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Towards Proving the Existence of ``Bound'' Information

Renato Renner and Stefan Wolf

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.