Abstract
The goal of this paper is to further study multiparty multicast quantum communication of different quantum states via partially entangled channels. We employ the partially entangled channels to preform two multicast remote state preparation schemes for transmitting different complex coefficient states from one sender to two receivers synchronously. The first scheme is used to transmit two complex coefficient four-qubit cluster-type states to two receivers with a certain probability. In order to improve success probability of this multicast scheme, we propose another scheme, which is a synchronous transfer of a complex coefficient single-qubit state and a complex coefficient two-qubit state from one sender to two receivers. The success probability of the second scheme reaches 1, and independent of the entanglement degree of the partially entangled channel.
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References
Streltsov, A., Adesso, G., Plebio, M.B.: Quantum coherence as a resource. Rev. Mod. Phys. 89, 041003 (2014)
Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridage (2000)
Horodecki, R., Horodecki, P., Horodecki, M., Horodecki, K.: Quantum entanglement. Rev. Mod. Phys. 81, 865–924 (2009)
Brunner, N., Cavalcanti, D., Pironio, S., Scarani, V., Wehiner, S.: Bell nonlocality. Rev. Mod. Phys. 86, 419 (2014)
Reid, M.D., Drummond, P.D., Bowen, W.P., et al.: The Einstein-Podolsky-Rosen paradox: from concepts to applications. Rev. Mod. Phys. 81, 1727 (2009)
Enary, C., Lambert, N., Nori, F.: Leggett-Garg inequalities. Rep. Prog. Phys. 77, 016001 (2014)
Bell, J.S.: Speakable and Unspeakable in Quantum Mechanics. Cambridage University Press, Cambridage (1987)
Peres, A.: Quantum theory: Concepts and Methods. Kluwer, Dordrecht (1993)
Ekert, A.K.: Quantum cryptography based on Bell’s theorem. Phys. Rev. Lett. 67, 661 (1991)
Bennett, C.H., Brassard, G.: Quantum cryptography: public key distribution and coin tossing. Theor. Comput. Sci. 560, 7 (2014)
Bennett, C.H., Wiesner, S.J.: Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states. Phys. Rev. Lett. 69, 2881 (1992)
Bennett, C.H., Brassard, G., Crepeau, C., et al.: Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys. Rev. Lett. 70, 1895 (1993)
Deutsch, D.: Quantum theory, the Church-Turing principle and the universal quantum computer. Proc. R. Soc. A 400, 1818 (1985)
Deutsch, D., Jozsa, R.: Rapid solution of problems by quantum computation. Proc. R. Soc. Lond. A 439, 553 (1992)
Gallager, R.G.: Information Theory and Reliable Communication. Wiley, New York (1968)
Cover, T.M., Thomas, J.A.: Elements of Information Theory. Wiley, New York (1991)
Huang, W.: Improved multiparty quantum key agreement in travelling mode. Sci. China, Physics, Mech. Astron. 59(12), 120311 (2016)
Liu, X.S., LongL, G.L., Tong, D.M., Li, F.: General scheme for superdense coding between multiparties. Phys. Rev. A 65, 022304 (2002)
Liu, B.H., Hu, X.M., Huang, Y.F., et al.: Experimental demonstration of efficient superdense coding in the presence of non-Markovian noise. Europhys. Lett. 114, 10005 (2016)
Bouwmeester, D., Pan, J.M., Mattle, K., ea al.: Experimental quantum teleportation. Nature 390, 575 (1997)
Peng, J.Y., He, Y.: Annular controlled teleportation. Int. J. Theor. Phys. 58, 3271 (2019)
Long, G.L., Deng, F.G.: Secure direct communication with a quantum one-time pad. Phys. Rev. A 69, 052319 (2004)
