Abstract
Analyzing shareability of correlations arising in any physical theory may be considered as a fruitful technique of studying the theory. Our present topic of discussion involves an analogous approach of studying quantum theory. For our purpose, we have deviated from the usual procedure of assessing monogamous nature of quantum correlations in the standard Bell-CHSH scenario. We have considered correlations arising in a quantum network involving independent sources. Precisely speaking, we have analyzed monogamy of nonbilocal correlations by deriving a relation restricting marginals. Interestingly, restrictions constraining distribution of nonbilocal correlations remain same irrespective of whether inputs of the nodal observers are kept fixed (in different bilocal networks) while studying nonbilocal nature of marginal correlations.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Horodecki, R., Horodecki, P., Horodecki, M., Horodecki, K.: Quantum entanglement. Rev. Mod. Phys. 81, 865 (2009)
Bell, J.S.: On the Einstein Podolsky Rosen Paradox. Physics 1, 195 (1964)
Bell, J.: Speakable and Unspeakable in Quantum Mechanics, 2nd edn. Cambridge University Press, Cambridge (2004)
Brunner, N., Cavalcanti, D., Pironio, S., Scarani, V., Wehner, S.: Bell nonlocality. Rev. Mod. Phys. 86, 419 (2014)
Bancal, J.-D., Gisin, N., Liang, Y.-C., Pironio, S.: Device-independent witnesses of genuine multipartite entanglement. Phys. Rev. Lett. 106, 250404 (2011)
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, 230501 (2007)
Barrett, J., Hardy, L., Kent, A.: No signaling and quantum key distribution. Phys. Rev. Lett. 95, 010503 (2005)
Mayers, D., Yao, A.: Proceedings of the 39th IEEE Symposiumon Foundations of Computer Science (IEEE Computer Society, p. 503. Los Alamitos CA, USA (1998p)
Acín, A., Gisin, N., Masanes, L.: From Bell’s theorem to secure quantum key distribution. Phys. Rev. Lett. 97, 120405 (2006)
Brunner, N., Linden, N.: Connection between Bell nonlocality and Bayesian game theory. Nat. Commun. 4, 2057 (2013)
Pironio, S., Acín, A., Massar, S., de la Giroday, A.B., Matsukevich, D.N., Maunz, P., Olmschenk, S., Hayes, D., Luo, L., Manning, T.A., Monroe, C.: Random numbers certified by Bell’s theorem. Nature 464, 1021 (2010)
Colbeck, R., Kent, A.: Private randomness expansion with untrusted devices. J. Phys. A Math. Theor. 44, 095305 (2011)
Toner, B.: Monogamy of non-local quantum correlations. Proc. R. Soc. A 465, 59–69 (2009)
Coffman, V., Kundu, J., Wootters, W.K.: Distributed entanglement. Phys. Rev. A 61, 052306 (2000)
Sadhukhan, D., Roy, S.S., Rakshit, D., Sen, A., Sen, U.: Beating no-go theorems by engineering defects in quantum spin models. New J. Phys. 17, 043013 (2015)
Toner, B., Verstraete, F.: Monogamy of Bell correlations and Tsirelson’s bound, arXiv:quant-ph/0611001
Kurzynski, P., Paterek, T., Ramanathan, R., Laskowski, W., Kaszlikowski, D.: Correlation complementarity yields Bell monogamy relations. Phys. Rev. Lett. 106, 180402 (2011)
Kay, A., Kaszlikowski, D., Ramanathan, R.: Optimal cloning and singlet monogamy. Phys. Rev. Lett. 103, 050501 (2009)
de Oliveira, T.R., Saguia, A., Sarandy, M.S.: Nonviolation of Bell’s inequality in translation invariant systems. Eur. Phys. Lett. 100(6), 60004 (2013)
Osborne, T.J., Verstraete, F.: General monogamy inequality for bipartite qubit entanglement. Phys. Rev. Lett. 96, 220503 (2006)
Seevinck, M.: Classification and monogamy of three-qubit biseparable Bell correlations. Phys. Rev. A 76, 012106 (2007)
Ou, Y.C., Fan, H.: Monogamy inequality in terms of negativity for three-qubit states. Phys. Rev. A 75, 062308 (2007)
Adesso, G., Serafini, A., Illuminati, F.: Multipartite entanglement in three-mode Gaussian states of continuous-variable systems: quantification, sharing structure, and decoherence. Phys. Rev. A 73, 032345 (2006)
Lee, S., Park, J.: Monogamy of entanglement and teleportation capability. Phys. Rev. A 79, 054309 (2009)
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)
Masanes, L., Acin, A., Gisin, N.: General properties of nonsignaling theories. Phys. Rev. A 73, 012112 (2006)
