×

Secure device-independent quantum bit-wise XOR summation based on a pseudo-telepathy game. (English) Zbl 1508.91120

Summary: We present a device-independent quantum bit-wise XOR summation protocol based on a pseudo-telepathy multi-partite GHZ game proposed by Brassard et al. In this game, \(n\) participants can win the game with certainty with a quantum strategy, but using any classical strategy, they can only win the game with a probability that differs from 1/2 by more than a fraction that is exponentially small in the number of participants. We also analyse the correctness and security of the proposed protocol, showing that it can resist well-known outside and participant attacks.

MSC:

91A81 Quantum games
81P45 Quantum information, communication, networks (quantum-theoretic aspects)
Full Text: DOI

References:

[1] Mayers, D., Yao, A.: In: Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No. 98CB36280). IEEE, pp. 503-509 (1998) · Zbl 0997.68503
[2] Acín, A.; Massar, S.; Pironio, S., Efficient quantum key distribution secure against no-signalling eavesdroppers, New J. Phys., 8, 8, 126 (2006) · doi:10.1088/1367-2630/8/8/126
[3] Acín, A.; Brunner, N.; Gisin, N.; Massar, S.; Pironio, S.; Scarani, V., Device-independent security of quantum cryptography against collective attacks, Phys. Rev. Lett., 98, 23, 230501 (2007) · doi:10.1103/PhysRevLett.98.230501
[4] Pironio, S.; Acin, A.; Brunner, N.; Gisin, N.; Massar, S.; Scarani, V., Device-independent quantum key distribution secure against collective attacks, New J. Phys., 11, 4, 045021 (2009) · doi:10.1088/1367-2630/11/4/045021
[5] McKague, M., Device independent quantum key distribution secure against coherent attacks with memoryless measurement devices, New J. Phys., 11, 10, 103037 (2009) · doi:10.1088/1367-2630/11/10/103037
[6] Masanes, L.; Pironio, S.; Acín, A., Secure device-independent quantum key distribution with causally independent measurement devices, Nat. Commun., 2, 238 (2011) · doi:10.1038/ncomms1244
[7] Barrett, J.; Colbeck, R.; Kent, A., Memory attacks on device-independent quantum cryptography, Phys. Rev. Lett., 110, 1, 010503 (2013) · doi:10.1103/PhysRevLett.110.010503
[8] Lim, CCW; Portmann, C.; Tomamichel, M.; Renner, R.; Gisin, N., Device-independent quantum key distribution with local Bell test, Phys. Rev. X, 3, 3, 031006 (2013)
[9] Vazirani, U.; Vidick, T., Fully device independent quantum key distribution, Commun. ACM, 62, 4, 133-133 (2019) · doi:10.1145/3310974
[10] Kaniewski, J.; Wehner, S., Device-independent two-party cryptography secure against sequential attacks, New J. Phys., 18, 5, 055004 (2016) · doi:10.1088/1367-2630/18/5/055004
[11] Silman, J.; Chailloux, A.; Aharon, N.; Kerenidis, I.; Pironio, S.; Massar, S., Fully distrustful quantum bit commitment and coin flipping, Phys. Rev. Lett., 106, 220501 (2011) · doi:10.1103/PhysRevLett.106.220501
[12] Adlam, E.; Kent, A., Device-independent relativistic quantum bit commitment, Phys. Rev. A, 92, 022315 (2015) · doi:10.1103/PhysRevA.92.022315
[13] Aharon, N.; Massar, S.; Pironio, S.; Silman, J., Device-independent bit commitment based on the CHSH inequality, New J. Phys., 18, 2, 025014 (2016) · Zbl 1456.81119 · doi:10.1088/1367-2630/18/2/025014
[14] Ribeiro, J.; Thinh, LP; Kaniewski, JMK; Helsen, J.; Wehner, S., Device independence for two-party cryptography and position verification with memoryless devices, Phys. Rev. A, 97, 062307 (2018) · doi:10.1103/PhysRevA.97.062307
[15] Zhou, L.; Sheng, YB; Long, GL, Device-independent quantum secure direct communication against collective attacks, Sci. Bull., 65, 1, 12 (2020) · doi:10.1016/j.scib.2019.10.025
[16] Roy, S.; Mukhopadhyay, S., Device independent quantum secret sharing in arbitrary even dimension, Phys. Rev. A, 100, 1, 012319 (2019) · doi:10.1103/PhysRevA.100.012319
[17] Brassard, G., Broadbent, A., Tapp, A.: In: WADS (2003)
[18] Boyer, M.:Extended GHZ n-player games with classical probability of winning tending to 0, eprint. arXiv:quant-ph/0408090v4 (2004)
