# Towards Proving the Existence of ``Bound'' Information

## Renato Renner and Stefan Wolf

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```In order to communicate secretly in the strong sense of information
theory, two parties have to share a secret key about which a
possible adversary has (virtually) no information. Such a
key can be generated based on correlated classical or quantum
information shared between the parties. The relationship that
has recently been shown between these two models suggests
that the concept of bound entanglement, i.e., shared quantum
information between the parties which can, however, not be
used to generate a quantum key, has a classical counterpart,
called ``bound information.'' Such information is a classical
correlation between the players' pieces of information (from
a possible adversary's viewpoint) that can, however, not be used
to generate a secret key. The existence of such information,
which could not be proven so far, would be somewhat surprising from the
purely classical perspective. In this paper we take a step towards
proving the existence of bound information. More specifically,
a bidirectional correspondence between quantum and classical
key bits (of a certain quality, called fidelity) is shown.
Here, the connection between quantum and classical
information is established by measuring the quantum system
in a fixed basis.