Cryptographic protocols in optical communication

Quantum key distribution (QKD) is a technique that allows two parties (Alice and Bob) to generate a secret key despite the computational and technological power of an eavesdropper (Eve) who interferes with the signals. Together with the Vernam cipher, QKD can be used for unconditionally secure data transmission. In a typical realization of QKD one can distinguish two phases in order to generate a secret key. In the first phase, an effective bipartite quantum mechanical state is distributed between Alice and Bob. This state creates correlations between them and it might contain as well hidden correlations with Eve. Next, a (restricted) set of measurements is used by the legitimate users to measure these correlations. As a result, Alice and Bob obtain a classical joint probability distribution P r(A, B) representing their measurement results. In the second phase, Alice and Bob use an authenticated public channel to process P r(A, B) in order to obtain a secret key. This procedure involves, typically, classical post-processing techniques such as post-selection of data, error correction to reconcile the data, and privacy amplification to decouple the data from Eve. An essential question in QKD is to determinate which kind of correlated data P r(A, B), generated in the first phase, enables Alice and Bob to extract a secret key at all from it during the second phase of the protocol. Security proofs for QKD usually fix Alice's and Bob's signal states and measurement devices and impose, additionally, the use of a particular classical communication protocol during the second phase of QKD. As a result, the obtained proofs can show certain achievable secret key rates as a function of the distance. These security proofs, however, leave open the possibility that the development of better proof techniques, or better classical post-processing protocols for the second phase of the QKD protocol, might lead to an increase of the covered distance and rate for a given P r(A, B). In this thesis we search for ultimate upper bounds on QKD based exclusively on the classical correlations P r(A, B) and on the knowledge of Alice's and Bob's physical devices, and not on the particular classical post-processing techniques used by the legitimate users during the second phase of QKD. In particular, we show that a necessary precondition for successful QKD is that sender and receiver can prove the presence of entanglement in the effective bipartite quantum state that is distributed …