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Quantum anonymous voting with unweighted continuous-variable graph states. (English) Zbl 1348.81082

Summary: Motivated by the revealing topological structures of continuous-variable graph state (CVGS), we investigate the design of quantum voting scheme, which has serious advantages over the conventional ones in terms of efficiency and graphicness. Three phases are included, i.e., the preparing phase, the voting phase and the counting phase, together with three parties, i.e., the voters, the tallyman and the ballot agency. Two major voting operations are performed on the yielded CVGS in the voting process, namely the local rotation transformation and the displacement operation. The voting information is carried by the CVGS established before hand, whose persistent entanglement is deployed to keep the privacy of votes and the anonymity of legal voters. For practical applications, two CVGS-based quantum ballots, i.e., comparative ballot and anonymous survey, are specially designed, followed by the extended ballot schemes for the binary-valued and multi-valued ballots under some constraints for the voting design. Security is ensured by entanglement of the CVGS, the voting operations and the laws of quantum mechanics. The proposed schemes can be implemented using the standard off-the-shelf components when compared to discrete-variable quantum voting schemes attributing to the characteristics of the CV-based quantum cryptography.

MSC:

81P40 Quantum coherence, entanglement, quantum correlations
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[1] Nielsen, M.A., Chuang, I.L.: Quantum computation and quantum information. Cambridge University Press, Cambridge (2010) · Zbl 1288.81001 · doi:10.1017/CBO9780511976667
[2] Lucamarini, M., Mancini, S.: Secure deterministic communication without entanglement. Phys. Rev. Lett. 94(14), 140501 (2005) · doi:10.1103/PhysRevLett.94.140501
[3] Hillery, M., Ziman, M., Bužek, V., Bieliková, M.: Towards quantum-based privacy and voting. Phys. Lett. A. 349(1), 75-81 (2006) · Zbl 1195.81032 · doi:10.1016/j.physleta.2005.09.010
[4] Dolev, S., Pitowsky, I., Tamir, B.: A quantum secret ballot. preprint arXiv:quant-ph/0602087 (2006)
[5] Vaccaro, J.A., Spring, J., Chefles, A.: Quantum protocols for anonymous voting and surveying. Phys. Rev. A. 75(1), 012333 (2007) · doi:10.1103/PhysRevA.75.012333
[6] Horoshko, D., Kilin, S.: Quantum anonymous voting with anonymity check. Phys. Lett. A. 375(8), 1172-1175 (2011) · Zbl 1242.81057 · doi:10.1016/j.physleta.2011.01.038
[7] Li, Y., Zeng, G.: Quantum anonymous voting systems based on entangled state. Opt. Rev. 15(5), 219-223 (2008) · doi:10.1007/s10043-008-0034-8
[8] Jiang, L., He, G., Nie, D., Xiong, J., Zeng, G.: Quantum anonymous voting for continuous variables. Phys. Rev. A 85(4), 042309 (2012) · doi:10.1103/PhysRevA.85.042309
[9] Hein, M., Eisert, J., Briegel, H.J.: Multiparty entanglement in graph states. Phys. Rev. A. 69(6), 062311 (2004) · Zbl 1232.81007 · doi:10.1103/PhysRevA.69.062311
[10] Yu, S., Chen, Q., Lai, C.H., Oh, C.H.: Nonadditive quantum error-correcting code. Phys. Rev. Lett. 101(9), 090501 (2008) · Zbl 1228.81145 · doi:10.1103/PhysRevLett.101.090501
[11] Dr, W., Aschauer, H., Briegel, H.J.: Multiparticle entanglement purification for graph states. Phys. Rev. Lett. 91(10), 107903 (2003) · doi:10.1103/PhysRevLett.91.107903
[12] Ghne, O., Tth, G., Hyllus, P., Briegel, H.J.: Bell inequalities for graph states. Phys. Rev. Lett. 95(12), 120405 (2005) · doi:10.1103/PhysRevLett.95.120405
