Squashed entanglement for multipartite states and entanglement measures based on the mixed convex roof

IEEE Transactions on Information Theory

Volumn 55, Issue 7, 2009, Pages 3375-3387

  Yang, Dong ^a   Horodecki, Karol ^b,c   Horodecki, Michał ^b   Horodecki, Paweł ^d   Oppenheim, Jonathan ^e   Song, Wei ^f,g  

^a CHINA JILIANG UNIVERSITY   (China)

^b UNIVERSITY OF GDA SK   (Poland)

^c UNIVERSITY OF WARSAW   (Poland)

^d GDANSK UNIVERSITY OF TECHNOLOGY   (Poland)

^e UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^f UNIVERSITY OF SCIENCE AND TECHNOLOGY OF CHINA   (China)

^g SOUTH CHINA NORMAL UNIVERSITY   (China)

Author keywords

C squashed entanglement; Mixed convex roof; Multipartite distillable key; Squashed entanglement

Indexed keywords

A-DENSITY; ADDITIVITY; C-SQUASHED ENTANGLEMENT; ENTANGLEMENT MEASURE; KEY AGREEMENT; MIXED CONVEX ROOF; MULTIPARTITE DISTILLABLE KEY; MULTIPARTITE ENTANGLEMENTS; MULTIPARTITE STATE; MUTUAL INFORMATIONS; PURE STATE; SQUASHED ENTANGLEMENT; UPPER BOUND;

ROOFS;

CORRELATION THEORY;

EID: 67650122783     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2009.2021373     Document Type: Article

References (37)

1. R. Tucci, Entanglement of Distillation and Conditional Mutual Information ArXiv: Quant-ph/0202144.
2. M. Christandl and A. Winter, "Squashed entanglements - An additive entanglement measure," J. Math. Phys., vol. 45, pp. 829-829, 2003.
3. G. Lindblad, "Entropy, information and quantum measurements," Commun. Math. Phys., vol. 33, pp. 111-119, 1973.
4. R. Horodecki, "Informationally coherent quantum systems," Phys. Lett. A, vol. 187, pp. 145-150, 1993.
5. N. J. Cerf, S. Massar, and S. Schneider, "Multipartite classical and quantum secrecy monotones," Phys. Rev. A, vol. 66, pp. 042309-042309, 2002.
6. A. Uhlmann, "Entropy and optimal decompositions of states relative to a maximal commutative subalgebra," Open Sys. Inf. Dyn., vol. 5, pp. 209-209, 1998.
7. M. Christandl, "The Quantum Analog to Intrinsic Information," Diploma, Institute for Theoretical Computer Science, ETH Zurich, Zurich, Switzerland, 2002.
8. B. Synak-Radtke and M. Horodecki, "On asymptotic continuity of functions of quantum states," J. Phys. A, vol. 39, pp. L423-L423, 2006.
9. D. Yang, M. Horodecki, R. Horodecki, and B. Synak-Radtke, "Irreversibility for all bound entangled states," Phys. Rev. Lett. vol. 95, pp. 190501-190501, 2005.
10. O. Nagel and G. Raggio, Another State Entanglement Measure ArXiv: quant-ph/0306024.
11. R. Alicki and M. Fannes, "Continuity of conditional quantum mutual information," J. Phys. A, vol. 37, pp. L55-L57, 2004.
12. M. Christandl, A. Ekert, M. Horodecki, P. Horodecki, J. Oppenheim, and R. Renner, On Distillation of Classical Key From Quantum States quant-ph/ 0608199.
13. R. Augusiak and P. Horodecki, "Multipartite Key Distillation and Bound Entanglement," 2007, arXiv:0811.3603.
14. T. M. Cover and J. A. Thomas, Elements of Information Theory. New York: Wiley, 1991.
15. G. Lindblad, "Completely positive maps and entropy inequalities," Commun. Math. Phys., vol. 40, pp. 147-147, 1975.
16. A. Uhlmann, "Relative entropy and the Wigner-Yanase-Dyson-Lieb concavity in an interpolation theory," Commun. Math. Phys., vol. 54, pp. 21-32, 1977.
17. M. Horodecki, J. Oppenheim, and A. Winter, "Partial quantum information," Nature, vol. 436, pp. 673-673, 2005.
18. M. Horodecki, "Simplifying monotonicity conditions for entanglement measures," Open Sys. Inf. Dyn., vol. 12, pp. 231-231, 2005.
19. J. Oppenheim, A Paradigm for Entanglement Theory Based on Quantum Communication arXiv:0801.0458.
20. D. Avis, P. Hayden, and I. Savov, "Distributed compression and multiparty squashed entanglement," J. Phys. A, vol. 41, 2008.
21. M. A. Nielsen, "Continuity bounds on entanglement of formation," Phys. Rev. A, vol. 61, pp. 064301-064301, 2000.
22. G. Vidal, "Entanglement monotones," J. Mod. Opt., vol. 47, pp. 355-355, 2000.
23. D. P. DiVincenzo, M. Horodecki, D. W. Leung, J. A. Smolin, and B. M. Terhal, "Locking classical correlations in quantum states," Phys. Rev. Lett., vol. 92, pp. 067902-067902, 2004.
24. K. Horodecki, M. Horodecki, P. Horodecki, and J. Oppenheim, "Locking entanglement with a single qubit," Phys. Rev. Lett., vol. 94, pp. 200501-200501, 2005.
25. R. Koenig, R. Renner, A. Bariska, and U. Maurer, "Locking of accessible information and implications for the security of quantum cryptography," Phys. Rev. Lett., vol. 98, pp. 140502-140502, 2007.
26. M. Christandl and A.Winter, "Uncertainty, monogamy, and locking of quantum correlations," IEEE Trans. Inf. Theory, vol. 51, 2005.
27. F. Brandao, "Entanglement Theory and the Quantum Simulation of Many-Body Physics," Ph.D., Imperial College, London, U.K., 2008.
28. M. Christandl, "The Structure of Bipartite Quantum States - Insights From Group Theory and Cryptography," Ph.D., Univ. Cambridge, Cambridge, U.K., 2006.
29. U. M. Maurer, "Secret key agreement by public discussion from common information," IEEE Trans. Inf. Theory, vol. 39, pp. 773-773, 1993.
30. A. D. Wyner, "The wire-tap channel," Bell System Technical Journal vol. 54, pp. 1355-1355, 1975.
31. I. Csisźar and J. Körner, "Broadcast channels with confidential messages," IEEE Trans. Inf. Theory, vol. 24, pp. 339-348, 1978.
32. P. Horodecki and R. Augusiak, Quantum States Representing Perfectly Secure Bits are Always Distillable ArXiv: Quant-ph/0602176.
33. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information. Cambridge, U.K.: Cambridge Univ. Press, 2000.
34. M. Fannes, "A continuity property of the entropy density for spin lattice systems," Commun. Math. Phys., vol. 31, 1973.
35. I. Devetak and A. Winter, "Distillation of secret key and entanglement from quantum states," Proc. R. Soc. Lond. A, vol. 461, 2005.
36. M. Christandl, R. Renner, and S. Wolf, "A property of the intrinsic mutual information," in Proc. Int. Symp. Inf. Theory (ISIT), 2003.
37. R. Renner and S. Wolf, "New bounds in secret-key agreement: The gap between formation and secrecy extraction," in Proc. Adv. Cryptology - EUROCRYPT '03, Lecture Notes in Computer Sci., 2003.