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Abstract

Understanding entanglement and nonlocal correlations is one of the most relevant challenges in quantum information.

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References

  1. R. Augusiak, J. Tura, M. Lewenstein, A note on the optimality of decomposable entanglement witnesses and completely entangled subspaces. J. Phys. A Math. Theor., 44(21), 212001 (2011). doi:10.1088/1751-8113/44/21/212001, Featured with insights. Editor’s choice: Highlights of 2011

  2. R. Augusiak, J. Tura, J. Samsonowicz, M. Lewenstein, Entangled symmetric states of N qubits with all positive partial transpositions. Phys. Rev. A, 86(4), 042316 (2012). doi:10.1103/PhysRevA.86.042316

  3. R. Augusiak, J. Bae, J. Tura, M. Lewenstein, Checking the optimality of entanglement witnesses: an application to structural physical approximations. J. Phys. A Math. Theo., 47(6), 065301 (2014). doi:10.1088/1751-8113/47/6/065301, Editor’s choice: Highlights of 2014

  4. R. Augusiak, M. Demianowicz, M. Pawłowski, J. Tura, A. Acín, Elemental and tight monogamy relations in nonsignaling theories. Phys. Rev. A, 90(5), 052323 (2014). doi:10.1103/PhysRevA.90.052323

  5. R. Augusiak, M. Demianowicz, J. Tura, A. Acín, Entanglement and nonlocality are inequivalent for any number of parties. Phys. Rev. Lett., 115(3), 030404 (2015). doi:10.1103/PhysRevLett.115.030404

  6. J.-D. Bancal, N. Gisin, S. Pironio, Looking for symmetric bell inequalities. J. Phys. A Math. Theo., 43(38), 385303 (2010). doi:10.1088/1751-8113/43/38/385303

  7. G. Blekherman, P.A. Parrilo, R.R. Thomas, Semidefinite Optimization and Convex Algebraic Geometry, Chap. 0, i–xix. doi:10.1137/1.9781611972290

  8. D.E. Chang, J.I. Cirac, H.J. Kimble, Self-organization of atoms along a nanophotonic waveguide. Phys. Rev. Lett., 110(11), 113606 (2013). doi:10.1103/PhysRevLett.110.113606

  9. R.H. Dicke, Coherence in spontaneous radiation processes. Phys. Rev., 93(1), 99–110 (1954). doi:10.1103/PhysRev.93.99

  10. K. Eckert, J. Schliemann, D. Bruß, M. Lewenstein, Quantum correlations in systems of indistinguishable particles. Ann. Phys., 299(1), 88–127 (2002). ISSN: 0003-4916. doi:10.1006/aphy.2002.6268

  11. N. Gisin, Hidden quantum nonlocality revealed by local filters. Phys. Lett. A, 210(3), 151–156 (1996). ISSN: 0375-9601. doi:10.1016/S0375-9601(96)80001-6

  12. T. Graß, M. Lewenstein, Trapped-ion quantum simulation of tunable-range Heisenberg chains. EPJ Quantum Technol., 1(1), 8 (2014). ISSN: 2196-0763. doi:10.1140/epjqt8

  13. J. Gouveia, R.R. Thomas, Chapter 7: Spectrahedral Approximations of Convex Hulls of Algebraic Sets. Semidefinite Optim. Convex Algebr. Geom., chap. 7, 293–340. doi:10.1137/1.9781611972290.ch7

  14. F. Hirsch, M.T. Quintino, J. Bowles, N. Brunner, Genuine hidden quantum nonlocality. Phys. Rev. Lett., 111(16), 160402 (2013). doi:10.1103/PhysRevLett.111.160402

  15. J. M. Leinaas, J. Myrheim, E. Ovrum, Extreme points of the set of density matrices with positive partial transpose. Phys. Rev. A, 76(3), 034304 (2007). doi:10.1103/PhysRevA.76.034304

  16. B. Lücke, J. Peise, G. Vitagliano, J. Arlt, L. Santos, G. Tóth, C. Klempt, Detecting multiparticle entanglement of dicke states. Phys. Rev. Lett., 112(15), 155304 (2014). doi:10.1103/PhysRevLett.112.155304

  17. W. Muessel, H. Strobel, D. Linnemann, D.B. Hume, M.K. Oberthaler, Scalable spin squeezing for quantum-enhanced magnetometry with Bose-Einstein condensates. Phys. Rev. Lett., 113(10), 103004 (2014). doi:10.1103/PhysRevLett.113.103004

