Abstract
Fusing the idea of short-distance teleportation and remote quantum state preparation (QSP), we first propose a novel deterministic QSP scheme to prepare an arbitrary two-particle state between two participants in a short distance by using a maximally entangled GHZ state as a quantum channel working together with auxiliary in the ground state \(|0\rangle \), wherein this GHZ state is pre-constructed by us via Hadamard gate, controlled-NOT gate and Pauli-X gate. Then, by replacing the maximally entangled GHZ state with a partially entangled GHZ state with real coefficients, we give two probabilistic short-distance QSP schemes to meet the communication demand in the real environment. One of these two schemes is based on projective measurement, and the other is based on positive operator-value measurement (POVM), both of which are extensions of the above ideal scheme. Finally, using our 4-order diagonal phase transformation, the above schemes can be extended to the case of complex coefficient GHZ channels. Our schemes require less entanglement resource, but at the cost of teleportation distance, and so they are the optimal choice for short-distance QSP. From the practical point of view, our schemes are very promising for application of QSP on chip.
Similar content being viewed by others
References
Nielsen, M.A., Chuang, I.L.: Quantum computation and quantum information. Cambridage University Press, Cambridge (2000)
Liu, X.S., Long, 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 supdense coging in the presence of non-Markovian noise. Europhys, Lett. 114, 2881(2016)
Gisin, N., Ribordy, G., Tittel, W., et al.: Quantum cryptography. Rev. Mod. Phys. 74, 145–195 (2002)
Xu, F.X., Chen, W., Wand, S., et al.: Field experiment on a robust hierarchical metroplitan quantum cryptography network. Chin. Sci. Bull. 54, 2991–2997 (2009)
Huang, W.: Improved multiparty quantum key agreement in travelling mode. Sci. Chin. Phys. Mech. Astron. 59(2), 120311(2016)
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, 1895–1899 (1993)
Peng, J.Y., He, Y.: Annular controlled teleportation. Int. J. Theor. Phys. 58, 3271 (2019)
Bouwmeester, D., Pan, J.W., Mattle, K., et al.: Experimental quantum teleportation. Nathre 390, 575 (1997)
Deng, F.G., Li, X.H., Li, C.Y., et al.: Multiparty quantum secret report. Chin. Phys. Lett. 23, 1676–1679 (2006)
Peng, J.Y., Yang, Z., Tangz, L., Peng, J.S.: Controlled quantum broadcast and multi-cast communications of complex coefficient single-qubit states. Quantum Info. Proce. 21, 287 (2022)
Deng, F.G., Long, G.L., Liu, X.S.: Two-step quantum direct communication protocol using the Einstein-Podolsky-Rosen pair block. Phys. Rev. A 68, 042317 (2003)
Wang, C., Deng, F.G., Li, Y.S., et al.: Quantum secure direct communication with high-dimension quantum superdense coding. Phys. Rev. A 71, 044305 (2005)
Peng, J.Y., Bai, M.Q., Mo, Z.W.: Bidirectional quantum states sharing. Int. J. Theor. Phys. 55, 2481–2489 (2016)
Hillery, M., Bužek, 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 |X> state. Chin. Phys. B 23, 010304 (2014)
Abulkasim, H., Hamad, S., Bahnasy, E. K., et al.: Authenticated quantum secret sharing with quantum dialogue based on Bell states. Physica Scripta 91(8), 085101(2016)
Peng, J.Y., Luo, M.X., Mo, Z.W.: Remote infromation concentration via four-particle cluster state and by positive operator-value measurement. Int. J. Mod. Phys. B 27, 1350091 (2013)
Peng, J.Y., Bai, M.Q., Mo, Z.W.: Remote information concentration via W state: rever of ancilla-free phase-covariant teecloning. Quantum Info. Proce. 13, 3511–3525 (2013)
Huelga, S. F., Vaccaro, J. A., Clefles, 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. Int. J. Theor. Phys. 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., Yang, Z., Tang, L., Peng, J.S.: Double-direction cyclic controlled remote implementation of partially known quantum operations. Int. J. Theor. Phys. 61, 256 (2022)
