Abstract
Quantum teleportation is a powerful protocol with applications in several schemes of quantum communication, quantum cryptography and quantum computing. The present work shows the required conditions for a two-qubit quantum gate to be deterministically and probabilistically teleported by a quantum gate teleportation scheme using different bases of measurement. Additionally, we present examples of teleportation of two-qubit gates that do not belong to Clifford group as well the limitations of the quantum gate teleportation scheme employing a four-qubit state with genuine four-way entanglement. At last, we provide a general decomposition of Clifford operations.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bennet, C.H., Brassard, G., Crépeau, C., Josza, R., peres, A., Wooters, W.K.: Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels. Phys. Rev. Lett. 70(13), 1895 (1993)
Zhan-Jun, Z., Yu-Min, L., Zhong-Xiao, M.: Many-agent controlled teleportation of multi-qubit quantum information via quantum entanglement swapping. Commun. Theor. Phys. 44(5), 847 (2005)
Chen, L., Lu, H., Chen, W.: Constructing a universal set of quantum gates via probabilistic teleportation. Chin. Opt. Lett. 3(4), 240 (2005)
Gottesman, D., Chuang, I.L.: Quantum teleportation is a universal computational primitive. Nature 402, 390 (1999)
Mendes, F.V., Ramos, R.V.: Schemes for teleportation of quantum gates. Quantum. Inf. Process. 10, 203 (2011)
Huang, Y.-F., Ren, X.-F., Zhang, Y.-S., Duan, L.-M., Guo, G.-C.: Experimental teleportation of a quantum controlled-NOT gate. Phys. Rev. Lett. 93, 240501 (2004)
Slodička, L., Ježek, M., Fiurášek, J.: Experimental demonstration of a teleportation-based programmable quantum gate. Phys. Rev. A 79, 050304R (2009)
Gaoa, W.-B., Goebelb, A.M., Lua, C.-Y., Daia, H.-N., Wagenknechtb, C., Zhanga, Q., Zhaoa, B., Penga, C.-Z., Chena, Z.-B., Chena, Y.-A., Pan, J.-W.: Teleportation-based realization of an optical quantum two-qubit entangling gate. PNAS 107(49), 20869–20874 (2010)
Stenholm, S., Bardroff, P.J.: Teleportation of N-dimensional states. Phys. Rev. A 58, 4373 (1998)
Xi, X.-Q., Hao, S.-R., Hou, B.-Y., Yue, R.H.: Quantum standard teleportation based on generic measurement bases. Commun. Theor. Phys. 40, 415 (2003)
Tucci, R. R.: An introduction to Cartan’s KAK decomposition for QC programmers (2005). arXiv:quant-ph/0507171
Yeo, Y., Chua, W.K.: Teleportation and dense coding with genuine multipartite entanglement. Phys. Rev. Lett. 96, 060502/1-4 (2006)
Backens, M.: The ZX-calculus is complete for stabilizers quantum mechanics (2013). arXiv:quant-ph/13077025
Córcoles, A.D., Gambetta, J.M., Chow, J.M., Smolin, J.: A: process verification of two-qubit quantum gates by randomized benchmarking. Phys. Rev. A 87, 030301 (2013)
Acknowledgments
This work was supported by the Brazilian agency CNPq via Grant No. 303514/2008-6. Also, this work was performed as part of the Brazilian National Institute of Science and Technology for Quantum Information.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Mendes, F.V., Ramos, R.V. On the role of the basis of measurement in quantum gate teleportation. Quantum Inf Process 14, 2323–2343 (2015). https://doi.org/10.1007/s11128-014-0898-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11128-014-0898-4