Wang, C.: Multi-step quantum secure direct communication using multi-particle Green-Horne-Zeiliger state. Opt. Commun. 253(1), 15–20 (2005)
Peng, J.Y., Bai, M.Q., Mo, Z.W.: Bidirectional quantum states sharing. Int. J. Theor. Phys. 55, 2481–2489 (2016)
Hillery, M., Buz̆ek, V., Berthiaume, A.: Quantum secret sharing. Phys. Rev. A 59, 1829 (1999)
Peng, J.Y., Bai, M.Q., Mo, Z.W.: Hierarchical and probabilistic quantum state sharing via a non- maximally entangled \(\lvert {\chi }\rangle\) state. Chinese Phys. B 23, 010304 (2014)
Huelga, S.F., Vaccaro, J.A., Chefles, A., et al.: Quantum remote control: Teleportation of unitary operations. Phys. Rev. A 63(4), 042303 (2001)
Peng, J.Y., He, Y.: Cyclic controlled remote implementation of partially unknown quantum operations. Internal Journal of Theoretical Physics 58, 3065–3072 (2019)
Wang, A.M.: Remote implementations of partially unknown quantum operations of multiqubits. Phys. Rev. A 74(3), 396–401 (2006)
Peng, J.Y., Bai, M.Q., Mo, Z.W.: Multicharacters remote rotation sharing with five-particle cluster state. Quantum Information Process. 18, 339 (2019)
Ye, B.L., Liu, Y.M., Liu, X.S., et al.: Remotely sharing a single-qubit operation with a five-qubit genuine state. Chin. Phys. Lett. 30(2), 020301 (2013)
Lo, H.K.: Classical-communication cost in distributed quantum-information processing: a generalization of quantum-communication complexity. Phys. Rev. A 62, 012313 (2000)
Peng, J.Y., Bai, M.Q., Mo, Z.W.: Joint remote state preparation of arbitrary two-particle states via GHZ-type states. Quantum Inf. Process. 12, 2325–2342 (2013)
Nguyen, B.A., Kim, J.: Joint remote state preparation. J. Phys. B At. Mol. Opt. Phys. 41, 095501 (2008)
Peng, J.Y., Bai, M.Q., Mo, Z.W.: Flexible deterministic joint remote state preparation of some states. International Journal of Quantum Information 11, 1350044 (2013)
Shukla, C., Thapliyal, K., Pathak, A.: Hierarchical joint remote state preparation in noisy environment. Quantum Inf. Process. 16, 205 (2017)
Peng, J.Y., Bai, M.Q., Mo, Z.W.: Joint remote state preparation of a four-dimensional quantum stste. Chin. Phys. Lett. 31, 010301 (2014)
Zhang, D., Zha, X.W., Duan, Y., et al.: Deterministic controlled bidirectional remote state preparation via a six-qubit entangled state. Quantum Inf. Process. 15, 2169 (2016)
Peng, J.Y., Bai, M.Q., Mo, Z.W.: Bidirectional controlled joint remote state preparation. Quantum Inf. Process. 14, 4263–4278 (2015)
Peng, J.Y., Bai, M.Q., Mo, Z.W.: Remote informatiom concentration via four-particle cluster state and by positive operator-value measurement. International Journal of Modern Physics B 27, 1350091 (2013)
Peng, J.Y., Bai, M.Q., Mo, Z.W.: Remote information concentration by W state. International Journal of Modern Physics B 27, 1350137 (2013)
Peng, J.Y., Bai, M.Q., Mo, Z.W.: Remote information concentration via W state: reverse of ancilla-free phase-covariant telecloning. Quantum Information Process 12, 3511–3525 (2013)
Bennett, C.H., Brassard, G., Popescu, S., Schumacher, B., Smolin, J.A.K., Wootters, W.: Purification of noisy entanglement and faithful teleportation via noisy channels. Phys. Rev. Lett. 76, 722 (1996)
Sheng, Y.B., Deng, F.G.: Deterministic entandlement purification and complete nonlocal Bell-state analysis with hyperentanglement. Phys. Rev. A 81, 032307 (2010)
Zhou, L., Sheng, Y.B.: Purification of logic-qubit entanglement. Sci. Rep. 6, 28813 (2016)
Bennett, C.H., Divincenzo, D.P., Shor, P.W., et al.: Remote state preparation. Phys. Rev. Lett. 87(7), 077902 (2001)
