Linking Classical and Quantum Key Agreement: Is There “Bound Information”?
After carrying out a protocol for quantum key agreement over a noisy quantum channel, the parties Alice and Bob must process the raw key in order to end up with identical keys about which the adversary has virtually no information. In principle, both classical and quantum protocols can be used for this processing. It is a natural question which type of protocols is more powerful. We show that the limits of tolerable noise are identical for classical and quantum protocols in many cases. More specifically, we prove that a quantum state between two parties is entangled if and only if the classical random variables resulting from optimal measurements provide some mutual classical information between the parties. In addition, we present evidence which strongly suggests that the potentials of classical and of quantum protocols are equal in every situation. An important consequence, in the purely classical regime, of such a correspondence would be the existence of a classical counterpart of so-called bound entanglement, namely “bound information” that cannot be used for generating a secret key by any protocol. This stands in sharp contrast to what was previously believed.
KeywordsSecret-key agreement intrinsic information secret-key rate quantum privacy amplification purification entanglement
- 3.C. H. Bennett and G. Brassard, Quantum cryptography: public key distribution and coin tossing, Proceedings of the IEEE International Conference on Computer, Systems, and Signal Processing, IEEE, pp. 175–179, 1984.Google Scholar
- 9.D. P. DiVincenzo, P. W. Shor, J. A. Smolin, B. M. Terhal, and A. V. Thapliyal, Evidence for bound entangled states with negative partial transpose, quant-ph/9910026, 1999.Google Scholar
- 21.U. Maurer and S. Wolf, Information-theoretic key agreement: from weak to strong secrecy for free, Proceedings of EUROCRYPT 2000, Lecture Notes in Computer Science, Vol. 1807, pp. 352–368, Springer-Verlag, 2000.Google Scholar
- 24.A. Peres, Quantum theory: concepts and methods, Kluwer Academic Publishers, 1993.Google Scholar
- 26.S. Popescu and D. Rohrlich, Thermodynamics and the measure of entanglement, quant-ph/9610044, 1996.Google Scholar
- 29.S. Wolf, Information-theoretically and computationally secure key agreement in cryptography, ETH dissertation No. 13138, Swiss Federal Institute of Technology (ETH Zurich), May 1999.Google Scholar