Abstract
We analyse the relationship between the full additivity of the entanglement cost and its full monotonicity under local operations and classical communication. We show that the two properties are equivalent for the entanglement cost. The proof works for the regularization of any convex, subadditive, and asymptotically continuous entanglement monotone, and hence also applies to the asymptotic relative entropy of entanglement.
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Bibliography
Plenio M.B., Virmani S. (2007). Quant. Inf. Comp. 7: 1
Horodecki M. (2001). Quant. Inf. Comp. 1, 3
Horodecki P., Horodecki R. (2001). Quant. Inf. Comp. 1, 45
Masanes Ll. (2006). Phys. Rev. Lett. 97, 150501
E. M. Rains, e-print: arxiv quant-ph/9707002.
Audenaert K., Plenio M.B. (2003). J. Eisert, Phys. Rev. Lett. 90, 027901
Bennett C.H., DiVincenzo D.P., Smolin J.A., Wootters W.K. (1996). Phys. Rev. A 54,3824
Wootters W.K. (1998). Phys. Rev. Lett. 80, 2245
Hayden P., Horodecki M., Terhal B.M. (2001). J. Phys. A 34: 6891
Bennett C.H., Bernstein H., Popescu S., Schumacher B. (1996). Phys. Rev. A 53: 2046
Vedral V., Plenio M.B. (1998). Phys. Rev. A 57: 1619
Christandl M., Winter A. (2004). J. Math. Phys. 45, 829
Eisert J., Audenaert K., Plenio M.B. (2003). J. Phys. A 36: 5605
Vollbrecht K.G.H., Werner R.F. (2001). Phys. Rev. A 64: 062307
DiVincenzo D.P., Shor P.W., Smolin J.A., Terhal B.M., Thapliyal A.V. (2000). Phys. Rev. A 61: 062312
Eggeling T., Vollbrecht K.G.H., Werner R.F., Wolf M.M. (2001). Phys. Rev. Lett. 87: 257902
Vollbrecht K.G.H., Wolf M.M. (2002). Phys. Rev. Lett. 88: 247901
Dür W., Cirac J.I., Lewenstein M., Bruss D. (2000). Phys. Rev. A 61: 062313
Shor P.W., Smolin J.A., Terhal B.M. (2001). Phys. Rev. Lett. 86: 2681
Shor P.W. (2004). Comm. Math. Phys. 246, 453
Matsumoto K., Shimono T., Winter A. (2004). Comm. Math. Phys. 246, 427
Audenaert K.M.R., Braunstein S.L. (2004). Comm. Math. Phys. 246, 443
Audenaert K., Eisert J., Jané E., Plenio M.B., Virmani S., De Moor (2001). B. Phys. Rev. Lett. 87: 217902
Horodecki M. (2005). Open Syst. Inf. Dyn. 12, 231
Donald M., Horodecki M., Rudolph O. (2002). J. Math. Phys. 43: 4252
T. Cover and J. Thomas, Elements of Information Theory, Wiley, 1991.
Nielsen M.A. (2000). Phys. Rev. A 61: 064301
M. Fukuda and M.M. Wolf, arXiv:0704.1092.
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Brandão, F.G.S.L., Horodecki, M., Plenio, M.B. et al. Remarks on the Equivalence of Full Additivity and Monotonicity for the Entanglement Cost. Open Syst Inf Dyn 14, 333–339 (2007). https://doi.org/10.1007/s11080-007-9056-0
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DOI: https://doi.org/10.1007/s11080-007-9056-0