In previous literature, two-way entanglement purification protocols have been proven secure against many forms of attack and noise, effectively disentangling any eavesdropper from the transmitted state. However, one-way entanglement purification protocols have not been examined as deeply. In this project I wanted to address this issue and make progress towards understanding the security of one-way protocols by suggesting a protocol and proving its security against a simple adversary restricted to single qubit Pauli gates.

This protocol circumvents the typical symmetry between Bob and Eve usually found in one-way protocols by assuming Alice and Bob have a pre-shared key, and then uses quantum sampling and an error correcting code to disentangle Eve from the transmitted state, or detect and discard the state if that is not possible. It would be interesting to investigate if this protocol is secure against arbitrary single or multi-qubit operations, but that would require an understanding of continuous logical operators, a problem I have also encountered in this project. The Arxiv version of the paper is attached below.