Abstract
In this paper, a cyclic preparation scheme is proposed. In our scheme, Alice, Bob and Charlie can cyclic prepare two-qubit state with the control of David. Firstly, the quantum channel can be constructed by using H, Z and CNOT operations. And we give the circuit diagram of the construction of the quantum channel and the processing of the scheme. Secondly, the participants perform a single-qubit measurement and three two-qubit measurements through appropriate measurement bases. Moreover, the prepared state can be recovered deterministically and all recovery operations are given. Thirdly, we consider our scheme in two noisy environments (amplitude-damping and phase-damping noisy environment). The fidelities of output states are calculated and the effect factors are discussed. Finally, we give some discussions with other schemes. Our scheme has better communication efficiency because it improves the number of quantum state particles transmitted without increasing the classical communication consumption.
Similar content being viewed by others
References
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. 70(13), 1895 (1993)
Lo, H.K.: Classical-communication cost in distributed quantum-information processing: a generalization of quantum-communication complexity. Phys. Rev. A 62, 012313 (2000)
Pati, A.K.: Minimum classical bit for remote preparation and measurement of a qubit. Phys. Rev. A. 6301(1), 4302–4430 (2001)
Bennett, C.H., DiVincenzo, D.P., Shor, P.W., et al.: Remote state preparation. Phys. Rev. Lett. 87(7), 077902(1–4) (2001)
Liu, L.L., Hwang, T.: Controlled remote state preparation protocols via AKLT states. Quantum Inf. Process 13(7), 1639–1650 (2014)
Chen, X.B., Ma, S.Y., Su, Y., et al.: Controlled remote state preparation of arbitrary two and three qubit states via the Brown state. Quantum Inf. Process 11(6), 1653–1667 (2012)
Zhou, K.H., Shi, L., Luo, B.B., et al.: Deterministic controlled remote state preparation of real-parameter multi-qubit states via maximal slice states. Int. J. Theor. Phys. 58, 12 (2019)
Cao, T.B., Nguyen, B.A.: Deterministic controlled bidirectional remote state preparation. Adv. Nat. Sci. Nanosci. Nanotechnol. 5(1), 015003 (2013)
Sun, Y.-R., Chen, Y.L., Ahmad, H., et al.: An asymmetric controlled bidirectional quantum state transmission protocol. Comput. Mater. Contin. (CMC) 59(1), 215–227 (2019)
Sharma, V., Shukla, C., Banerjee, S., et al.: Controlled bidirectional remote state preparation in noisy environment: a generalized view. Quantum Inf. Process 14(9), 3441–3464 (2015)
Sun, Y.-R., Xu, G., Chen, X.-B., et al.: Asymmetric controlled bidirectional remote preparation of single-and three-qubit equatorial state in noisy environment. IEEE Access 7, 2811–2822 (2019)
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(5), 2169–2179 (2016)
Chen, X.-B., Sun, Y.-R., Xu, G., et al.: Controlled bidirectional remote preparation of three-qubit state. Quantum Inf. Process 16(10), 244 (2017)
Song, Y., Ni, J.L., Wang, Z.Y., et al.: Deterministic bidirectional remote state preparation of a-and symmetric quantum states with a proper quantum channel. Int. J. Theor. Phys. 56(10), 3175–3187 (2017)
Sun, Y.-R., Xiang, N., Dou, Z., et al.: A universal protocol for controlled bidirectional quantum state transmission. Quantum Inf. Process 18(9), 281 (2019)
Ma, P.C., Chen, G.B., Li, X.W., et al.: Asymmetric bidirectional controlled remote preparation of an arbitrary four-qubit cluster-type state and a single-qubit state. Quantum Inf. Process 16(12), 308 (2017)
Fang, S., Jiang, M.: A novel scheme for bidirectional and hybrid quantum information transmission via a seven-qubit state. Int. J. Theor. Phys. 57(2), 523–532 (2018)
Sun, Y.-R., Chen, X.-B., Xu, G., et al.: Asymmetric controlled bidirectional remote preparation of two-and three-qubit equatorial state. Sci. Rep. 9(1), 2081 (2019)
Chen, Y.-X., Du, J., Liu, S.-Y., et al.: Cyclic quantum teleportation. Quantum Inf. Process 16, 8 (2017)
Cao, L.Y., Jiang, M., Chen, C.: Joint remote state preparation of an arbitrary eight-qubit cluster-type state. Pramana 94(1), 1–8 (2020)
