Entropic uncertainty relations-a survey

New Journal of Physics

Volumn 12, Issue , 2010, Pages

  Wehner, Stephanie ^a,c   Winter, Andreas ^b,c  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^b UNIVERSITY OF BRISTOL   (United Kingdom)

^c NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

[No Author keywords available]

Indexed keywords

QUANTUM INFORMATION; QUANTUM MECHANICS; QUANTUM-CRYPTOGRAPHIC PROTOCOLS; UNCERTAINTY RELATION;

CRYPTOGRAPHY; NETWORK PROTOCOLS; NETWORK SECURITY; QUANTUM OPTICS; QUANTUM THEORY; SURVEYS;

UNCERTAINTY ANALYSIS;

EID: 77949524530     PISSN: 13672630     EISSN: None     Source Type: Journal    
DOI: 10.1088/1367-2630/12/2/025009     Document Type: Article

References (74)

1. Ambainis A 2009 Limits on entropic uncertainty relations for 3 and more MUBs arXiv:0909.3720
2. Ambainis A and Emerson J 2007 Proc. 22nd Annu. IEEE Conf. on Computational Complexity (CCC'07) pp 129-140 arXiv:quant-ph/0701126
3. Azarchs A 2004 Entropic uncertainty relations for incomplete sets of mutually unbiased observables. arXiv:quantph/0412083
4. Ballester M and Wehner S 2007 Phys. Rev. A 75 022319
5. Ballester M, Wehner S and Winter A 2008 IEEE Trans. Inf. Theory 54 4183
6. Bandyopadhyay S, Boykin P, Roychowdhury V and Vatan F 2002 Algorithmica 34 512
7. Beckner W 1975 Ann. Math. 102 159
8. Berta M, Christandl M, Colbeck R, Renes J and Renner R 2009 An entropic uncertainty relation with quantum side information. arXiv:0909.0950
9. Białynicki-Birula I 1984 Phys. Lett. A 103 253
10. Białynicki-Birula I 2006 Phys. Rev. A 74 052102
11. Białynicki-Birula I and Madajczyk J L 1985 Phys. Lett. A 108 384
12. Białynicki-Birula I and Mycielski J 1975 Commun. Math. Phys. 44 129
13. Christandl M and Winter A 2005 Uncertainty, monogamy and locking of quantum correlations. arXiv:quantph/0501090
14. Cover T M and Thomas J A 1991 Elements of Information Theory (New York: Wiley)
15. Damgaard I, Fehr S, Renner R, Salvail L and Schaffner C 2007 A tight high-order entropic uncertainty relation with applications in the bounded quantum-storage model Proc. CRYPTO 2007
16. Damgaard I, Fehr S, Salvail L and Schaffner C 2005 Proc. 46th IEEE FOCS pp 449-458
17. Deutsch D 1983 Phys. Rev. Lett. 50 631
18. Dietz K 2006 J. Phys. A: Math. Gen. 36 1433
19. DiVincenzo D, Horodecki M, Leung D, Smolin J and Terhal B 2004 Phys. Rev. Lett. 92 067902
20. Dodonov V V and Man'ko V I 1989 Invariants and the evolution of nonstationary quantum Systems Proc. Lebedev Physics Institute vol 183 ed M A Markov (Commack, NY: Nova Science) pp 3-101
21. Ghirardi G, Marinatto L and Romano R 2003 Phys. Lett. A 317 32
22. Gibilisco P, Hiai F and Petz D 2009 IEEE Trans. Inf. Theory 55 439
23. Grassl M 2004 Proc. ERATO Conf. Quantum Information Science pp 60-61 (arXiv:quant-ph/0406175)
24. Guehne O 2004 Phys. Rev. Lett. 92 117903
25. Hall M J W 1997 Phys. Rev. A 55 100
26. Hall M J W 2008 J. Phys. A: Math. Gen. 41 255301
27. Hayden P, Leung D, Shor P and Winter A 2004 Commun. Math. Phys. 250 371
28. Heisenberg W 1927 Z. Phys. 43 172
