Geometric discord: A resource for increments of quantum key generation through twirling

Abstract

In the present work, we consider a scenario where an arbitrary two-qubit pure state is applied for the quantum key generation (QKG). Using the twirling procedure to convert the pure state into a Werner state, the error rate of the key can be reduced by a factor of 2/3. This effect indicates that entanglement is not the sufficient resource of QKG protocol since it is not increased in the twirling procedure. Based on the fact that the geometric discord is increased in the twirling procedure, we argue that the geometric discord should be taken as a necessary resource for the QKG task. Besides the pure state, we also give other two types of mixtures where twirling may increase the discord and reduce the error rate of the generated key.