# Workshop Programme

## for period 6 - 10 September 2004

### Focus Week: Quantum Cryptography

6 - 10 September 2004

Timetable

 Wednesday 8 September 11:00-11:30 Coffee 11:30-12:15 Barrett, J (Universite Bruxelles Libre) Non-local correlations and key distribution Sem 2 We present a quantum key distribution scheme that is secure even against eavesdroppers who can break the laws of quantum mechanics, as long as superluminal signalling is impossible. The scheme is based on violation of a Bell inequality, and its security stems from the fact that non-local correlations are monogamous, in analogy with the monogamy of entanglement. 14:15-15:00 Duer, W (Austria) Graph states - stability under decoherence, entanglement purification and possible applications Sem 2 We will consider a specific family of multipartite entangled states, namely (weighted) graph states. We investigate the influence of decoherence on the entanglement properties of the states for various decoherence models. We show that the lifetime of entanglement of GHZ states decreases with the number of particles, while cluster (and similar) graph states the lifetime is independent of the size of the system. We discuss several multiparty entanglement purification protocols which allow one to create and/or maintain two colorable graph states with high fidelity. We compare direct multiparty entanglement purification protocols with protocols based on bipartite purification and show that the former are more efficient. We investigate the influence of imperfections in local control operations, where we find a remarkable robustness against errors for protocols which allow one, e.g., to purify cluster states. The achievable fidelity using direct multiparty purification is higher than purification based on bipartite protocols. We discuss possible applications of multiparty entanglement purification protocols for secure multiparty communication. 15:30-16:15 Pederson, T (Colombia) On the key-uncertainty of quantum ciphers and the computational security of one-way quantum transmission Sem 2 We consider the scenario where Alice wants to send a secret (classical) $n$-bit message to Bob using a classical key, and where only one-way transmission from Alice to Bob is possible. In this case, quantum communication cannot help to obtain perfect secrecy with key length smaller then $n$. We study the question of whether there might still be fundamental differences between the case where quantum as opposed to classical communication is used. In this direction, we show that there exist ciphers with perfect security producing quantum ciphertext where, even if an adversary knows the plaintext and applies an optimal measurement on the ciphertext, his Shannon uncertainty about the key used is almost maximal. This is in contrast to the classical case where the adversary always learns $n$ bits of information on the key in a known plaintext attack. We also show that there is a limit to how different the classical and quantum cases can be: the most probable key, given matching plain- and ciphertexts, has the same probability in both the quantum and the classical cases. We suggest an application of our results in the case where only a short secret key is available and the message is much longer. Namely, one can use a pseudorandom generator to produce from the short key a stream of keys for a quantum cipher, using each of them to encrypt an $n$-bit block of the message. Our results suggest that an adversary with bounded resources in a known plaintext attack may potentially be in a much harder situation against quantum stream-ciphers than against any classical stream-cipher with the same parameters.