Branciard, C., Gisin, N., Pironio, S.: Characterizing the nonlocal correlations created via entanglement swapping. Phys. Rev. Lett. 104, 170401 (2010)
Branciard, C., Rosset, D., Gisin, N., Pironio, S.: Bilocal versus nonbilocal correlations in entanglement-swapping experiments. Phys. Rev. A 85, 032119 (2012)
Tavakoli, A., Skrzypczyk, P., Cavalcanti, D., Acín, A.: Nonlocal correlations in the star-network configuration. Phys. Rev. A 90, 062109 (2014)
Mukherjee, K., Paul, B., Sarkar, D.: Correlations in n-local scenario. Quantum Inf. Process. 14, 2025 (2015)
Chaves, R.: Polynomial Bell inequalities. Phys. Rev. Lett. 116, 010402 (2016)
Rosset, D., Branciard, C., Barnea, T.J., Putz, G., Brunner, N., Gisin, N.: Nonlinear Bell inequalities tailored for quantum networks. Phys. Rev. Lett. 116, 010403 (2016)
Mukherjee, K., Paul, B., Sarkar, D.: Revealing advantage in a quantum network. Quantum Inf. Process. 15(7), 2895–2921 (2016)
Mukherjee, K., Paul, B., Sarkar, D.: Nontrilocality: exploiting nonlocality from three-particle systems. Phys. Rev. A 96, 022103 (2017)
Tavakoli, A., Renou, M.O., Gisin, N., Brunner, N.: Correlations in star networks: from Bell inequalities to network inequalities. New J. Phys. 119, 073003 (2017)
Andreoli, F., Carvacho, G., Santodonato, L., Chaves, R., Sciarrino, F.: Maximal qubit violation of n-locality inequalities in a star-shaped quantum network. New J. Phys. 19, 113020 (2017)
Gisin, N., Mei, Q., Tavakoli, A., Renou, M.O., Brunner, N.: All entangled pure quantum states violate the bilocality inequality. Phys. Rev. A 96, 020304 (2017)
Marc-Olivier R.Y., Wang, S., Boreiri, S., Beigi, N., Gisin, N.: Limits on Correlations in Networks for Quantum and No-Signaling Resources. Brunner arXiv:1901.08287 [quantph] (2019)
Gisin, N., Gisin, B.: A local variable model for entanglement swapping exploiting the detection loophole. Phys. Lett. A 297, 279 (2002)
Greenberger, D.M., Horne, M., Zeilinger, A., Z̈ukowski, M.: Bell theorem without inequalities for two particles. II. Inefficient detectors. Phys. Rev. A 78, 022111 (2008)
Aćin, A., Cirac, J.I., Lewenstein, M.: Entanglement percolation in quantum networks. Nat. Phys. 3, 256–259 (2007)
Sangouard, N., Simon, C., de Riedmatten, H., Gisin, N.: Quantum repeaters based on atomic ensembles and linear optics. Rev. Mod. Phys. 83, 33 (2011)
Hammerer, K., Sorensen, A.S., Polzik, E.S.: Quantum interface between light and atomic ensembles. Rev. Mod. Phys. 82, 1041 (2010)
Qin, H.H., Fei, S.M., Jost, X.L.: Trade-off relations of Bell violations among pairwise qubit systems. Phys. Rev. A 92, 062339 (2015)
Ekert, A.K.: Quantum cryptography based on Bell’s theorem. Phys. Rev. Lett. 67, 661 (1991)
Barrett, J., Hardy, L., Kent, A.: No signaling and quantum key distribution. Phys. Rev. Lett. 95, 010503 (2005)
Acin, A., Gisin, N., Masanes, L.: From Bell’s theorem to secure quantum key distribution. Phys. Rev. Lett. 97, 120405 (2006)
Ajoy, A., Rungta, P.: Svetlichny’s inequality and genuine tripartite nonlocality in three-qubit pure states. Phys. Rev. A 81, 052334 (2010)
Horodecki, R., Horodecki, P., Horodecki, M.: Violating Bell inequality by mixed states: necessary and sufficient condition. Phys. Lett. A 200, 340 (1995)
Cirelson, B.S.: Quantum generalizations of Bell’s inequality. Lett. Math. Phys. 4, 93 (1980)
Cheng, S., Hall, M.J.W.: Anisotropic invariance and the distribution of quantum correlations. Phys. Rev. Lett. 118, 010401 (2017)
Gong, L.H., Li, J.F., Zhou, N.R.: Continuous variable quantum network dialogue protocol based on single-mode squeezed states. Laser Phys. Lett. 15, 105204 (2018)
Gong, L., Tian, C., Li, J., Zou, X.: Quantum network dialogue protocol based on continuous-variable GHZ states. Quantum Inf. Process. 17, 331 (2018)
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Mukherjee, K., Paul, B. & Sarkar, D. Restricted distribution of quantum correlations in bilocal network. Quantum Inf Process 18, 212 (2019). https://doi.org/10.1007/s11128-019-2328-0
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11128-019-2328-0