Reliability of Calderbank-Shor-Steane codes and security of quantum key distribution

Journal of Physics A: Mathematical and General

Volumn 37, Issue 34, 2004, Pages 8303-8328

  Hamada, Mitsuru ^a  

^a JAPAN SCIENCE AND TECHNOLOGY AGENCY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 4444337898     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/37/34/009     Document Type: Article

References (58)

1. Bennett C H and Brassard G 1984 Quantum cryptography: public key distribution and coin tossing Proc. IEEE Int. Conf. Computers, Systems and Signal Processing (Bangalore, India) pp 175-9
2. Wiesner S 1983 Conjugate coding SIGACT News 15 78-88
3. Mayers D 1996 Quantum key distribution and string oblivious transfer in noisy channels Advances in Cryptography: Proc. Crypto'96 pp 343-57
4. Mayers D 2001 Unconditional security in quantum cryptography J. Assoc. Comput. Mach. 48 351-406
5. Biham E, Boyer M, Boykin P O, Mor T and Roychowdhury V 2000 A proof of the security of quantum key distribution Proc. 32nd Annual ACM Symp. on Theory of Computing pp 715-24 (1999 Preprint quant-ph/9912053 LANL)
6. Shor P and Preskill J 2000 Simple proof of security of the BB84 quantum key distribution protocol Phys. Rev. Lett. 85 441-4
7. Gottesman D and Preskill J 2001 Secure quantum key distribution using squeezed states Phys. Rev. A 63 022309
8. Gottesman D, Lo H-K, Lütkenhaus N and Preskill J 2002 Security of quantum key distribution with imperfect devices Preprint quant-ph/0212066, LANL
9. Tamaki K, Koashi M and Imoto N 2003 Unconditionally secure key distribution based on two nonorthogonal states Phys. Rev. Lett. 90 167904
10. Calderbank A R and Shor P W 1996 Good quantum error correcting codes exist Phys. Rev. A 54 1098-105
11. Steane A M 1996 Multiple particle interference and quantum error correction Proc. R. Soc. A 452 2551-77
12. Holevo A S 2001 Statistical Structure of Quantum Theory (Berlin: Springer)
13. Kraus K 1971 General state changes in quantum theory Ann. Phys., NY 64 311-35
14. Hellwig K-E 1995 General scheme of measurement processes Int. J. Theor. Phys. 34 1467-79 Hellwig K-E 2000 General scheme of measurement processes Quantum Computation and Quantum Information Theory ed C Macchiavello et al (Singapore: World Scientific) (Reprint)
15. Hellwig K-E 1995 General scheme of measurement processes Int. J. Theor. Phys. 34 1467-79 Hellwig K-E 2000 General scheme of measurement processes Quantum Computation and Quantum Information Theory ed C Macchiavello et al (Singapore: World Scientific) (Reprint)
16. Kraus K 1983 States, Effects, and Operations (Lecture Notes in Physics vol 190) (Berlin: Springer)
17. Preskill J 1998 Lecture Notes for Physics 229: Quantum Information and Computation Available at http://www.theory.caltech.edu/people/preskill/ph229
18. Csiszár I and Körner J 1981 Information Theory: Coding Theorems for Discrete Memoryless Systems (New York: Academic)
19. Csiszár I and Körner J 1981 Graph decomposition: a new key to coding theorems IEEE Trans. Inf. Theory 27 5-12
20. Calderbank A R, Rains E M, Shor P W and Sloane N J A 1997 Quantum error correction and orthogonal geometry Phys. Rev. Lett. 78 405-8
21. Calderbank A R, Rains E M, Shor P W and Sloane N J A 1998 Quantum error correction via codes over GF(4) IEEE Trans. Inf. Theory 44 1369-87
22. Gottesman D 1996 Class of quantum error-correcting codes saturating the quantum Hamming bound Phys. Rev. A 54 1862-8
23. Dembo A and Zeitouni O 1998 Large Deviations Techniques and Applications 2nd edn (Berlin: Springer)
24. Cover T M and Thomas J A 1991 Elements of Information Theory (New York: Wiley)
25. Hamada M 2002 Exponential lower bound on the highest fidelity achievable by quantum error-correcting codes Phys. Rev. A 65 052305 (2001 Preprint quant-ph/0109114 LANL)
26. Hamada M 2002 Lower bounds on the quantum capacity and highest error exponent of general memoryless channels IEEE Trans. Inf. Theory 48 2547-57 (2001 Preprint quant-ph/0112103 LANL)
