Correlations in \(n\) -local scenario

详细信息    查看全文

• 作者：Kaushiki Mukherjee ; Biswajit Paul ; Debasis Sarkar
• 关键词：Nonlocal correlation ; Bell inequality ; Bilocality ; n ; Locality
• 刊名：Quantum Information Processing
• 出版年：2015
• 出版时间：June 2015
• 年：2015
• 卷：14
• 期：6
• 页码：2025-2042
• 全文大小：647 KB
• 参考文献：1.Acin, A., Brunner, N., Gisin, N., Massar, S., Pironio, S., Scarani, V.: Device-independent security of quantum cryptography against collective attacks. Phys. Rev. Lett. 98, 230501 (2007)View Article ADS
  2.Mayers, D., Yao, A.: Unconditional security in quantum cryptography, In: Proceedings of the 39th IEEE Symposium on Foundations of Computer Science IEEE Computer Society, p. 503. Los Alamitos (1998)
  3.Pironio, S., Acin, A., Massar, S., de la Giroday, A.B., Matsukevich, D.N., Maunz, P., Olmschenk, S., Hayes, D., Luo, L., Manning, T.A., Monroe, C.: More randomness from noisy sources. Nature 464, 1021 (2010)View Article ADS
  4.Colbeck, R., Kent, A.: Private randomness expansion with untrusted devices. J. Phys. A Math. Theor. 44, 095305 (2011)View Article ADS MathSciNet
  5.Bancal, J.-D., Gisin, N., Liang, Y.-C., Pironio, S.: Device-independent witnesses of genuine multipartite entanglement. Phys. Rev. Lett. 106, 250404 (2011)View Article ADS
  6.Cleve, R., Buhrman, H.: Substituting quantum entanglement for communication. Phys. Rev. A 56, 1201 (1997)View Article ADS
  7.Acin, A., et al.: Device-independent security of quantum cryptography against collective attacks. Phys. Rev. Lett. 98, 230501 (2007)View Article ADS
  8.Briegel, H.-J., et al.: Quantum repeaters: the role of imperfect local operations in quantum communication. Phys. Rev. Lett. 81, 5932 (1998)View Article ADS
  9.Raussendorf, R., Briegel, H.J.: A one-way quantum computer. Phys. Rev. Lett. 86, 5188 (2001)View Article ADS
  10.Bell, J.: Speakable and Unspeakable in Quantum Mechanics, 2nd edn. Cambridge University Press, Cambridge (2004)View Article MATH
  11.Bell, J.S.: On the Einstein Podolsky Rosen paradox. Physics 1, 195 (1964)
  12.Hammerer, K., S酶rensen, A.S., Polzik, E.S.: Quantum interface between light and atomic ensembles. Rev. Mod. Phys. 82, 1041 (2010)View Article ADS
  13.Zukowski, M., et al.: Event-ready-detectors Bell experiment via entanglement swapping. Phys. Rev. Lett. 71, 4287 (1993)View Article ADS
  14.Branciard, C., Gisin, N., Pironio, S.: Characterizing the nonlocal correlations created via entanglement swapping. Phys. Rev. Lett. 104, 170401 (2010)View Article ADS
  15.Fritz, T.: Beyond Bell鈥檚 theorem: correlation scenarios. New J. Phys. 14, 103001 (2012)View Article ADS MathSciNet
  16.Fritz, T.: Beyond Bell鈥檚 theorem II: scenarios with arbitrary causal structure, arXiv:鈥?404.鈥?812 (2014)
  17.Henson, J., Lal, R., Pusey, M.F.: Theory-independent limits on correlations from generalized Bayesian networks. New J. Phys. 16, 113043 (2014)View Article ADS
  18.Tavakoli, A., Skrzypczyk, P., Cavalcanti, D., Acin, A.: Nonlocal correlations in the star-network configuration. Phys. Rev. A 90, 062109 (2014)View Article ADS
  19.Branciard, C., Rosset, D., Gisin, N., Pironio, S.: Bilocal versus non-bilocal correlations in entanglement swapping experiments. Phys. Rev. A 85, 032119 (2012)View Article ADS
  20.Gisin, N., Gisin, B.: A local variable model for entanglement swapping exploiting the detection loophole. Phys. Lett. A 297, 279 (2002)View Article ADS MATH MathSciNet
  21.Greenberger, D.M., Horne, M., Zeilinger, A.: Bell theorem without inequalities for two particles. II. Inefficient detectors. Phys. Rev. A 78, 022111 (2008)View Article ADS MathSciNet
  22.Clauser, J.F., Horne, M.A., Shimony, A., Holt, R.A.: Proposed experiment to test local hidden-variable theories. Phys. Rev. Lett. 23, 880 (1969)View Article ADS
  23.Vertesi, T., Pironio, S., Brunner, N.: Closing the detection loophole in Bell experiments using qudits. Phys. Rev. Lett. 104, 060401 (2010)View Article ADS
  24.Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976)MATH
  25.Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)MATH
  
• 作者单位：Kaushiki Mukherjee (1)
  Biswajit Paul (2)
  Debasis Sarkar (1)
  
  1. Department of Applied Mathematics, University of Calcutta, 92, A.P.C. Road, Kolkata, 700009, India
  2. Department of Mathematics, St.Thomas鈥?College of Engineering and Technology, 4, Diamond Harbour Road, Alipore, Kolkata, 700023, India
  
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Physics
  Mathematics
  Engineering, general
  Computer Science, general
  Characterization and Evaluation Materials
  
• 出版者：Springer Netherlands
• ISSN：1573-1332

文摘

Recently Bell-type inequalities were introduced in Branciard et al. (Phys Rev A 85:032119, 2012) to analyze the correlations emerging in an entanglement swapping scenario characterized by independence of the two sources shared between three parties. The corresponding scenario was referred to as bilocal scenario. Here, we derive Bell-type inequalities in \(n+1\) party scenario, i.e., in \(n\)-local scenario. Considering the two different cases with several number of inputs and outputs, we derive local and \(n\)-local bounds. The \(n\)-local inequality studied for two cases are proved to be tight. Replacing the sources by maximally entangled states for two binary inputs and two binary outputs and also for the fixed input and four outputs, we observe quantum violations of \(n\)-local bounds. But the resistance offered to noise cannot be increased as compared to the bilocal scenario. Thus increasing the number of parties in a linear fashion in source-independent scenario does not contribute in lowering down the requirements of revealing quantumness in a network in contrast to the star configuration (Tavakoli et al. in Phys Rev A 90:062109, 2014) of \(n+1\) parties.