Linking Classical and Quantum Key Agreement: Is There "Bound Information"?

TL;DR

This paper explores the relationship between classical and quantum key agreement protocols, demonstrating their equivalence in potential and revealing that bound entanglement has a classical counterpart, with implications for secure communication.

Contribution

It proves the equivalence of classical and quantum protocols under certain conditions and introduces the concept of bound intrinsic information as a classical analogue of bound entanglement.

Findings

Classical and quantum key agreement potentials are equivalent under certain conditions.

Bound entanglement has a classical counterpart called bound intrinsic information.

Classical intrinsic information can be non-distillable, similar to bound entanglement.

Abstract

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 prove for general states but under the assumption of incoherent eavesdropping that Alice and Bob share some so-called intrinsic information in their classical random variables, resulting from optimal measurements, if and only if the parties' quantum systems are entangled. In addition, we provide evidence that the potentials of classical and of quantum protocols are equal in every situation. Consequently, many techniques and results from quantum information theory directly apply to problems in classical information theory, and vice versa. For instance, it was previously believed that two parties can carry out unconditionally secure key agreement as long as they share some intrinsic information in the adversary's view. The analysis of this purely classical problem from the quantum information-theoretic viewpoint shows that this is true in the binary case, but false in general. More explicitly, bound entanglement, i.e., entanglement that cannot be purified by any quantum protocol, has a classical counterpart. This "bound intrinsic information" cannot be distilled to a secret key by any classical protocol. As another application we propose a measure for entanglement based on classical information-theoretic quantities.