Devetak, I., Berger, T.: Low-entanglement remote state preparation. Phys. Rev. Lett. 87, 197901 (2001)
Nguyen, B.A., Cao, T.B., Nung, V.D.: Joint remote preparation of four-qubit cluster-type states revisited. J. Phys. B At. Mol. Opt. Phys. 44, 135506 (2011)
Liang, H.Q., Liu, J.M., Feng, S.S., et al.: Effects of noises on joint remote state preparation via a GHZ-class channel. Quantum Inf. Process. 14, 3857 (2015)
Mikami, H., Kobayashi, T.: Remote preparation of qutrit states with biphotons. Phys. Rev. A 75, 022325 (2007)
Wei, J., Shi, L., Zhu, Y., et al.: Deterministic remote preparation of arbitrary multi-qubit equatorial states via two-qubit entangled states. Quantum Inf. Process. 17, 70 (2018)
D. Wang, Hu, Y.D., Wang, Z.Q., Ye, L.: Efficient and faithful remote preparation of arbitrary three- and four-particle W-class entangled states. Quantum Inf. Process. 14, 2015 (2135)
Kurucz, Z., Adam, P., Kis, Z., Janszky, J.: Continuous variable remote state preparation. Phys. Rev. A 72, 052315 (2005)
Xiang, G.Y., Li, J., Yu, B., Guo, G.C.: Remote preparation of mixed states via noisy entanglement. Phys. Rev. A 72, 012315 (2005)
Jeffrey, E., Peters, N.A., Kwiat, P.G.: Towards a periodic deterministic source of arbitrary single-photon states. New J. Phys. 6, 100 (2004)
Wu, W., Liu, W.T., Ou, B.Q., et al.: Remote stste preparatation with classically correlated state. Opt. Commun. 281, 1751 (2008)
Barreiro, J.T., Wei, T.C., Kwiat, P.G.: Remoote preparatation of single-photon hybrid entangled and vector-polarization states. Phys. Rev. Lett. 105, 030407 (2010)
Wang, X., Mo, Z.W.: Bidirectional controlled joint remote state preparation via a seven-qubit entangled state. Int. J. Theor. Phys. 56, 1052 (2017)
Peng, J.Y., Xiang, Y.: Bidirectional remote state preparation in noisy environment assisted by weak measurement. Optics Communications 499, 127285 (2021)
Chen, Y.X., Du, J., Liu, S.Y., et al.: Cyclic quantum teleportation. Quantum Information Processing 16(8), 1–9 (2017)
Zha, X.W., Yu, X.Y., Cao, Y.: Tripartite controlled remote state preparation via a seven-qubit entangled state and three auxiliary particles. International Journal of Theoretical Physics 58, 282–293 (2019)
Peng, J.Y., Lei, H.X.: Cyclic Remote State Preparation. Int. J. Theoretical Phys. 60(8), 1593–1602 (2021)
Sang, Z.W.: Cyclic controlled joint remote preparation by using a ten-qubit entangled state. Int. J. Theoretical Phys. 58, 255–260 (2019)
Zhang, C.Y., Bai, M.Q., Zhou, S.Q.: Cyclic joint remote state preparation in noisy environment. Quantum Inf. Process. 17, 146 (2018)
Sun, S.Y., Zhang, H.S.: Quantum double-direction cyclic controlled communication via a thirteen-qubit entangled state. Quantum Inf. Process. 19, 120 (2020)
Sun, S.Y., Zhang, H.S.: Double-direction quantum cyclic controlled remote stste preparation of two-qubit states. Quantum Inf. Process. 2, 211 (2021)
Jiang, S.X., Zhou, R.G., Xu, R.Q., et al.: Cyclic hybrid double-channel quantum communication via Bell-state and GHZ-state in noisy environments. IEEE Acces 7, 80530–80541 (2019)
Yu, Y., Zhao, N.: General quantum broadcast and multi-cast communications based on entanglemet. Optics Express 26(22), 29296–29310 (2018)
Yu, Y., Zhao, N., Pei, C.X.: Multicast-based multiparty remote state preparation schemes of two-qubit states. Quantum Inf. Process. 18, 319 (2019)
Carmichael, H., An, open quanyum systems: Approach to Quantum Optics. Springer, Berlin (1991)
