# Linking Classical and Quantum Key Agreement: Is There ``Bound Information''?

## Nicolas Gisin and Stefan Wolf

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```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.