Choudhury, B.S., Dhara, A.: Joint remote state preparation for two-qubit equatorial states. Quantum Inf. Process. 14(1), 373–379 (2015)
Du, Z.L., Li, X.L.: Deterministic joint remote state preparation of four-qubit cluster type with tripartite involvement. Quantum Inf. Process 19, 10 (2019)
Wei, J.H., Shi, L., Zhao, S.H., et al.: Deterministic joint remote preparation of arbitrary multi-qubit states via three-qubit entangled states. Quantum Inf. Process 18, 8 (2019)
Zhang, Y.Q., Jin, X.R., Zhang, S.: Probabilistic remote preparation of a two-atom entangled state. Chin. Phys. 14(9), 1732 (2005)
Chen, Q.Q., Xia, Y., Song, J.: Probabilistic joint remote preparation of a two-particle high-dimensional equatorial state. Opt. Commun. 284(20), 5031–5035 (2011)
Qian, Y.-J., Xue, S.B., Jiang, M.: Deterministic remote preparation of arbitrary single-qubit state via one intermediate node in noisy environment. Phys. Lett. A 384, 10 (2020)
Luo, M.X., Chen, X.B., Ma, S.Y., et al.: Deterministic remote preparation of an arbitrary W-class state with multiparty. J. Phys. B At. Mol. Opt. Phys. 43(6), 065501 (2010)
Shao, Z.L., Long, Y.X.: Circular controlled quantum teleportation by a genuine seven-qubit entangled state. Int. J. Theor. Phys. 58(6), 1957–1967 (2019)
Wang, M.M., Yang, C., Mousoli, R.: Controlled cyclic remote state preparation of arbitrary qubit states. CMC Comput. Mater. Contin. 55(2), 321–329 (2018)
Zhang, C.Y., Bai, M.-Q., Zhou, S.-Q.: Cyclic joint remote state preparation in noisy environment. Quantum Inf. Process 17(6), 146 (2018)
Sang, Z.-W.: Cyclic controlled joint remote state preparation by using a ten-qubit entangled state. Int. J. Theor. Phys. 58(1), 255–260 (2019)
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 Access 7, 80530–80541 (2019)
Zhou, R.G., Hou, C.Q.: Cyclic and bidirectional quantum teleportation via pseudo multi-qubit states. IEEE Access 7, 42445–42449 (2019)
Shi, J., Zhang, X., Zhu, Y.: Cyclic controlled quantum teleportation using three-dimensional hyper-entangled state. Int. J. Theor. Phys. 58(9), 3036–3048 (2019)
Wu, F., Bai, M.-Q., Zhang, Y.-C., et al.: Cyclic quantum teleportation of an unknown multi-particle high-dimension state. Mod. Phys. Lett. B. 34(5), 2050073 (2020)
Zhang, C.-Y., Bai, M.-Q.: Multi-hop cyclic joint remote state preparation. Int. J. Theor. Phys. 59(4), 1277–1290 (2020)
Gu, J., Hwang, T., Tsai, C.-W.: On the controlled cyclic quantum teleportation of an arbitrary two-qubit entangled state by using a ten-qubit entangled state. Int. J. Theor. Phys. 59(1), 200–205 (2020)
Sun, S.Y., Li, L.X., Zhang, H.S.: Quantum cyclic controlled teleportation of unknown states with arbitrary number of qubits by using seven-qubit entangled channel. Int. J. Theor. Phys. 59(4), 1017–1030 (2020)
Xiao, H., Zhang, Z., Chronopoulos, A.T.: New construction of quantum error avoiding codes via group representation of quantum stabilizer codes. Eur. Phys. J. C 77(10), 667–680 (2017)
Xiao, H., Ni, J., Xie, W., et al.: Construction of quantum turbo product codes based on CSS-type quantum convolutional codes. Int. J. Quantum Inf. 15(1), 1750003(1–14) (2017)
Liang, X.-T.: Classical information capacities of some single qubit quantum noisy channels. Commun. Theor. Phys. 39(5), 37 (2003)
Yuan, H., Liu, Y.M., Zhang, W., et al.: Optimizing resource consumption, operation complexity and efficiency in quantum-state sharing. J. Phys. B At. Mol. Opt. Phys. 41(14), 145506 (2008)
Acknowledgements
This project is supported by the Open Foundation of State key Laboratory of Networking and Switching Technology (Beijing University of Posts and Telecommunications) (SKLNST-2021-1-16) and the National Natural Science Foundation of China (No. 62072404).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Sun, YR., Chen, XB., Shao, J. et al. Cyclic preparation of two-qubit state in two noisy environments. Quantum Inf Process 21, 40 (2022). https://doi.org/10.1007/s11128-021-03373-w
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11128-021-03373-w