Abstract
It was recently pointed out that there is a close connection between information-theoretic key agreement and quantum entanglement purification. This suggests that the concept of bound entanglement (entanglement which cannot be purified) has a classical counterpart: bound information, which cannot be used to generate a secret key by any protocol. We analyse a probability distribution which results when a specific bound entangled quantum state is measured. We show strong evidence for the fact that the corresponding mutual information is indeed bound. The probable existence of such information stands in contrast to previous beliefs in classical information theory.
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References
W. Diffie and M. E. Hellman, New directions in cryptographyIEEE Transactions on Information TheoryVol. 22, No. 6, pp. 644–654, 1976.
N. Gisin and S. Wolf, Linking classical and quantum key agreement: is there “bound information”?Advances in Cryptology - Proceedings of Crypto 2000Lecture Notes in Computer Science, Vol. 1880, pp. 482–500, 2000.
N. Gisin and S. Wolf, Quantum cryptography on noisy channels• quantum versus classical key agreement protocolsPhys. Rev. Lett.Vol. 83, pp. 4200–4203, 1999.
M. Horodecki, P. Horodecki, and R. Horodecki, Inseparable 2 spin 1/2 density matrices can be distilled to a singlet formPhys. Rev. Lett., Vol.78, p. 574, 1997.
P. Horodecki, Separability criterion and inseparable mixed states with positive partial transpositionPhys. Lett. A Vol. 232, p. 333, 1997.
P. Horodecki, M. Horodecki, and R. Horodecki, Bound entanglement can be activatedPhys. Rev. Lett. Vol. 82, pp. 1056–1059, 1999. quant-ph/9806058.
R. Landauer, Information is inevitably physicalFeynman and Computation 2, Addison Wesley, Reading, 1998.
R. Landauer, The physical nature of informationPhys. Lett. A, Vol. 217, p. 188, 1996.
U. Maurer, Secret key agreement by public discussion from common informationIEEE Transactions on Information Theory, Vol.39, No. 3, pp. 733–742, 1993.
U. Maurer and S. Wolf, Unconditionally secure key agreement and the intrinsic conditional informationIEEE Transactions on Information Theory, Vol.45, No. 2, pp. 499–514, 1999.
A. Peres, Quantum theory: concepts and methods, Kluwer Academic Publishers, 1993.
A. Peres, Separability criterion for density matricesPhys. Rev. Lett. Vol. 77, pp. 1413–1415, 1996.
C. E. Shannon, Communication theory of secrecy systemsBell System Technical Journal Vol. 28, pp. 656–715, 1949.
S. Wolf, Information-theoretically and computationally secure key agreement in cryptography, ETH dissertation No. 13138, ETH ZÜrich, 1999.
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Gisin, N., Renner, R., Wolf, S. (2001). Bound Information: The Classical Analog to Bound Quantum Entanglemen. In: Casacuberta, C., Miró-Roig, R.M., Verdera, J., Xambó-Descamps, S. (eds) European Congress of Mathematics. Progress in Mathematics, vol 202. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8266-8_38
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DOI: https://doi.org/10.1007/978-3-0348-8266-8_38
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