The Geometric Structure of Quantum Resources for Bell-diagonal states

Abstract: Two-qubit Bell-diagonal states can be depicted as a tetrahedron in three dimensions. We investigate the structure of quantum resources, including coherence and quantum discord, in the tetrahedron. The ordering of different resources measures is a common problem in resource theories, and which measure should be chosen to investigate the structure of resources is still an open question. We consider the structure of quantum resources which is not affected by the choice of measure. Our work provides a complete structure of coherence and quantum discord for Bell-diagonal states. The pictorial approach also indicates how to explore the structure of resources even when we don't have consistent measure of a concrete quantum resource.