Optimal compression of quantum information for one-qubit source at incomplete data: A new aspect of Jaynes principle

Acta Physica Slovaca

Volumn 48, Issue 3, 1998, Pages 133-140

  Horodecki, Michał ^a   Horodecki, Ryszard ^a   Horodecki, Paweł ^b  

^a UNIVERSITY OF GDA SK   (Poland)

^b GDANSK UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032343741     PISSN: 03230465     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (29)

1. C. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, W. K. Wootters: Phys. Rev. Lett. 70 (1993) 1895
2. D. Bouwmeester, J.-W. Pan, K. Mattle, M. Elbl, H. Weinfurter, A. Zeilinger: Nature (London) 390 (1997) 575 ; D. Boschi, S. Brance, F. de Martini, L. Hardy, S. Popescu: Phys. Rev. Lett. 80 (1998) 1121
3. D. Bouwmeester, J.-W. Pan, K. Mattle, M. Elbl, H. Weinfurter, A. Zeilinger: Nature (London) 390 (1997) 575 ; D. Boschi, S. Brance, F. de Martini, L. Hardy, S. Popescu: Phys. Rev. Lett. 80 (1998) 1121
4. C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. Smolin, W. K. Wootters: Phys. Rev. Lett. 76 (1996) 722; C. H. Bennett, D. P. Di Vincenzo, J. Smolin, W. K. Wootters: Phys. Rev. A 54 (1997) 3814; M. Horodecki, P. Horodecki, R. Horodecki: Phys. Rev. Lett. 78 (1997) 574.
5. C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. Smolin, W. K. Wootters: Phys. Rev. Lett. 76 (1996) 722; C. H. Bennett, D. P. Di Vincenzo, J. Smolin, W. K. Wootters: Phys. Rev. A 54 (1997) 3814; M. Horodecki, P. Horodecki, R. Horodecki: Phys. Rev. Lett. 78 (1997) 574.
6. C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. Smolin, W. K. Wootters: Phys. Rev. Lett. 76 (1996) 722; C. H. Bennett, D. P. Di Vincenzo, J. Smolin, W. K. Wootters: Phys. Rev. A 54 (1997) 3814; M. Horodecki, P. Horodecki, R. Horodecki: Phys. Rev. Lett. 78 (1997) 574.
7. B. Schumacher: Phys. Rev. A 51 (1995) 2738
8. R. Jozsa, B. Schumacher: J. Mod. Opt. 41 (1994) 2343
9. R. Horodecki, M. Horodecki, P. Horodecki: Los Alamos e-print quant-ph/9709010
10. E. Jaynes: Phys. Rev. 108 (1957) 171; ibid 108 (1957) 620; Am. J. Phys. 31 (1963) 66
11. E. Jaynes: Phys. Rev. 108 (1957) 171; ibid 108 (1957) 620; Am. J. Phys. 31 (1963) 66
12. E. Jaynes: Phys. Rev. 108 (1957) 171; ibid 108 (1957) 620; Am. J. Phys. 31 (1963) 66
13. By complete set of observables one means the maximal set of linearly independent observables (where the trivial observable represented by identity operator is excluded). A set which does not fulfil the above conditions is called incomplete one.
14. Throughout this paper we will use the base-2 logarithm rather than natural one.
15. See e.g. V. Bužek, G. Drobný, G. Adam, R. Derka, P. L. Knight: J. Mod. Opt. 44 (1997) 2607; for an extensive presentation of the use of Jaynes principle see W. T. Grandy, Am. J. Phys 65 (1997) 466
16. See e.g. V. Bužek, G. Drobný, G. Adam, R. Derka, P. L. Knight: J. Mod. Opt. 44 (1997) 2607; for an extensive presentation of the use of Jaynes principle see W. T. Grandy, Am. J. Phys 65 (1997) 466
17. A. Wehrl: Rev. Mod. Phys. 50 (1978) 221
18. H. Barnum, Ch. Fuchs, R. Jozsa, B. Schumacher: Phys. Rev. A 54 (1996) 4707
19. A. Uhlmann: Rep. Math. Phys. 9 (1976) 273; R. Jozsa: J. Mod. Opt. 41 (1994) 2315
20. A. Uhlmann: Rep. Math. Phys. 9 (1976) 273; R. Jozsa: J. Mod. Opt. 41 (1994) 2315
21. R. Jozsa (unpublished); Hoi-Kwong Lo: Opt. Commun. 119 (1995) 552; A. E. Allahverdyan, D. B. Saakian: Los Alamos e-print quant-ph/9702034
22. R. Jozsa (unpublished); Hoi-Kwong Lo: Opt. Commun. 119 (1995) 552; A. E. Allahverdyan, D. B. Saakian: Los Alamos e-print quant-ph/9702034
23. R. Jozsa (unpublished); Hoi-Kwong Lo: Opt. Commun. 119 (1995) 552; A. E. Allahverdyan, D. B. Saakian: Los Alamos e-print quant-ph/9702034
24. M. Horodecki: Phys. Rev. A 57 (1998) 3348; H. Barnum, C. Caves, Ch. Fuchs, R. Jozsa, B. Schumacher (unpublished).
25. M. Horodecki: Phys. Rev. A 57 (1998) 3348; H. Barnum, C. Caves, Ch. Fuchs, R. Jozsa, B. Schumacher (unpublished).
26. ⊗N. However, to prove the lemma one does not need to make such an assumption.
27. K. Kraus: States, Effects and Operations: Fundamental Notions of Quantum Theory (Wiley, New York, 1991)
28. R. Jozsa: private communication.
29. R. Jozsa, M. Horodecki, P. Horodecki, R. Horodecki: Los Alamos e-print quant-ph/9805017