Nothing Special   »   [go: up one dir, main page]

skip to main content
article

Security bounds in quantum cryptography using d-level systems

Published: 01 November 2003 Publication History

Abstract

We analyze the security of quantum cryptography schemes for d-level systems using 2 or d + 1 maximally conjugated bases, under individual eavesdropping attacks based on cloning machines and measurement after the basis reconciliation. We consider classical advantage distillation protocols, that allow to extract a key even in situations where the mutual information between the honest parties is smaller than the eavesdropper's information. In this scenario, advantage distillation protocols are shown to be as powerful as quantum distillation: key distillation is possible using classical techniques if and only if the corresponding state in the entanglement based protocol is distillable.

References

[1]
N. Gisin, G. Ribordy, W. Tittel, H. Zbinden, Rev. Mod. Phys 74, 145 (2002); The Physics of Quantum Information, ed. by D. Bouwmeester, A. Ekert and A. Zeilinger, Springer-Verlag (2000).
[2]
This argument has to be understood in a rather qualitative way. Proofs of unconditional security are much more involved, D. Mayers, quant-ph/9802025; H.-K. Lo and H. F. Chau, Science 283, 2050 (1999); P. W. Shor and J. Preskill, Phys. Rev. Lett. 85, 441 (2000).
[3]
I. Csiszár and J. Körner, IEEE Trans. Inf. Theory IT-24, 339 (1978).
[4]
C. H. Bennett, G. Brassard, C. Crépeau and U. Maurer, IEEE Trans. Inf. Theory 41, 1915 (1995).
[5]
U.M. Maurer, IEEE Trans. Inf. Theory 39, 733 (1993).
[6]
N. Gisin and S. Wolf, Phys. Rev. Lett. 83, 4200 (1999).
[7]
N.J. Cerf, M. Bourennane, A. Karlsson and N. Gisin, Phys. Rev. Lett. 88, 127902 (2002).
[8]
B. Huttner and N. Gisin, Phys. Lett. A 228, 13 (1997).
[9]
C. Fuchs, N. Gisin, R.B. Griffiths, C.-S. Niu and A. Peres, Phys. Rev. A 56, 1163 (1997).
[10]
C. H. Bennett and G. Brassard, in Proceedings IEEE Int. Conf. on Computers, Systems and Signal Processing, Bangalore, India (IEEE, New York, 1984), pp. 175-179.
[11]
The existence of d + 1 bases has been (constructively) demonstrated only when d is a power of a prime number: W.K. Wootters and B.D. Fields, Ann. Phys. (N.Y.) 191, 363 (1989).
[12]
C. H. Bennett, G. Brassard and N. D. Mermin, Phys. Rev. Lett. 86, 557 (1992).
[13]
The use of two-qubit entangled states for a secure key distribution was originally proposed in A. Ekert, Phys. Rev. Lett. 67, 661 (1991). There, Eve's intervencion is detected by checking the violation of a Bell inequality.
[14]
J. I. Cirac and N. Gisin, Phys. Lett. A 229, 1 (1997).
[15]
Note that it is assumed the (unproven) existence of the d + 1 maximally conjugated bases for all dimension.
[16]
D. Brass, Phys. Rev. Lett. 81, 3018 (1998); H. Bechmann-Pasquinucci and N. Gisin, Phys. Rev. A 59, 4238 (1999).
[17]
D. Brass and C. Macchiavello, Phys. Rev. Lett. 88, 127901 (2002).
[18]
N. J. Cerf, Phys. Rev. Lett. 84, 4497 (2000); J. Mod. Opt. 47, 187 (2000); Acta Phys. Slov. 48, 115 (1998).
[19]
A. Chefles, Contemp. Phys. 41, 401 (2000) and references therein.
[20]
In order to transform the quantum state |Ψ〉 ABE probability distribution P(A, B, E), Eve's measurements should be specified. As said in section 2, we consider the measurements of Ref. {7}, designed for maximizing Eve's information.
[21]
N. Gisin and S. Wolf, Proceedings of CRYPTO 2000, Lecture Notes in Computer Science 1880, 482, Springer-Verlag, 2000.
[22]
M. Horodecki, P. Horodecki and R. Horodecki, Phys. Rev. Lett. 80 5239 (1998).
[23]
M. Horodecki and P. Horodecki, Phys. Rev. A 59, 4206 (1999).
[24]
In general, the vanishing of intrinsic information does not imply the existence of a channel C: strictly speaking, it would be enough to have a sequence of channels Cn such that the intrinsic information converges to 0 when n goes to infinity.
[25]
C. H. Bennett, D. P. DiVincenzo, J. A. Smolin and W. K. Wootters, Phys. Rev. A 54, 3824 (1996).
[26]
M. Horodecki, P. Horodecki and M. Horodecki, Phys. Lett. A 200, 340 (1995).
[27]
J. F. Clauser, M. A. Home, A. Shimony and R. A. Holt, Phys. Rev. Lett. 23, 880 (1969).
[28]
C. Sliwa, quant-ph/0305190.
[29]
D. Collins and N. Gisin, quant-ph/0306129.
[30]
D. Collins, N. Gisin, N. Linden, S. Massar and S. Popescu, Phys. Rev. Lett. 88, 040404 (2002).
[31]
H. Bechmann-Pasquinucci and N. Gisin, Phys. Rev. A 67, 062310 (2003).
[32]
Ll. Masanes, Quant. Inf. Comp. Vol. 3, No. 4, 345 (2003).
[33]
A. Acín, Ll. Masanes and N. Gisin, Phys. Rev. Lett. 91, 167901 (2003).
[34]
N. Lütkenhaus, Phys. Rev. A 54, 97 (1996).
[35]
T. Mor, PhD Thesis, April 97, Technion, Haifa, Israel, also available as quant-ph/9906073.
[36]
This type of attacks is not entirely individual, in spite of the fact that the interaction is done symbol by symbol, because the final measurement may include a global entangling operation among all the qudits kept by Eve.
[37]
Some results in this direction can be found in A. Wojcik, A. Grudka and R. W. Chhajlany, quant-ph/0305034.
[38]
T. Durt and B. Nagler, Phys. Rev. A 68, 042323 (2003).
[39]
D. Bruss, M. Christandl, A. Ekert, B.-G. Englert, D. Kaszlikowski and C. Macchiavello, Phys. Rev. Lett. 91, 097901 (2003).

Cited By

View all
  1. Security bounds in quantum cryptography using d-level systems

    Recommendations

    Comments

    Please enable JavaScript to view thecomments powered by Disqus.

    Information & Contributors

    Information

    Published In

    cover image Quantum Information & Computation
    Quantum Information & Computation  Volume 3, Issue 6
    November 2003
    81 pages

    Publisher

    Rinton Press, Incorporated

    Paramus, NJ

    Publication History

    Published: 01 November 2003
    Revised: 22 July 2003
    Received: 10 March 2003

    Author Tags

    1. key distillation
    2. quantum cryptography
    3. quantum distillation

    Qualifiers

    • Article

    Contributors

    Other Metrics

    Bibliometrics & Citations

    Bibliometrics

    Article Metrics

    • Downloads (Last 12 months)0
    • Downloads (Last 6 weeks)0
    Reflects downloads up to 16 Nov 2024

    Other Metrics

    Citations

    Cited By

    View all

    View Options

    View options

    Login options

    Media

    Figures

    Other

    Tables

    Share

    Share

    Share this Publication link

    Share on social media