On the Schmidt robustness of pure states

Journal of Physics A: Mathematical and General

Volumn 39, Issue 16, 2006, Pages 4239-4249

  Clarisse, Lieven ^a  

^a UNIVERSITY OF YORK   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33645680221     PISSN: 03054470     EISSN: 13616447     Source Type: Journal    
DOI: 10.1088/0305-4470/39/16/010     Document Type: Article

References (34)

1. Horodecki M 2001 Entanglement measures Quantum Infor. Comput. 1 3
2. Plenio M B and Virmani S 2005 An introduction to entanglement measures Preprint quant-ph/0504163
3. Bennett C H, DiVincenzo D P, Smolin J A and Wootters W K 1996 Mixed-state entanglement and quantum error correction Phys. Rev. A 54 3824 (Preprint quant-ph/9604024)
4. Rains E M 1999 Rigorous treatment of distillable entanglement Phys. Rev. A 60 173 (Preprint quant-ph/9809078)
5. Hayden P M, Horodecki M and Terhal B M 2001 The asymptotic entanglement cost of preparing a quantum state J. Phys. A: Math. Gen. 34 6891 (Preprint quant-ph/0008134)
6. Vedral V, Plenio M B, Rippin M A and Knight P L 1997 Quantifying entanglement Phys. Rev. Lett. 78 2275 (Preprint quant-ph/9702027)
7. Vedral V and Plenio M B 1998 Entanglement measures and purification procedures Phys. Rev. A 57 1619 (Preprint quant-ph/9707035)
8. Vollbrecht K G H and Werner R F 2001 Entanglement measures under symmetry Phys. Rev. A 64 062307 (Preprint quant-ph/0010095)
9. Wei T-C and Goldbart P M 2003 Geometric measure of entanglement and applications to bipartite and multipartite quantum states Phys. Rev. A 68 042307 (Preprint quant-ph/0307219)
10. Karnas S and Lewenstein M 2001 Separable approximations of density matrices of composite quantum systems J. Phys. A: Math. Gen. 34 6919 (Preprint quant-ph/0011066)
11. Lewenstein M and Sanpera A 1998 Separability and entanglement of composite quantum systems Phys. Rev. Lett. 80 2261 (Preprint quant-ph/9707043)
12. Steiner M 2003 Generalized robustness of entanglement Phys. Rev. A 67 054305 (Preprint quant-ph/0304009)
13. Harrow A W and Nielsen M A 2003 How robust is a quantum gate in the presence of noise Phys. Rev. A 68 012308 (Preprint quant-ph/0301108)
14. Vidal G and Tarrach R 1999 Robustness of entanglement Phys. Rev. A 59 141 (Preprint quant-ph/9806094)
15. Brandão F G S L 2005 Quantifying entanglement with witness operators Phys. Rev. A 72 022310 (Preprint quant-ph/0503152)
16. Horodecki M, Horodecki P and Horodecki R 1996 Separability of mixed states: necessary and sufficient conditions Phys. Lett. A 223 1 (Preprint quant-ph/9605038)
17. Bruß D, Horodecki J I, Cirac P, Hulpke F, Kraus B, Lewenstein M and Sanpera A 2002 Reflections upon separability and distillability J. Mod. Opt. 49 1399 (Preprint quant-ph/0110081)
18. Rockafellar R T 1970 Convex Analysis (Princeton, NJ: Princeton University Press)
19. Lax P D 2002 Functional Analysis (New York: Wiley)
20. Terhal B M 2001 Detecting quantum entanglement Theor. Comput. Sci. 287 313 (Preprint quant-ph/0101032)
21. Brandão F G S L 2005 Quantifying the activation power of bipartite entangled states Preprint quant-ph/0510078
22. Verstraete F and Verschelde H 2003 Optimal teleportation with a mixed state of two qubits Phys. Rev. Lett. 90 097901 (Preprint quant-ph/0303007)
23. Brandão F G S L and Vianna R O 2004 Witnessed entanglement Preprint quant-ph/0405096
24. Schmidt E 1907 Zur Theorie der linearen und nichtlinearen Integralgleichungen Math. Ann. 63 433
25. Nielsen M A and Chuang I L 2000 Quantum Computation and Quantum Information (Cambridge: Cambridge University Press)
26. Terhal B M and Horodecki P 2000 A Schmidt number for density matrices Phys. Rev. A 61 040301 (Preprint quant-ph/9911117)
27. Sanpera A, Bruß D and Lewenstein M 2001 Schmidt number witnesses and bound entanglement Phys. Rev. A 63 050301 (Preprint quant-ph/0009109)
28. Hulpke F, Bruß D, Lewenstein M and Sanpera A 2004 Simplifying Schmidt number witnesses via higher-dimensional embeddings Quantum Infor. Comput. 4 207 (Preprint quant-ph/0401118)
29. Clarisse L 2005 Characterization of distillability of entanglement in terms of positive maps Phys. Rev. A 71 032332 (Preprint quant-ph/0403073)
30. Horodecki M and Horodecki P 1999 Reduction criterion of separability and limits for a class of distillation protocols Phys. Rev. A 59 4206 (Preprint quant-ph/9708015)
31. Rains E M 1999 Bound on distillable entanglement Phys. Rev. A 60 179 (Preprint quant-ph/9809082)
32. Dür W, Cirac J I, Lewenstein M and Bruß D 2000 Distillability and partial transposition in bipartite systems Phys. Rev. A 61 062313 (Preprint quant-ph/9910022)
33. Peres A 1996 Separability criterion for density matrices Phys. Rev. Lett. 77 1413 (Preprint quant-ph/9604005)
34. Cerf N J, Adami C and Gingrich R M 1997 Reduction criterion for separability Phys. Rev. A 60 898 (Preprint quant-ph/9710001)