# Linking Classical and Quantum Key Agreement: Is There a Classical Analog to Bound Entanglement?

## Nicolas Gisin and Renato Renner 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 contrast to what was previously believed. The studied
connection between the classical and quantum protocols makes it
natural to conjecture that (classical and quantum) distillability is
possible only if single-copy distillability is already possible.