[19] Heinrich, S., Quantum summation with an application to integration, J. Complex., 18, 1, 1 (2002) · Zbl 1050.68043 · doi:10.1006/jcom.2001.0629
[20] Heinrich, S.; Novak, E., On a problem in quantum summation, J. Complex., 19, 1, 1 (2003) · Zbl 1051.68066 · doi:10.1016/S0885-064X(02)00003-1
[21] Heinrich, S., Kwas, H., Wozniakowski, M.: Quantum Boolean summation with repetitions in the worst-average setting. arXiv:quant-ph/0311036 (2003) · Zbl 1044.65003
[22] Du, JZ; Chen, XB; Wen, QY; Zhu, FC, Secure multiparty quantum summation, Acta Phys. Sin., 56, 11, 6214 (2007) · doi:10.7498/aps.56.6214
[23] Chen, XB; Xu, G.; Yang, YX; Wen, QY, An efficient protocol for the secure multi-party quantum summation, Int. J. Theor. Phys., 49, 11, 2793 (2010) · Zbl 1203.81047 · doi:10.1007/s10773-010-0472-5
[24] Lo, HK, Insecurity of quantum secure computations, Phys. Rev. A, 56, 1154 (1997) · doi:10.1103/PhysRevA.56.1154
[25] Crépeau, C., Gottesman, D., Smith, A.: In: Proceedings of the Thiry-Fourth Annual ACM Symposium on Theory of Computing (ACM, 2002), pp. 643-652
[26] Chau, HF, Quantum-classical complexity-security tradeoff in secure multiparty computations, Phys. Rev. A, 61, 032308 (2000) · doi:10.1103/PhysRevA.61.032308
[27] Ben-Or, M., Crepeau, C., Gottesman, D., Hassidim, A., Smith, A.: In: 47th Annual IEEE Symposium on Foundations of Computer Science, 2006. FOCS’06. IEEE, pp. 249-260 (2006)
[28] Smith, A.: Multi-party Quantum Computation. arXiv:quant-ph/0111030 (2010)
[29] Zhang, C.; Sun, Z.; Huang, Y.; Long, D., High-capacity quantum summation with single photons in both polarization and spatial-mode degrees of freedom, Int. J. Theor. Phys., 53, 3, 933 (2014) · Zbl 1284.81079 · doi:10.1007/s10773-013-1884-9
[30] Zhang, C.; Sun, ZW; Huang, X.; Long, DY, Three-party quantum summation without a trusted third party, Int. J. Quantum Inf., 13, 2, 1550011 (2015) · Zbl 1328.81076 · doi:10.1142/S0219749915500112
[31] Zhang, C.; Situ, H.; Huang, Q.; Yang, P., Multi-party quantum summation without a trusted third party based on single particles, Int. J. Quantum Inf., 15, 1, 1750010 (2017) · Zbl 1375.81079 · doi:10.1142/S0219749917500101
[32] Shi, RH; Mu, Y.; Zhong, H.; Cui, J.; Zhang, S., Sci. Rep., 6, 19655 (2016) · doi:10.1038/srep19655
[33] Shi, RH; Zhang, S., Secure multiparty quantum computation for summation and multiplication, Quantum Inf. Process., 16, 9, 225 (2017) · Zbl 1387.81193 · doi:10.1007/s11128-017-1676-x
[34] Liu, W.; Wang, YB; Fan, WQ, An novel protocol for the quantum secure multi-party summation based on two-particle bell states, Int. J. Theor. Phys., 56, 9, 2783 (2017) · Zbl 1379.81039 · doi:10.1007/s10773-017-3442-3
[35] Yang, HY; Ye, TY, Secure multi-party quantum summation based on quantum Fourier transform, Quantum Inf. Process., 17, 6, 129 (2018) · Zbl 1448.81176 · doi:10.1007/s11128-018-1890-1
[36] Ramzan, M., Three-player quantum Kolkata restaurant problem under decoherence, Quantum Inf. Process., 12, 1, 577 (2013) · Zbl 1263.81091 · doi:10.1007/s11128-012-0405-8
[37] Sharif, P., Heydari, H.: In: AIP Conference Proceedings (American Institute of Physics, 2012), pp. 492-496
[38] Kastampolidou, K., Papalitsas, C., Andronikos, T.: DKPRG or how to succeed in the kolkata paise restaurant gamevia TSP. arXiv preprint arXiv:2101.07760 (2021) · Zbl 1501.91018
[39] Šupić, I.; Coladangelo, A.; Augusiak, R.; Acín, A., Self-testing multipartite entangled states through projections onto two systems, New J. Phys., 20, 8, 083041 (2018) · doi:10.1088/1367-2630/aad89b
[40] Breiner, S., Kalev, A., Miller, C.A.: Parallel self-testing of the GHZ state with a proof by diagrams. arXiv preprint arXiv:1806.04744 (2018) · Zbl 1486.81058
[41] Hoeffding, W.: In: The Collected Works of Wassily Hoeffding (Springer, 1994), pp. 409-426 · Zbl 0807.01034
[42] Serfling, R.J.: Probability inequalities for the sum in sampling without replacement. Ann. Stat, pp. 39-48 (1974) · Zbl 0288.62005
[43] Cavalcanti, D.; Brandão, FG; Cunha, MT, Are all maximally entangled states pure?, Phys. Rev. A, 72, 4, 040303 (2005) · doi:10.1103/PhysRevA.72.040303
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.