27. Hamada M 2002 Information rates achievable with algebraic codes on quantum discrete memoryless channels Preprint quant-ph/0207113 LANL
28. Hamada M 2003 Notes on the fidelity of symplectic quantum error-correcting codes Int. J. Quantum Inf. vol 1 443-63 (Preprint quant-ph/0311003 LANL)
29. Schumacher B 1996 Sending entanglement through noisy quantum channels Phys. Rev. A 54 2614-28
30. Gottesman D and Lo H-K 2003 Proof of security of quantum key distribution with two-way classical communications IEEE Trans. Inf. Theory 49 457-75 (2001 Preprint quant-ph/0105121 LANL)
31. Steane A M 1999 Efficient fault-tolerant quantum computing Nature 399 124-6
32. Gottesman D 1997 Stabilizer codes and quantum error correction PhD Thesis, California Institute of Technology (Preprint quant-ph/9705052 LANL)
33. Weyl H 1928 Gruppentheorie und Quantenmechanik (Leipzig: Verlag von S Hirzel) Weyl H 1950 The Theory of Groups and Quantum Mechanics Reprint 2nd edn (1931) (New York: Dover) (Engl. Transl.)
34. Weyl H 1928 Gruppentheorie und Quantenmechanik (Leipzig: Verlag von S Hirzel) Weyl H 1950 The Theory of Groups and Quantum Mechanics Reprint 2nd edn (1931) (New York: Dover) (Engl. Transl.)
35. Knill E and Laflamme R 1997 Theory of quantum error-correcting codes Phys. Rev. A 55 900-11
36. Artin E 1957 Geometric Algebra (New York: Interscience)
37. Serre J-P 1977 Cours d'Arithmétique 2nd edn (Paris: Presses Universitaires des France)
38. Aschbacher M 2000 Finite Group Theory 2nd edn (Cambridge: Cambridge University Press)
39. Grove L C 2001 Classical Groups and Geometric Algebra (Providence, RI: American Mathematical Society)
40. Ashikhmin A E, Barg A M, Knill E and Litsyn S N 2000 Quantum error detection II IEEE Trans. Inf. Theory 46 789-800
41. Barg A 2002 A low-rate bound on the reliability of a quantum discrete memoryless channel IEEE Trans. Inf. Theory 48 3096-100
42. Lo H-K and Chau H F 1999 Unconditional security of quantum key distribution over arbitrarily long distances Science 283 2050-56
43. Holevo A S 1973 Bounds for the quantity of information transmitted by a quantum communication channel Probl. Inf. Trans. 9 177-83 (Translated from Problemy Peredachi informatsii pp 3-11)
44. Holevo A S 1973 Bounds for the quantity of information transmitted by a quantum communication channel Probl. Inf. Trans. 9 177-83 (Translated from Problemy Peredachi informatsii pp 3-11)
45. Choi M-D 1975 Completely positive linear maps on complex matrices Linear Algebr. Appl. 10 285-90
46. Werner R F 2001 All teleportation and dense coding schemes J. Phys. A: Math. Gen. 34 7081-94
47. Billingsley P 1995 Probability and Measure 3rd edn (New York: Wiley)
48. Lo H-K 2001 Proof of unconditional security of six-state quantum key distribution scheme Quantum Inform. Comput. 1 81-94
49. Lo H-K, Chau H F and Ardehali M 2000 Efficient quantum key distribution scheme and proof of its unconditional security Preprint quant-ph/0011056 LANL
50. Biham E and Mor T 1997 Secure of quantum cryptography against collective attacks Phys. Rev. Lett. 78 2256-9
51. Yuen H P 2003 KCQ: A new approach to quantum cryptography: I. General principles and qubit key Preprint qunat-ph/0311061 LANL
52. Devetak I 2003 The private classical information capacity and quantum information capacity of a quantum channel Preprint qunat-ph/0304127 LANL
53. Hamada M 2003 Teleportation and entanglement distillation in the presence of correlation among bipartite mixed states Phys. Rev. A 68 012301-1-7 (Preprint quant-ph/0302054 LANL)
54. Horodecki M, Horodecki P and Horodecki R 1999 General teleportation channel, singlet fraction, and quasidistillation Phys. Rev. A 60 1888-98
55. Hayashi M 2003 Private communication
56. Hoeffding W 1963 Probability inequalities for sums of bounded random variables Am. Stat. Assoc. J. 58 13-30
57. Inamori H, Lütkenhaus N and Mayers D 2001 Unconditional security of practical quantum key distribution Preprint qunat-ph/0107017 LANL
58. Nielsen M A and Chuang I L 2000 Quantum Computation and Quantum Information (Cambridge: Cambridge University Press)