A security study of two non-tomographic quantum communication protocols

Abstract

The aim of this thesis is to study the security of two particular quantum communication protocols. We want to investigate what is the maximum amount of channel noise for which the protocols can still be secure. We do this by using well known bounds for limiting the information that an eavesdropper can obtain. The first protocol that we study is a direct communication protocol using two-qubit states. We find the security threshold by analyzing the protocol in an enanglement based setting. The Holevo bound was used to put an upper bound on the information of an eavesdropper. To arrive at a manageable optimisation probem, we restrict the eavesdropper's attack strategy such that the noise introduced will be unbiased. Furthermore, we also impose some additional constraints on the eavesdropper that arises from the symmetry of the protocol. After doing this we then optimise the remaining parameters to arrive at the eavesdropper's optimal strategy and find out what is the maximum amount of information she can obtain. Once the eavesdropper's maximum information is known, the security threshold for secure communication was obtained by comparing that information with the information between the legitimate communicating parties. The second protocol studied is a continuous variable quantum key distribution protocol using post-selection. For this protocol, we investigate the maximum amount of information the eavesdropper can get under individual and collective attacks in the presence of Gaussian excess noise in the channel. By providing the eavesdropper with additional information, we can use known results on the accessible information for pure input states to bound the eavesdropper's information. For individual attacks, Levitin's result on the optimal measurement was used while for collective attacks, Holevo's bound was used to arrive at an upper bound for the eavesdropper's information. From this we can then arrive at the post-selection region where the legitimate communicating parties have more information than the eavesdropper. We can then find the maximum amount of noise that the protocol can tolerate before the eavesdropper knows too much and the protocol fails.