  18. C. Palazuelos, Superactivation of quantum nonlocality. Phys. Rev. Lett., 109(19), 190401 (2012). doi:10.1103/PhysRevLett.109.190401

  19. D. Porras, J.I. Cirac, Effective quantum spin systems with trapped ions. Phys. Rev. Lett., 92(20), 207901 (2004). doi:10.1103/PhysRevLett.92.207901

  20. M. Perarnau-Llobet, K.V. Hovhannisyan, M. Huber, P. Skrzypczyk, J. Tura, A. Acín, Most energetic passive states. Phys. Rev. E, 92(4), 042147 (2015). doi:10.1103/PhysRevE.92.042147

  21. S. Popescu, Bell’s inequalities and density matrices: revealing “hidden” nonlocality. Phys. Rev. Lett., 74(14), 2619–2622 (1995). doi:10.1103/PhysRevLett.74.2619

  22. N. Schuch, J.I. Cirac, Matrix product state and mean-field solutions for one-dimensional systems can be found efficiently. Phys. Rev. A, 82(1), 012314 (2010). doi:10.1103/PhysRevA.82.012314

  23. J. Tura, R. Augusiak, P. Hyllus, M. Kuś, J. Samsonowicz, M. Lewenstein, Four-qubit entangled symmetric states with positive partial transpositions. Phys. Rev. A, 85(6), 060302 (2012). doi:10.1103/PhysRevA.85.060302, Published as a Rapid Communication

  24. J. Tura, R. Augusiak, A.B. Sainz, T. Vértesi, M. Lewenstein, A. Acín, Detecting nonlocality in many-body quantum states. Science, 344(6189), 1256–1258 (2014). doi:10.1126/science.1247715

  25. J. Tura, A.B. Sainz, T. Vértesi, A. Acín, M. Lewenstein, R. Augusiak, Translationally invariant multipartite Bell inequalities involving only two-body correlators. J. Phys. A Math. Theo., 47(42), 424024 (2014). doi:10.1088/1751-8113/47/42/424024, Part of the special issue 50 years of Bell’s Theorem

  26. J. Tura, A.B. Sainz, T. Graß, R. Augusiak, A. Acín, M. Lewenstein, Entanglement and nonlocality in many-body systems: a primer. Proc. Int. Sch. Phys. “Enrico Fermi” 191(1), 505–535 (2015). doi:10.3254/978-1-61499-694-1-505, Course 191 - Quantum Matter at Ultralow Temperatures

  27. J. Tura, R. Augusiak, A.B. Sainz, B. Lücke, C. Klempt, M. Lewenstein, A. Acín, Nonlocality in many-body quantum systems detected with two-body correlators. Ann. Phys., 362, 370–423 (2015). ISSN: 0003-4916. doi:10.1016/j.aop.2015.07.021

  28. J.W. Britton, B.C. Sawyer, A.C. Keith, C.-C.J. Wang, J.K. Freericks, H. Uys, M.J. Biercuk, J.J. Bollinger, Engineered two-dimensional Ising interactions in a trapped-ion quantum simulator with hundreds of spins. Nature, 484(7395), 489492 (2012). ISSN: 0028-0836. doi:10.1038/nature10981

  29. D. Cavalcanti, M.L. Almeida, V. Scarani, A. Acín, Quantum networks reveal quantum nonlocality. Nat. Commun., 2(184), (2011). doi:10.1038/ncomms1193

  30. K. Eckert, O. Romero-Isart, M. Rodriguez, M. Lewenstein, E.S. Polzik, A. Sanpera, Quantum nondemolition detection of strongly correlated systems. Nat. Phys., 4(1), 5054 (2008). ISSN: 1745-2473. doi:10.1038/nphys776

  31. M. Napolitano, M. Koschorreck, B. Dubost, N. Behbood, R.J. Sewell, M.W. Mitchell, Interaction-based quantum metrology showing scaling beyond the Heisenberg limit. Nature, 471(7339), 86489 (2011). ISSN: 0028-0836. doi:10.1038/nature09778

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Tura i Brugués, J. (2017). Conclusions and Outlook. In: Characterizing Entanglement and Quantum Correlations Constrained by Symmetry. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-49571-2_7

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