Renato Renner, ETH Zürich

Information-theoretic security proof for QKD protocols

Quantum cryptography, the art of exploiting quantum physics to achieve information-theoretic security, has rapidly grown over the last decade from the level of a nice idea into an entire branch of physics. Today, one of the main challenges on the theoretical side is to prove the security of real-world quantum cryptosystems, taking into account all the impurities due to the imperfect physical devices on which they are built.

In this talk, we present a new and conceptually simple method for proving the security of quantum key distribution (QKD) protocols. Unlike most of the existing security proofs, the method can

be applied to a large class of QKD schemes, including those which cannot be translated into entanglement purification protocols. This is of particular interest for analyzing real-world implementations on imperfect devices.

The proof technique is based on two different information-theoretic results:

- Security of privacy amplification: Two-universal hashing transforms a partially secure string into a highly secure key. This holds even with respect to an adversary holding quantum information on the

initial string.

- Finite quantum de Finetti representation: An n-partite quantum state which is symmetric under permutations of the n subsystems is close (with respect to the trace distance) to a convex combination of n-fold product states.