All inequalities for the relative entropy

Communications in Mathematical Physics

Volumn 269, Issue 1, 2007, Pages 223-238

  Ibinson, Ben ^a   Linden, Noah ^a   Winter, Andreas ^a  

^a UNIVERSITY OF BRISTOL   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33751102113     PISSN: 00103616     EISSN: 14320916     Source Type: Journal    
DOI: 10.1007/s00220-006-0081-6     Document Type: Article

References (25)

1. Benaloh, J., Leichter, J.: Generalising Secret Sharing and Monotone Functions. Advances in Cryptology, CRYPTO 1998, LNCS 403, Berlin: Springer Verlag, 1990, pp. 27-35
2. Bennett, C.H., DiVincenzo, D.P., Smolin, J.A., Wootters, W.K.: Mixed state entanglement and quantum error correction. Phys. Rev. A 54, 3824-3851 (1996)
3. Cerf, N.J., Adami, C.: Negative entropy and information in quantum mechanics. Phys. Rev. Lett. 79, 5194-5197 1997
4. Christandl, M., Winter, A.: Squashed entanglement - An additive entanglement measure. J. Math. Phys. 45(3), 829-840 (2004)
5. Cover, T.M., Thomas, J.A.: Elements of Information Theory. New York Wiley & Sons, 1991
6. nd ed. prepared by V. Kaibel, V. Klee, G. Ziegler, Graduate Texts in Mathematics 221, Berlin: Springer Verlag, 2003
7. Holevo, A.S.: Bounds for the quantity of information transmitted by a quantum channel. Probl. Inform. Transm. 9(3), 177-183 (1973)
8. Ito, M., Saito, A., Nishizeki, T.: Secret Sharing Schemes releasing General Access Structure. In: Proc. IEEE Globecom '87, Berlin-Heidelberg-New York: Springer, 1987, pp. 99-102
9. Lieb, E.H., Ruskai, M.B.: Proof of the strong subadditivity of quantum-mechanical entropy. J. Math. Phys. 14, 1938-1941 (1973)
10. Lindblad, G.: Expectations and entropy inequalities for finite quantum systems. Commun. Math. Phys. 39(2), 111-119 (1974)
11. Lindblad, G.: Completely positive maps and entropy inequalities. Commun. Math. Phys. 40(2), 147-151 (1975)
12. Linden, N., Maneva, E., Massar, S., Popescu, S., Roberts, D., Schumacher, B., Smolin, J.A., Thapliyal, A.V.: In preparation
13. Linden, N., Winter, A.: A new inequality for the von Neumann entropy. Commun. Math. Phys. 259, 129-138 (2005)
14. Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge: Cambridge University Press, 2000
15. Petz, D.: Monotonicity of quantum relative entropy revisited. Rev. Math. Phys. 15(1), 79-91 (2003)
16. Pippenger, N.: The inequalities of quantum information theory. IEEE Trans. Inf. Theory 49(4), 773-789 (2003)
17. Shamir, A.: How to Share a Secret. Commun. ACM 22(11). 612-613 (1979)
18. Stinson, D.R.: An explication of secret sharing schemes. Designs, Codes and Cryptography 2(4), 357-390 (1992)
19. Uhlmann, A.: Relative entropy and the Wigner-Yanase-Dyson-Lieb concavity in an interpolation theory. Commun. Math. Phys. 54, 21-32 (1977)
20. Vedral, V.: The role of relative entropy in quantum information Theory. Rev. Mod. Phys. 74(1), 197-234 (2002)
21. Vedral, V., Plenio, M.B.: Entanglement measures and purification procedures. Phys. Rev. A 57, 1619-1633 (1998)
22. Vedral, V., Plenio, M.B., Rippin, M.A., Knight, P.L.: Quantifying entanglement. Phys. Rev. Lett. 78, 2275-2279 (1996)
23. Yeung, R.W.: A Framework for linear information inequalities. IEEE Trans. Inf. Theory 43(6), 1924-1934 (1997)
24. Yuen, H.P., Ozawa, M.: Ultimate information carrying limit of quantum systems. Phys. Rev. Lett. 70(4), 363-366 (1993)
25. Zhang, Z., Yeung, R.W.: On characterization of entropy function via information inequalities. IEEE Trans. on Inform. Theory 44(4), 1440-1452 (1998)