Peng, J.Y., Tang, L., Yang, Z., Lei, H.X., Bai, M.Q.: Many-party comntrolled remote implementations of multiple partially unknown quantum operations. Quantum Info. Proce. 22, 2 (2023)
Peng, J.Y., Bai, M.Q., Mo, Z.W.: Multicharactoers remote rotation sharing with five-particle cluster state. Quantum Infor. Proce. 18, 339 (2019)
Pati, A.K.: Minimum classical bit of for remote preparation and measurement of a qubit. Phys. Rev. A 63, 014302 (2000)
Peng, J.Y.: Remote preparation of general one-, two- and three-qubit states via \(\chi \)-type entangled tates. Int. J. Theor. Phys. 59, 3789–3803 (2020)
Bennett, C. H., Divincenzo, D. P., Shor. P. W., et al.: Remote State Preparation. Phys. Rev. Lett. 87, 077902(2001)
Peng, J. Y., Luo, M. X., Mo, Z. W., et al.: Flexible deterministic joint remote state preparation of some states. Int. J. Quantum Inf. 11(4), 1350044(2013)
Chen, N., Yan, B., Chen, G., Zhang, M. J., Pei, C. X.: Determinstic herarchical joint remote state preparation with six-particle partially entangled state. Chin. Phys. B 27(9) , 090304(2018)
Peng, J. Y., Bai, M. Q., Mo, Z. W.: Joint remote state preparation of a four-dimensional quantum state. Chin. Phys. Lett. 31(1), 010301(2014)
Nguyen, B.A.: Joint remote state prepartation via W and W-type states. Opt. Commun. 283, 4113–4120 (2010)
Peng, J.Y., Luo, M.X., Mo, Z.W.: Joint remote state preparation of arbitrary two-particle states via GHZ-type states. Quantum Info. Proce. 12, 2325–2342 (2013)
Zhang, Z.H., Sun, M.: Enhanced deterministic joint remote state preparation under Pauli channels with memory. Physica Scripta 95, 055107 (2020)
Zhou, K.H., Shi, L., Luo, B.B., Xue, Y., Huang, C., Ma, Z.Q., Wei, J.H.: Deterministic controlled remote state preparation of real-parameter multi-qubit states via maximal slice states. Int. J. Theor. Phys. 58, 4079–4092 (2019)
Nguyen, B.A.: Quantum dialogue. Phys. Lett. A 328, 6–10 (2004)
Leung, D.W., Shor, P.W.: Obliviosr remote stste preparation. Phys. Rev. Lett. 90, 127905 (2003)
Paris, N.G.A., Cola, M., Bonifacio, R.: Remote state preparation and teleportation in phase space. J. Opt. B-Quant. Semiclass. Opt. 5, S360–S364 (2003)
Wang, Z.Y., Liu, Y.M., Zuo, X.Q., Zhang, Z.J.: Controlled remote state preparation. Commun. Theor. Phys. 52, 235–240 (2009)
Peng, J.Y., Bai, M.Q., Tang, L., Yang, Z.: Perfect controlled joint remote state preparation of arbitrary multi-qubit states independent of entanglement degree of the quantum channel. Quantum Info. Proce. 20, 340 (2021)
Peng, J.Y., Bai, M.Q., Mo, Z.W.: Bidirectional controlled joint remote state prepartion. Quantum Infor. Proce. 14, 4263–4278 (2015)
Sun, Y.R., Chen, X.B., Xu, G., Yuan, K.G., Yang, Y.X.: Asymmetric controlled bidirectional remote preparation of two- and three-qubit equatorial state. Sci. Rep. 9, 2081 (2019)
Peng, J.Y., Xiang, Y.: Bidirectional remote state preparation in noisy environment assisted by weak measurement. Optic Communications 499, 127285 (2021)
Sang, Z.W.: Asymmetric bidirectional controlled remote state preparation by using a seven-particle entangled state. Int. J. Theor. Phys. 56, 3209–3212 (2017)
Wang, M.M., Yang, C., Mousoli, R.: Controlled cyclic remote state preparation of arbitrary qubit states. CMC-Comput. Mater. Contin. 55, 321–329 (2018)
Peng, J.Y., Lei, H.X.: Cyclic remote state preparation. Int. J. Theor. Phys. 60(4), 1593–1602 (2021)
Sang, Z.W.: Cyclic controlled joint remote state preparation by using a ten-qubit entangled state. Int. J. Theor. Phys. 58, 255–260 (2019)
Sun, S.Y., Zhang, H.S.: Quantum double-directional cyclic controlled communication via a thirteen-qubit entangled state. Quantum Info. Proce. 19, 120 (2020)
Sun, S.Y., Zhang, H.S.: Double-directional quantum cyclic controlled remote state preparation of two-qubit states. Quantum Inf. Proce. 20, 211 (2021)
