Foundations of Physics

, Volume 33, Issue 11, pp 1629–1647

Hiding Quantum Data

  • David P. DiVincenzo
  • Patrick Hayden
  • Barbara M. Terhal
Article

Abstract

Recent work has shown how to use the laws of quantum mechanics to keep classical and quantum bits secret in a number of different circumstances. Among the examples are private quantum channels, quantum secret sharing and quantum data hiding. In this paper we show that a method for keeping two classical bits hidden in any such scenario can be used to construct a method for keeping one quantum bit hidden, and vice–versa. In the realm of quantum data hiding, this allows us to construct bipartite and multipartite hiding schemes for qubits from the previously known constructions for hiding bits.

data hiding quantum cryptography secret sharing nonlocality without entanglement 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    P. O. Boykin and V. Roychowdhury, “Optimal encryption of quantum bits”, LANL e-print quant-ph/0003059.Google Scholar
  2. 2.
    A. Ambainis, M. Mosca, A. Tapp, and R. de Wolf, “Private quantum channels”, in IEEE Symposium on Foundations of Computer Science (FOCS), pp. 547–553, 2000; LANL e-print quant-ph/0003101.Google Scholar
  3. 3.
    R. Cleve, D. Gottesman, and H. K. Lo, “How to share a quantum secret”, Phys. Rev. Lett. 83(3), 648–651 (1999); LANL e-print quant-ph/9901025.Google Scholar
  4. 4.
    B. M. Terhal, D. P. DiVincenzo, and D. W. Leung, “Hiding bits in Bell states”, Phys. Rev. Lett. 86(25), 5807–5810 (2001); LANL e-print quant-ph/0011042.Google Scholar
  5. 5.
    D. P. DiVincenzo, D. W. Leung, and B. M. Terhal, “Quantum data hiding”, IEEE Trans. Information Theory 48(3), 580–598 (2002); LANL e-print quant-ph/0103098.Google Scholar
  6. 6.
    T. Eggeling and R. F. Werner, “Hiding classical data in multi-partite quantum states”, LANL e-print quant-ph/0203004.Google Scholar
  7. 7.
    C. H. Bennett and S. Wiesner, “Communication via one-and two-particle operators on Einstein–Podolsky–Rosen states”, Phys. Rev. Lett. 69(20), 2881–2884 (1992).Google Scholar
  8. 8.
    C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels”, Phys. Rev. Lett. 70, 1895–1899 (1993).Google Scholar
  9. 9.
    D. Gottesman, “Theory of quantum secret sharing”, Phys. Rev. A 61(4), 042311(2000); LANL e-print quant-ph/9910067.Google Scholar
  10. 10.
    J. Jamiołkowski, “Linear transformations which preserve trace and positive semidefiniteness of operators”, Rep. Math. Phys. 3(4), 275–278 (1972).Google Scholar
  11. 11.
    C. E. Shannon, “Communication theory of secrecy systems”, Bell System Tech. J. 28, 656–715 (1949).Google Scholar
  12. 12.
    M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, 2000).Google Scholar

Copyright information

© Plenum Publishing Corporation 2003

Authors and Affiliations

  • David P. DiVincenzo
    • 1
    • 2
  • Patrick Hayden
    • 2
  • Barbara M. Terhal
    • 1
    • 2
  1. 1.Watson Research CenterIBMYorktown Heights
  2. 2.Institute for Quantum InformationPasadena

Personalised recommendations