No Access
Remarks on the Equivalence of Full Additivity and Monotonicity for the Entanglement Cost
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.
Presented at the 38th Symposium on Mathematical Physics “Quantum Entanglement & Geometry”, Toruń, June 4–7, 2006.
References
- Quant. Inf. Comp. 7, 1 (2007). ISI, Google Scholar
- Quant. Inf. Comp. 1, 3 (2001). Google Scholar
- Quant. Inf. Comp. 1, 45 (2001). ISI, Google Scholar
- Phys. Rev. Lett. 97, 150501 (2006), DOI: 10.1103/PhysRevLett.97.050503. Google Scholar
- E. M. Rains, e-print , arXiv:quant-ph/9707002 . Google Scholar
- Phys. Rev. Lett. 90, 027901 (2003), DOI: 10.1103/PhysRevLett.90.027901. Crossref, ISI, Google Scholar
- Phys. Rev. A 54, 3824 (1996), DOI: 10.1103/PhysRevA.54.3824. Crossref, ISI, Google Scholar
- Phys. Rev. Lett. 80, 2245 (1998), DOI: 10.1103/PhysRevLett.80.2245. Crossref, ISI, Google Scholar
- J. Phys. A 34, 6891 (2001), DOI: 10.1088/0305-4470/34/35/314. Crossref, Google Scholar
- Phys. Rev. A 53, 2046 (1996), DOI: 10.1103/PhysRevA.53.2046. Crossref, ISI, Google Scholar
- Phys. Rev. A 57, 1619 (1998), DOI: 10.1103/PhysRevA.57.1619. Crossref, ISI, Google Scholar
- J. Math. Phys. 45, 829 (2004), DOI: 10.1063/1.1643788. Crossref, ISI, Google Scholar
- J. Phys. A 36, 5605 (2003), DOI: 10.1088/0305-4470/36/20/316. Crossref, Google Scholar
- Phys. Rev. A 64, 062307 (2001), DOI: 10.1103/PhysRevA.64.062307. Crossref, ISI, Google Scholar
- Phys. Rev. A 61, 062312 (2000), DOI: 10.1103/PhysRevA.61.062312. Crossref, ISI, Google Scholar
- Phys. Rev. Lett. 87, 257902 (2001), DOI: 10.1103/PhysRevLett.87.257902. Crossref, ISI, Google Scholar
- Phys. Rev. Lett. 88, 247901 (2002), DOI: 10.1103/PhysRevLett.88.247901. Crossref, ISI, Google Scholar
- Phys. Rev. A 61, 062313 (2000). Crossref, ISI, Google Scholar
- Phys. Rev. Lett. 86, 2681 (2001), DOI: 10.1103/PhysRevLett.86.2681. Crossref, ISI, Google Scholar
- Comm. Math. Phys. 246, 453 (2004), DOI: 10.1007/s00220-003-0981-7. Crossref, ISI, Google Scholar
- Comm. Math. Phys. 246, 427 (2004), DOI: 10.1007/s00220-003-0919-0. Crossref, ISI, Google Scholar
- Comm. Math. Phys. 246, 443 (2004), DOI: 10.1007/s00220-003-0987-1. Crossref, ISI, Google Scholar
- Phys. Rev. Lett. 87, 217902 (2001), DOI: 10.1103/PhysRevLett.87.217902. Crossref, ISI, Google Scholar
- Open Syst. Inf. Dyn. 12, 231 (2005), DOI: 10.1007/s11080-005-0920-5. Link, ISI, Google Scholar
- J. Math. Phys. 43, 4252 (2002), DOI: 10.1063/1.1495917. Crossref, ISI, Google Scholar
-
T. Cover and J. Thomas , Elements of Information Theory ( Wiley , 1991 ) . Crossref, Google Scholar - Phys. Rev. A 61, 064301 (2000), DOI: 10.1103/PhysRevA.61.064301. Crossref, ISI, Google Scholar
- M. Fukuda and M. M. Wolf , arXiv:0704.1092 . Google Scholar