Peng, X.H., Zhu, X.W., Fang, X.M., et al.: Experimental implementation of remote state preparation by nuclear magnetic resonance. Phys. Lett. A 306(5–6), 271–276 (2003)
Peters, N.A., Meyers, R.E., Shih, Y., et al.: Remote state preparation: arbitrary remote control of photon polarizations for quantum communication. International Society for Optics and Photonics 5893, 589308 (2005)
Rosenfeld, W., Berner, S., Volz, J., et al.: Remote preparation of an atomic quantum memory. Phys. Rev. Lett. 98(5), 050504(2007)
Peters, N. A., Barreiro, J. T., Goggin, M. E., et al.: Arbitrary remote state preparation of photon polarization. Quantum Electronics and Laser Science Conference (2005)
Cong, S., Kuang, S.: Control theory and methods of quantum systems. Press of University of Science and Technology of China, Hefei (2020)
Ma, P.C., Zhan, Y.B.: Scheme for probabilistic remotely preparing a multi-particle entangled GHZ state. Chin. Phys. B 17(2), 445–450 (2008)
Wei, Z.H., Zha, X.W., Yu, Y.: Efficient schemes of remote state preparation for four-qubit entangled cluster-type state via two non-maximally entangled GHZ-type states. Int. J. Theor. Phys. 56(4), 1–8 (2017)
Chen, W. L., Ma, S. Y., Qu, Z. G.: Controlled remote preparation of an arbitrary four-qubit cluster-type state. Chin. Phys. B 25(10), 100304(2016)
Liu, J., Feng, X., Oh, C. H.: Remote preparation of a three-particle state via positive operator-valued measurement. J. Phys. B-At. Mol. Opt. 42(5),055508(2009)
Wang, Z.Y.: Symmetric remote single-qubit state preparation via positive perator-valued measurement. Int. J. Theor. Phys. 49(6), 1357–1369 (2010)
Song, J. F., Wang, Z. Y.: Controlled remote preparation of a two-qubit state via positive operator-valued measure and two three-qubit entanglements. Int. J. Theor. Phys. 50(8), 2410-2425(2011,)
Zhou, P.: Joint remote preparation of an arbitrary m-qubit state with a pure entangled quantum channel via positive operator-value measurement. J. Phys A-Math. Theor. 45, 215306 (2012)
Gong, R. Z., Wei, Y. Z., Xue, S. B., Jiang, Min.: Joint remote state preparation of an abitrary multi-qubit state in a chain nrtwork. Quantum Info. Proce. 21, 341(2022)
Tan, X.D., Han, J.Q.: Short-distance teleportation of an arbitrary two-qubit state via a Bell state. Int. J. Theor. Phys. 50(60), 1275–1282 (2021)
Xiong, S. Y., Tang, L., Zhang, Q., et al.: The rotation scheme of quantum tates based on EPR pairs. Mod. Phys. Lett. B 36(5), 2150579(2022)
Schoelkopf, R.J., Girvin, S.M.: Wiring up quantum systems. Nature 451, 664–669 (2008)
Steffen, L., et al.: Deterministic quantum teleportation with feed-forward in a solid state system. Nature 500, 319–322 (2013)
Metcalf, B.J., et al.: Quantum teleportation on a photonic chip. Nature Photon. 8, 770–774 (2014)
Acknowledgements
This work is supported by Natural Science Foundation of China (No. 11071178, 11671284), Sichuan Province Education Department Scientific Research Innovation Team Foundation (NO. 15TD0027), and Taizhou University high level talents research initiation fund (No. TZXY2017QDJJ011).
Funding
This work is supported by Natural Science Foundation of China (No. 11071178, 11671284), Sichuan Province Education Department Scientific Research Innovation Team Foundation (NO. 15TD0027), and Taizhou University high level talents research initiation fund (No. TZXY2017QDJJ011).
Author information
Authors and Affiliations
Contributions
All authors contributed to the study conception and design. All authors read and approved the final manuscript.
Corresponding author
Ethics declarations
Conflict of interest
The authors have no relevant financial or non-financial interests to disclose.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Peng, Jy., Lei, Hx. & Liu, M. Short-distance quantum state preparation of an arbitrary two-qubit state via GHZ state. Int J Theor Phys 62, 139 (2023). https://doi.org/10.1007/s10773-023-05380-2
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10773-023-05380-2