Chin. Phys. Lett. 19(4), 456 (2002). https://doi.org/10.1088/0256-307X/19/4/303
Agrawal, P., Pati, A.: Perfect teleportation and superdense coding with W states. Phys. Rev. A 74(6), 062320 (2006). https://doi.org/10.1103/PhysRevA.74.062320
Van Houwelingen, J., Brunner, N., Beveratos, A., Zbinden, H., Gisin, N.: Quantum teleportation with a three-Bell-state analyzer. Phys. Rev. Lett. 96(13), 130502 (2006). https://doi.org/10.1103/PhysRevLett.96.130502
Nie, Yy, Li, Yh, Liu, Jcq, Sang, Mh: Perfect teleportation of an arbitrary three-qubit state by using W-class states. Int. J. Theor. Phys. 50(10), 3225 (2011). https://doi.org/10.1007/s10773-011-0825-8
Yuan, W.: Quantum teleportation of an arbitrary three-qubit state using GHZ-like states. Int. J. Theor. Phys. 54(3), 851 (2015). https://doi.org/10.1007/s10773-014-2279-2
Fang, J., Lin, Y., Zhu, S., Chen, X.: Probabilistic teleportation of a three-particle state via three pairs of entangled particles. Phys. Rev. A 67, 014305 (2003). https://doi.org/10.1103/PhysRevA.67.014305
Zhang, Z., Liu, Y., Wang, D.: Perfect teleportation of arbitrary n-qudit states using different quantum channels. Phys. Lett. A 372(1), 28 (2007). https://doi.org/10.1016/j.physleta.2007.07.017
Werner, R.F.: All teleportation and dense coding schemes. J. Phys. A: Math. Gen. 34(35), 7081 (2001). https://doi.org/10.1088/0305-4470/34/35/332
Durt, T., Englert, B.G., Bengtsson, I., Życzkowski, K.: On mutually unbiased bases. Int. J. Quantum Inf. 8(04), 535 (2010). https://doi.org/10.1142/S0219749910006502
Brierley, S., Weigert, S., Bengtsson, I.: All mutually unbiased bases in dimensions two to five arXiv preprint arXiv:0907.4097 (2009)
Schwinger, J.: Unitary operator bases. Proc. Natl. Acad. Sci. USA 46(4), 570 (1960). https://doi.org/10.1073/pnas.46.4.570
Bennett, C.H., Brassard, G.: Quantum cryptography: public key distribution and coin tossing. Theor. Comput. Sci. 560(12), 7 (2014). https://doi.org/10.1016/j.tcs.2011.08.039
Gottesman, D.: Class of quantum error-correcting codes saturating the quantum Hamming bound. Phys. Rev. A 54(3), 1862 (1996). https://doi.org/10.1103/PhysRevA.54.1862
Calderbank, A.R., Rains, E.M., Shor, P.W., Sloane, N.J.: Quantum error correction and orthogonal geometry. Phys. Rev. Lett. 78(3), 405 (1997). https://doi.org/10.1103/PhysRevLett.78.405
Wootters, W.K., Fields, B.D.: Optimal state-determination by mutually unbiased measurements. Ann. Phys. 191(2), 363 (1989). https://doi.org/10.1016/0003-4916(89)90322-9
Ivonovic, I.: Geometrical description of quantal state determination. J. Phys. A Math. Gen. 14(12), 3241 (1981). https://doi.org/10.1088/0305-4470/14/12/019
Jaming, P., Matolcsi, M., Móra, P., Szöllősi, F., Weiner, M.: A generalized Pauli problem and an infinite family of MUB-triplets in dimension 6. J. Phys. A Math. Theor. 42(24), 245305 (2009). https://doi.org/10.1088/1751-8113/42/24/245305
Grassl, M.: arXiv preprint arXiv:quant-ph/0406175 (2004)
Bengtsson, I., Bruzda, W., Ericsson, Å., Larsson, J.Å., Tadej, W., Życzkowski, K.: Mutually unbiased bases and Hadamard matrices of order six. J. Math. Phys. 48(5), 052106 (2007). https://doi.org/10.1063/1.2716990
Klappenecker, A., Rötteler, M.: In: Mullen, G.L., Poli, A., Stichtenoth, H. (eds.) Finite Fields and Applications, pp. 137–144. Springer, Berlin Heidelberg, (2004)
Roa, L., Delgado, A., Fuentes-Guridi, I.: Optimal conclusive teleportation of quantum states. Phys. Rev. A 68, 022310 (2003). https://doi.org/10.1103/PhysRevA.68.022310
Mirhosseini, M., Magaña-Loaiza, O.S., O’Sullivan, M.N., Rodenburg, B., Malik, M., Lavery, M.P.J., Padgett, M.J., Gauthier, D.J., Boyd, R.W.: High-dimensional quantum cryptography with twisted light. N. J. Phys. 17(3), 033033 (2015). https://doi.org/10.1088/1367-2630/17/3/033033
Bouchard, F., Heshami, K., England, D., Fickler, R., Boyd, R.W., Englert, B.G., Sánchez-Soto, L.L., Karimi, E.: Experimental investigation of high-dimensional quantum key distribution protocols with twisted photons. Quantum 2, 111 (2018). https://doi.org/10.22331/q-2018-12-04-111
Wang, F., Wang, Y., Liu, R., Chen, D., Zhang, P., Gao, H., Li, F.: Demonstration of quantum permutation algorithm with a single photon ququart. Sci. Rep. 5, 10995 (2015). https://doi.org/10.1038/srep10995
Wang, X.L., Cai, X.D., Su, Z.E., Chen, M.C., Wu, D., Li, L., Liu, N.L., Lu, C.Y., Pan, J.W.: Quantum teleportation of multiple degrees of freedom of a single photon. Nature 518(7540), 516 (2015). https://doi.org/10.1038/nature14246
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This work is supported by Science, Technology and Innovation Commission of Shenzhen Municipality (Nos. ZDSYS20170303165926217, JCYJ20170412152620376) and Guangdong Innovative and Entrepreneurial Research Team Program (Grant No. 2016ZT06D348).
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Chen, D., Zhang, L. & Zhang, J. Quantum teleportation with mutually unbiased bases. Quantum Inf Process 19, 121 (2020). https://doi.org/10.1007/s11128-020-2621-y
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DOI: https://doi.org/10.1007/s11128-020-2621-y