Breuer, H.P., Petruccione, F.: The theory of open quantum systems. Oxford University Press, Oxford (2006)
Zhang, Y.: Controlled remote preparation of a two-qubit state via an asymmetric quantum channel. Communications in Theoretical Physics 55(2), 244–244 (2011)
Chen, N., Quan, D.X., Xu, F.F., et al.: Deterministic joint remote state preparation of arbitrary single- and two-qubit states. Chinese Phys. B 24, 100307 (2015)
Cao, T.B., Nguyen, V.H., Guyen, N.B.A.: Flexible controlled joint remote preparation of an arbitrary two-qubit state via non-maximally entangled quantum channels. Advances in Natural Sciences: Nanoscience and Nanotechnology 7(2), 025007 (2016)
Yu, Y., Zhao, N., Pei, C.X.: Multicast-based multiparty remote state preparation schemes of two-qubit states. Quantum Inf. Process. 18, 319 (2019)
Zhao, N., Li, W.D., Yu, Y.: Quantum broadcast and multicast schemes based on partially entangled channel. IEEE Access 8, 29658–29666 (2020)
Yu, Y.Y., Zhao, N., Pei, C.X., Wei, L.: Quantum multicast schemes of different quantum states via non-maximally entangled channels with multiparty involvement. Chinese Physics B 30(9), 090302 (2021)
Zhang, Z.J., Yang, J., Man, Z.X., et al.: Multiparty secret sharing of quantum information using and identifying Bell states. Eur. Phys. J. D 33, 133–136 (2005)
Xiao, L., Long, G.L., Deng, F.G., et al.: Efficient multiparty quantum-secret-sharingschemes. Phys. Rev. A 69, 052307 (2004)
Li, C.Y., Li, X.H., Deng, F.G., et al.: Efficient Quantum Cryptography Network without Entanglement and Quantum Memory. Chin. Phys. Lett. 23, 2896–2899 (2006)
Ikram, M., Zhu, S.Y., Zubairy, M.S.: Quantum teleportation of an entangled state. Phys. Rev. A 62, 022307 (2000)
Riebe, M., et al.: Deterministic quantum teleportation with atoms. Nature 429, 734 (2004)
Boschi, D., Branca, S., Martini, F.D., Hardy, L., Popescu, S.: Experimental realization of teleporting an unknown pur quantum state via dual classical and Einstein-Podolsky-Rosen channels, Phys. Rev. Lett. 80, 1121 (1998)
Acknowledgements
This work is supported by the National Natural Science Foundation of China (No. 11071178, No. 11671284), the Comprehensive Professional Reform of Mathematics and Applied Mathematics in the Ministry of Education and Sichuan Province (No.ZG0464), Major frontier project of Sichuan Science and Technology Department (No. 2017JY0197), Fund of Scientific Research and Innovation team of Sichuan Education Department (No. 15TD0027), and Taizhou University high level talents research initiation fund (No. TZXY2017QDJJ011).
Funding
This work is supported by the National Natural Science Foundation of China (No. 11071178, No. 11671284), the Comprehensive Professional Reform of Mathematics and Applied Mathematics in the Ministry of Education and Sichuan Province (No. ZG0464), Major frontier project of Sichuan Science and Technology Department (No. 2017JY0197), Fund of Scientific Research and Innovation team of Sichuan Education Department (No. 15TD0027), and Taizhou University high level talents research initiation fund (No. TZXY2017QDJJ011).
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Peng, Jy., Lei, Hx. Multiparty multicast schemes for remote state preparation of complex coefficient quantum states via partially entangled channels. Int J Theor Phys 61, 130 (2022). https://doi.org/10.1007/s10773-022-05087-w
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DOI: https://doi.org/10.1007/s10773-022-05087-w