Entropic uncertainty relations for extremal unravelings of super-operators

Journal of Physics A: Mathematical and Theoretical

Volumn 44, Issue 9, 2011, Pages

  Rastegin, Alexey E ^a  

^a IRKUTSK STATE UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 79951846130     PISSN: 17518113     EISSN: 17518121     Source Type: Journal    
DOI: 10.1088/1751-8113/44/9/095303     Document Type: Article

References (50)

1. Heisenberg W 1927 Z. Phys. 43 172
2. Hall M J W 1999 Phys. Rev. A 59 2602
3. Busch P, Heinonen T and Lahti P J 2007 Phys. Rep. 452 155
4. Robertson H P 1929 Phys. Rev. 34 163
5. Lynch R 1995 Phys. Rep. 256 357
6. Barnett S M and Pegg D T 1989 J. Mod. Opt. 36 7
7. Maassen H and Uffink J B M 1988 Phys. Rev. Lett. 60 1103
8. Wehner S and Winter A 2010 New J. Phys. 12 025009
9. Hirschman I I 1957 Am. J. Math. 79 152
10. Mamojka B 1974 Int. J. Theor. Phys. 11 73
11. Deutsch D 1983 Phys. Rev. Lett. 50 631
12. Ivanovic I D 1992 J. Phys. A: Math. Gen. 25 L363
13. Sanchez J 1993 Phys. Lett. A 173 233
14. Hall M J W 2008 J. Phys. A: Math. Theor. 41 255301
15. Man'ko M A 2009 J. Russ. Laser Res. 30 514
16. Berta M, Christandl M, Colbeck R, Renes J M and Renner R 2009 The uncertainty principle in the presence of quantum memory arXiv:0909.0950[quant- ph]
17. Massar S and Spindel P 2008 Phys. Rev. Lett. 100 190401
18. Urizar-Lanz I and Tóth G 2010 Phys. Rev. A 81 052108
19. Kraus K 1983 States, Effects, and Operations: Fundamental Notions of Quantum Theory (Lecture Notes in Physics vol 190) (Berlin: Springer)
20. Il'ichev L V 2003 JETP 96 982
21. http://tsallis.cat.cbpf.br/biblio.htm
22. Aczél J and Daróczy Z 1975 On Measures of Information and Their Characterizations (New York: Academic)
23. Tsallis C 1988 J. Stat. Phys. 32 479
24. Havrda J and Charvát F 1967 Kybernetika (Prague) 3 30
25. Rényi A 1961 On measures of entropy and information Proc. 4th Berkeley Symp. on Mathematical Statistics and Probability (Berkeley, CA: University of California Press) pp 547-61
26. Życzkowski K 2003 Open Syst. Inf. Dyn. 10 297
27. Watrous J 2008 Theory of Quantum Information (Computer Science vol 798) (Ontario, Canada: University of Waterloo) (available at http://www.cs.uwaterloo. ca/~watrous/quant-info/)
28. Holevo A S 1982 Probabilistic and Statistical Aspects of Quantum Theory (Statistics and Probability vol 1) (Amsterdam: North-Holland)
29. Ferraro A, Galbiati M and Paris M G A 2006 J. Phys. A: Math. Gen. 39 L219
30. Rastegin A E 2010 Quantum Inf. Comput. 10 0971
31. Preskill J 1998 Quantum Computation and Information (Lecture Notes in Physics vol 229) (California: California Institute of Technology) (available at http://www.theory.caltech.edu/people/preskill/ph229/)
32. Carmichael H J 1993 An Open Systems Approach to Quantum Optics (Lecture Notes in Physics vol 18) (Berlin: Springer)
33. Hardy G H, Littlewood J E and Polya G 1934 Inequalities (London: Cambridge University Press)
34. Breslin J K and Milburn G J 1997 J. Mod. Opt. 44 2469
35. Hughston L P, Jozsa R and Wootters W K 1993 Phys. Lett. A 183 14
36. Wehrl A 1978 Rev. Mod. Phys. 50 221
37. Rastegin A E 2010 Fano type quantum inequalities in terms of q-entropies arXiv:1010.1811[quant-ph]
38. Rastegin A E 2010 J. Phys. A: Math. Theor. 43 155302
39. Krishna M and Parthasarathy K R 2002 Sankhya A 64 842
40. Bialynicki-Birula I 2006 Phys. Rev. A 74 052101
41. Rajagopal A K 1995 Phys. Lett. A 205 32
42. Majernik V and Majernikova E 2001 Rep. Math. Phys. 47 381
43. Majernik V, Majernikova E and Shpyrko S 2003 Cent. Eur. J. Phys. 3 393
44. Zhan X 2002 Matrix Inequalities (Berlin: Springer)
45. Kraus K 1987 Phys. Rev. D 35 3070
46. Zygmund A 1959 Trigonometric Series vol 2 (Cambridge: Cambridge University Press)
47. Beckner W 1975 Ann. Math. 102 159
48. Lesche B 1982 J. Stat. Phys. 27 419
49. Abe S 2002 Phys. Rev. E 66 046134
50. Rastegin A E 2010 Lett. Math. Phys. 94 229