[13] Qian, Y., Shen, Z., He, G., Zeng, G.: Quantum-cryptography network via continuous-variable graph states. Phys. Rev. A. 86(5), 052333 (2012) · doi:10.1103/PhysRevA.86.052333
[14] Guo, Y., Lv, G., Zeng, G.: Balancing continuous-variable quantum key distribution with source-tunable linear optics cloning machine. Quant. Infor. Proces. 14(11), 4323-4338 (2015) · Zbl 1327.81159 · doi:10.1007/s11128-015-1100-3
[15] Braunstein, S.L., van Loock, P.: Quantum information with continuous variables. Rev. Mod. Phys. 77(2), 513-577 (2005) · Zbl 1205.81010 · doi:10.1103/RevModPhys.77.513
[16] Braunstein, S.L., Pati, A.K.: Quantum Information with Continuous Variables. Springer Science and Business Media, Berlin (2012) · Zbl 1013.00018
[17] Zhang, J., Braunstein, S.L.: Continuous-variable Gaussian analog of cluster states. Phys. Rev. A. 73(3), 032318 (2006) · doi:10.1103/PhysRevA.73.032318
[18] van Loock, P., Weedbrook, C., Gu, M.: Building Gaussian cluster states by linear optics. Phys. Rev. A. 76(3), 032321 (2007) · doi:10.1103/PhysRevA.76.032321
[19] Menicucci, N.C., Flammia, S.T., Zaidi, H., Pfister, O.: Ultracompact generation of continuous-variable cluster states. Phys. Rev. A. 76(1), 010302 (2007) · doi:10.1103/PhysRevA.76.010302
[20] Su, X., Tan, A., Jia, X., Zhang, J., Xie, C., Peng, K.: Experimental preparation of quadripartite cluster and Greenberger-Horne-Zeilinger entangled states for continuous variables. Phys. Rev. Lett. 98(7), 070502 (2007) · doi:10.1103/PhysRevLett.98.070502
[21] Yukawa, M., Ukai, R., van Loock, P., Furusawa, A.: Experimental generation of four-mode continuous-variable cluster states. Phys. Rev. A. 78(1), 012301 (2008) · Zbl 1191.81041 · doi:10.1103/PhysRevA.78.012301
[22] Wu, Y., Cai, R., He, G., Zhang, J.: Quantum secret sharing with continuous variable graph state. Quantum Inf. Process. 13(5), 1085-1102 (2014) · Zbl 1291.81124 · doi:10.1007/s11128-013-0713-7
[23] Lau, H.K., Weedbrook, C.: Quantum secret sharing with continuous-variable cluster states. Phys. Rev. A. 88(4), 042313 (2013) · doi:10.1103/PhysRevA.88.042313
[24] Wang, G.Y., Li, T., Deng, F.G.: High-efficiency atomic entanglement concentration for quantum communication network assisted by cavity QED. Quantum Inf. Process. 14(4), 1305-1320 (2015) · Zbl 1328.81051 · doi:10.1007/s11128-015-0938-8
[25] Wang, M., Xiang, Y., He, Q., Gong, Q.: Detection of quantum steering in multipartite continuous-variable Greenberger-Horne-Zeilinger Clike states. Phys. Rev. A. 91(1), 012112 (2015) · doi:10.1103/PhysRevA.91.012112
[26] Menicucci, N.C., Demarie, T.F., Brennen, G.K.: Anonymous broadcasting with a continuous-variable topological quantum code. arXiv preprint arXiv:1503.00717 (2015) · Zbl 1242.81057
[27] Hein, M., Dr, W., Eisert, J., Raussendorf, R., Van den Nest, M., Briegel, H.-J.: Entanglement in graph states and its applications. arXiv preprint arXiv:quant-ph/0602096 (2006)
[28] Guo, Y., Qiu, D., Huang, P., Zeng, G.: Controlling continuous-variable quantum key distribution with tuned linear optics cloning machines. J. Phys. Soc. Jpn. 84, 094003 (2015) · doi:10.7566/JPSJ.84.094003
[29] Wang, M., Sun, Y.: A practical, precise method for frequency tracking and phasor estimation. IEEE Trans. Power Del. 19(4), 1547-1552 (2004) · doi:10.1109/TPWRD.2003.822544
[30] Wang, M., Sun, Y.: A practical method to improve phasor and power measurement accuracy of DFT algorithm. IEEE Trans. Power Del. 21(3), 1054-1062 (2006) · doi:10.1109/TPWRD.2005.858769
[31] Briegel, H.J., Raussendorf, R.: Persistent entanglement in arrays of interacting particles. Phys. Rev. Lett. 86(5), 910 (2001) · doi:10.1103/PhysRevLett.86.910
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