29. Hirschmann I I 1957 Am. J. Math. 79 152
30. Ivanovic I D 1992 J. Phys. A: Math. Gen. 25 363
31. Jordan P and Wigner E 1928 Z. Phys. 47 631
32. Klappenecker A and Rötteler M 2004 Int. Conf. on Finite Fields and Applications (Fq7) (Lecture Notes in Computer Science vol 2948) (New York: Springer) pp 137-144
33. Klappenecker A and Rötteler M 2005 Proc. IEEE Int. Symp. on Information Theory pp 1740-1744
34. Koashi M 2005 Simple security proof of quantum key distribution via uncertainty principle arXiv: quantph/0505108
35. König R, Renner R and Schaffner C 2008 The operational meaning of min- and max-entropy arXiv:0807.1338
36. König R, Wehner S and Wullschleger J 2009 Unconditional security in the noisy-storage model arXiv:0906.1030
37. Kraus K 1987 Phys. Rev. D 35 3070
38. Krishna M and Parthasarathy K R 2002 Ind. J. Stat. A 64 (arXiv:quant-ph/0110025)
39. Landau H J and Pollack H O 1961 Bell Syst. Tech. J. 40 65
40. Larsen U 1990 J. Phys. A: Math. Gen. 23 1041
41. Lawrence J, Brukner C and Zeilinger A 2002 Phys. Rev. A 65 032320
42. Lounesto P 2001 Clifford Algebras and Spinors (Cambridge: Cambridge University Press)
43. Maassen H and Uffink J 1988 Phys. Rev. Lett. 60 1103
44. Majernik V and Majernikova E 2001 Rep. Math. Phys. 47 381
45. Mandayam P and Wehner S 2009 in preparation
46. Massar S 2007 Phys. Rev. A 76 042114
47. Partovi M H 1983 Phys. Rev. Lett. 50 24
48. Rajagopal A K 1995 Phys. Lett. A 205 32
49. Rastegin A E 2008a Comment on 'uncertainty relations for positive-operator-valued measures' arXiv:0810.0038
50. Rastegin A E 2008b arXiv:0807.2691
51. Rastegin A E 2008c arXiv:0805.1777
52. Renes J M and Boileau J-C 2009 Phys. Rev. Lett. 103 020402
53. Renner R 2005 Security of quantum key distribution PhD Thesis ETH Zurich (arXiv:quant-ph/0512258)
54. Rényi A 1960 Proc. 4th Berkeley Symp. on Mathematics, Statistics and Probability pp 547-561
55. Riesz M 1929 Acta Math. 49 465
56. Robertson H 1929 Phys. Rev. 34 163
57. Sanchez J 1993 Phys. Lett. A 173 233
58. Sanchez-Ruiz J 1995 Phys. Lett. A 201 125
59. Sanchez-Ruiz J 1998 Phys. Lett. A 244 189
60. Shannon C E 1948 Bell Syst. Tech. J. 27 379
61. Srikanth R and Banerjee S 2009 Eur. Phys. J. D 53 217
62. Tomamichel M, Colbeck R and Renner R 2008 A fully quantum asymptotic equipartition property. arXiv:0811.1221
63. Toth G and Guehne O 2005 Phys. Rev. A 72 022340
64. Tsallis C 1988 J. Stat. Phys. 51 479
65. Ver Steeg G and Wehner S 2009 Quantum Inf. Comput. 9 801
66. de Vicente J I and Sanchez-Ruiz J 2008 Phys. Rev. A 77 042110
67. Wehner S 2008 Cryptography in a quantum world PhD Thesis University of Amsterdam (arXiv:0806.3483)
68. Wehner S, Schaffner C and Terhal B M 2008 Phys. Rev. Lett. 100 220502
69. Wehner S and Winter A 2008 J. Math. Phys. 49 062105
70. Wocjan P and Beth T 2005 Quantum Inf. and Comput. 5 93
71. Wootters W and Fields B 1989 Ann. Phys. 191 368
72. Wootters W K and Sussman D M 2007 arXiv:0704.1277
73. Wu S, Yu S and Molmer K 2009 Phys. Rev. A 79 022104
74. Zauner G 1999 Quantendesigns-Grundzüge einer nichtkommutativen designtheorie PhD Thesis UniversitätWien