A complementary resource relation of concurrence and roughness for a two-qubit state

Quantum resources lie at the core of quantum computation as they are responsible for the computational advantage in many tasks. The complementary relations are a pathway to understanding how the physical quantities are related. This work presents a complementary relationship between the quantumness of a two qubits state and the degree of entanglement, respectively measured by roughness and concurrence. There is a finite R² region that can be used to characterize the two qubits subspace. Heat maps for accumulation points over the surfaces of pure and non-pure randomly sampled states are presented, also an investigation of a decoherence process using a bath under zero and non-zero temperature is performed using the roughness versus concurrence parameter space.