Quantum random networks

Nature Physics

Volumn 6, Issue 7, 2010, Pages 539-543

  Perseguers, S ^a   Lewenstein, M ^b,c   Acin A ^b,c   Cirac, J I ^a  

^a MAX PLANCK INSTITUT FÜR QUANTENOPTIK   (Germany)

^b ICFO INSTITUT DE CIENCIES FOTONIQUES   (Spain)

^c INSTITUCIÓ CATALANA DE RECERCA I ESTUDIS AVANÇATS ICREA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

GRAPH THEORY;

CLASSICAL RANDOM GRAPHS; COMPUTATIONAL TASK; CRITICAL PROBABILITIES; CRYPTOGRAPHIC PROTOCOLS; ENTANGLED STATE; LOCAL OPERATIONS AND CLASSICAL COMMUNICATIONS; QUANTUM NETWORK; SUPERPOSITION PRINCIPLE;

QUANTUM ENTANGLEMENT;

EID: 77954348574     PISSN: 17452473     EISSN: 17452481     Source Type: Journal    
DOI: 10.1038/nphys1665     Document Type: Article

References (30)

1. Kimble, H. J. The quantum Internet. Nature 453, 1023-1030 (2008).
2. Gisin, N. & Thew, R. Quantum communication. Nature Photon. 1, 165-171 (2007).
3. Bennett, C. H. & Brassard, G. in Proc. IEEE Int. Conf. on Computers, Systems and Signal Processing 175-179 (IEEE, 1984).
4. Perseguers S. Entanglement Distribution in Quantum Networks. PhD thesis, Technische Univ. München (2010).
5. Bennett, C. H. et al. Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys. Rev. Lett. 70, 1895-1899 (1993).
6. Ekert, A. K. Quantum cryptography based on Bell's theorem. Phys. Rev. Lett. 67, 661-663 (1991).
7. Bennett, C. H. & Wiesner, S. J. Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states. Phys. Rev. Lett. 69, 2881-2884 (1992).
8. Hillery, M., Buek, V. & Berthiaume, A. Quantum secret sharing. Phys. Rev. A 59, 1829-1834 (1999).
9. Acín, A., Cirac, J. I. & Lewenstein, M. Entanglement percolation in quantum networks. Nature Phys. 3, 256-259 (2007).
10. Perseguers, S., Cirac, J. I., Acín, A., Lewenstein, M. & Wehr, J. Entanglement distribution in pure-state quantum networks. Phys. Rev. A 77, 022308 (2008).
11. Erd s, P. & Rényi, A. On random graphs. Publ. Math. Debrecen 6, 290-297 (1959).
12. Erd s, P. & Rényi, A. On the evolution of random graphs. Publ. Math. Inst. Hung. Acad. Sci. 5, 17-61 (1960).
13. Erd s, P. & Rényi, A. On the evolution of random graphs. II. Bull. Inst. Int. Stat. 38, 343-347 (1961).
14. Kochen, M. The Small World (Ablex, 1989).
15. Watts, D. J. & Strogatz, S. H. Collective dynamics of small-world networks. Nature 393, 440-442 (1998).
16. Barabási, A-L. & Albert, R. Emergence of scaling in random networks. Science 286, 509-512 (1999).
17. Bollobás, B. Random Graphs (Academic, 1985).
18. Werner, R. F. Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model. Phys. Rev. A 40, 4277-4281 (1989).
19. Nielsen, M. A. Conditions for a class of entanglement transformations. Phys. Rev. Lett. 83, 436-439 (1999).
20. Vidal, G. Entanglement of pure states for a single copy. Phys. Rev. Lett. 83, 1046-1049 (1999).
21. Bennett, C. H. et al. Purification of noisy entanglement and faithful teleportation via noisy channels. Phys. Rev. Lett. 76, 722-725 (1996).
22. Hastings, M. B. Superadditivity of communication capacity using entangled inputs. Nature Phys. 5, 255-257 (2009).
23. Greenberger, D. M., Horne, M. A. & Zeilinger, A. Bell's Theorem, Quantum Theory, and Conceptions of the Universe (Kluwer Academics, 1989).
24. Nielsen, M. A. & Chuang, I. L. Quantum Computation and Quantum Information (Cambridge Univ. Press, 2000).
25. Bollobás, B. Degree sequences of random graphs. Discrete Math. 33, 1-19 (1981).
26. Kraus, B.&Cirac, J. I. Discrete entanglement with squeezed light. Phys. Rev. Lett. 92, 013602 (2004).
27. Bornholdt, S. & Schuster, H. G. Handbook of Graphs and Networks: From the Genome to the Internet (Wiley-VCH, 2003).
28. Watts, D. J. Small Worlds: The Dynamics of Networks Between Order and Randomness (Princeton Univ. Press, 2004).
29. Newman, M., Barabási, A-L. & Watts, D. J. The Structure and Dynamics of Networks (Princeton Univ. Press, 2006).
30. Albert, R. & Barabási, A-L. Statistical mechanics of complex networks. Rev. Mod. Phys. 74, 47-97 (2002).